UNITS(1)		    General Commands Manual		      UNITS(1)



NAME
       units -- unit conversion and calculation program

SYNOPSIS
       units [from-unit [to-unit]]

       units [-hcemnSpqsv1trUVI] [-d digits] [-f units file] [-L logfile]
	     [-l locale] [-o format] [-u unit system]
	     [from-unit [to-unit]]

       units [--help] [--check] [--check-verbose] [--verbose-check]
	     [--digits digits] [--exponential] [--file units file]
	     [--log logfile] [--locale locale] [--minus] [--oldstar]
	     [--newstar] [--nolists] [--show-factor] [--conformable]
	     [--output-format format] [--product] [--quiet] [--silent]
	     [--strict] [--verbose] [--compact] [--one-line] [--terse]
	     [--round] [--unitsfile] [--units units system] [--version]
	     [--info]
	     [from-unit [to-unit]]

DESCRIPTION
       The  units  program converts quantities expressed in various systems of
       measurement to their equivalents in other systems of measurement.  Like
       many  similar programs, it can handle multiplicative scale changes.  It
       can also handle nonlinear conversions such as  Fahrenheit  to  Celsius;
       see  Temperature Conversions.  The program can also perform conversions
       from and to sums of units, such as converting between meters  and  feet
       plus inches.

       But  Fahrenheit to Celsius is linear, you insist.  Not so.  A transfor-
       mation T	 is  linear  if	 T(x + y) = T(x) + T(y)	 and  this  fails  for
       T(x) = ax + b.	This  transformation  is  affine,  but not linear--see
       https://en.wikipedia.org/wiki/Linear_map.

       Basic operation is simple: you enter the units that you want to convert
       from  and  the units that you want to convert to.  You can use the pro-
       gram interactively with prompts, or you can use	it  from  the  command
       line.

       Beyond  simple unit conversions, units can be used as a general-purpose
       scientific calculator that keeps track of units	in  its	 calculations.
       You  can	 form arbitrary complex mathematical expressions of dimensions
       including sums, products, quotients, powers, and even roots  of	dimen-
       sions.	Thus  you can ensure accuracy and dimensional consistency when
       working with long expressions that involve many	different  units  that
       may  combine in complex ways; for an illustration, see Complicated Unit
       Expressions.

       The units are defined in several external data files.  You can use  the
       extensive  data	files  that  come with the program, or you can provide
       your own data file to suit your needs.  You can also use your own  data
       file to supplement the standard data files.

       You can change the default behavior of units with various options given
       on the command line. See Invoking Units for a description of the avail-
       able options.

INTERACTING WITH UNITS
       To  invoke  units for interactive use, type units at your shell prompt.
       The program will print something like this:

       Currency exchange rates from FloatRates (USD base) on 2023-07-08
       3612 units, 109 prefixes, 122 nonlinear units
       You have:

       At the 'You have:' prompt, type the quantity and	 units	that  you  are
       converting  from.   For	example,  if you want to convert ten meters to
       feet, type 10 meters.  Next, units will print 'You want:'.  You	should
       type  the  units you want to convert to.	 To convert to feet, you would
       type feet.  If the readline library was compiled in, then tab will com-
       plete unit names. See Readline Support for more information about read-
       line.  To quit the program type quit or exit at either prompt.

       The result will be displayed in two ways.  The first  line  of  output,
       which is marked with a '*' to indicate multiplication, gives the result
       of the conversion you have asked for.  The second line of output, which
       is  marked  with	 a  '/' to indicate division, gives the inverse of the
       conversion factor.  If you convert 10 meters to feet, units will print

	   * 32.808399
	   / 0.03048

       which tells you that 10 meters equals about 32.8 feet.  The second num-
       ber  gives  the conversion in the opposite direction.  In this case, it
       tells you that 1 foot is equal  to  about  0.03	dekameters  since  the
       dekameter is 10 meters.	It also tells you that 1/32.8 is about 0.03.

       The  units  program  prints  the inverse because sometimes it is a more
       convenient number.  In the example  above,  for	example,  the  inverse
       value  is  an  exact  conversion: a foot is exactly 0.03048 dekameters.
       But the number given the other direction is inexact.

       If you convert grains to pounds, you will see the following:

       You have: grains
       You want: pounds
	       * 0.00014285714
	       / 7000

       From the second line of the output, you	can  immediately  see  that  a
       grain  is equal to a seven thousandth of a pound.  This is not so obvi-
       ous from the first line of the output.  If you find the	output	format
       confusing, try using the '--verbose' option:

       You have: grain
       You want: aeginamina
	       grain = 0.00010416667 aeginamina
	       grain = (1 / 9600) aeginamina

       If  you	request a conversion between units that measure reciprocal di-
       mensions, then units will display the conversion results with an	 extra
       note indicating that reciprocal conversion has been done:

       You have: 6 ohms
       You want: siemens
	       reciprocal conversion
	       * 0.16666667
	       / 6

       Reciprocal conversion can be suppressed by using the '--strict' option.
       As usual, use the '--verbose' option to get more comprehensible output:

       You have: tex
       You want: typp
	       reciprocal conversion
	       1 / tex = 496.05465 typp
	       1 / tex = (1 / 0.0020159069) typp
       You have: 20 mph
       You want: sec/mile
	       reciprocal conversion
	       1 / 20 mph = 180 sec/mile
	       1 / 20 mph = (1 / 0.0055555556) sec/mile

       If you enter incompatible unit types, the units program	will  print  a
       message	indicating that the units are not conformable and it will dis-
       play the reduced form for each unit:

       You have: ergs/hour
       You want: fathoms kg^2 / day
       conformability error
	       2.7777778e-11 kg m^2 / sec^3
	       2.1166667e-05 kg^2 m / sec

       If you only want to find the reduced form or definition of a unit, sim-
       ply press Enter at the 'You want:' prompt.  Here is an example:

       You have: jansky
       You want:
	       Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2

       The  output from units indicates that the jansky is defined to be equal
       to a fluxunit which in turn is defined to be a certain  combination  of
       watts, meters, and hertz.  The fully reduced (and in this case somewhat
       more cryptic) form appears on the far right.  If the  ultimate  defini-
       tion and the fully reduced form are identical, the latter is not shown:

       You have: B
       You want:
	       Definition: byte = 8 bit

       The  fully  reduced form is shown if it and the ultimate definition are
       equivalent but not identical:

       You have: N
       You want:
	       Definition: newton = kg m / s^2 = 1 kg m / s^2

       Some named units are  treated  as  dimensionless	 in  some  situations.
       These  units  include  the  radian  and steradian.  These units will be
       treated as equal to 1 in units conversions.  Power is equal  to	torque
       times  angular  velocity.  This conversion can only be performed if the
       radian is dimensionless.

       You have: (14 ft lbf) (12 radians/sec)
       You want: watts
	       * 227.77742
	       / 0.0043902509

       It is also possible to compute roots and other  non-integer  powers  of
       dimensionless  units;  this allows computations such as the altitude of
       geosynchronous orbit:

       You have: cuberoot(G earthmass / (circle/siderealday)^2) - earthradius
       You want: miles
	       * 22243.267
	       / 4.4957425e-05

       Named dimensionless units are not treated  as  dimensionless  in	 other
       contexts.    They   cannot   be	used  as  exponents  so	 for  example,
       'meter^radian' is forbidden.

       If you want a list of options you can type ? at the 'You want:' prompt.
       The  program  will  display  a list of named units that are conformable
       with the unit that you entered at the 'You have:' prompt	 above.	  Con-
       formable unit combinations will not appear on this list.

       Typing  help  at	 either prompt displays a short help message.  You can
       also type help followed by a unit name.	This will invoke  a  pager  on
       the  units  data base at the point where that unit is defined.  You can
       read the definition and comments that may give more details or histori-
       cal  information about the unit.	 If your pager allows, you may want to
       scroll backwards, e.g. with 'b', because	 sometimes  a  longer  comment
       about  a unit or group of units will appear before the definition.  You
       can generally quit out of the pager by pressing 'q'.

       Typing search text will display a list of all of the units whose	 names
       contain	text  as  a  substring along with their definitions.  This may
       help in the case where you aren't sure of the right unit name.

USING UNITS NON-INTERACTIVELY
       The units program can perform units conversions non-interactively  from
       the command line.  To do this, type the command, type the original unit
       expression, and type the new units you want.   If  a  units  expression
       contains	 non-alphanumeric  characters, you may need to protect it from
       interpretation by the shell using single or double quote characters.

       If you type

       units "2 liters" quarts

       then units will print

	   * 2.1133764
	   / 0.47317647

       and then exit.  The output tells you that 2 liters is about 2.1 quarts,
       or alternatively that a quart is about 0.47 times 2 liters.

       units  does not require a space between a numerical value and the unit,
       so the previous example can be given as

       units 2liters quarts

       to avoid having to quote the first argument.

       If the conversion is successful, units will return  success  (zero)  to
       the  calling  environment.   If	you  enter non-conformable units, then
       units will print a message giving the reduced form of each unit and  it
       will return failure (nonzero) to the calling environment.

       If the '--conformable' option is given, only one unit expression is al-
       lowed, and units will print all units conformable with that expression;
       it is equivalent to giving ? at the 'You want:' prompt.	For example,

       units --conformable gauss
       B_FIELD	 tesla
       Gs	 gauss
       T	 tesla
       gauss	 abvolt sec / cm^2
       stT	 stattesla
       statT	 stattesla
       stattesla statWb/cm^2
       tesla	 Wb/m^2

       If  you give more than one unit expression with the '--conformable' op-
       tion, the program will exit with an error message and  return  failure.
       This option has no effect in interactive mode.

       If  the	'--terse'  ('-t') option is given with the '--conformable' op-
       tion, conformable units are shown without definitions; with the	previ-
       ous example, this would give

       units --terse --conformable gauss
       B_FIELD
       Gs
       T
       gauss
       stT
       statT
       stattesla
       tesla

       When  the '--conformable' option is not given and you invoke units with
       only one argument, units will print the	definition  of	the  specified
       unit.  It will return failure if the unit is not defined and success if
       the unit is defined.

UNIT DEFINITIONS
       The conversion information is  read  from  several  units  data	files:
       'definitions.units',	'elements.units',     'currency.units',	   and
       'cpi.units', which are usually located in the '/usr/share/units' direc-
       tory.   If you invoke units with the '-V' option, it will print the lo-
       cation of these files.  The default main file includes definitions  for
       all  familiar  units,  abbreviations  and metric prefixes.  It also in-
       cludes many obscure or archaic units.  Many common spelled-out  numbers
       (e.g., 'seventeen') are recognized.

   Physical Constants
       Many constants of nature are defined, including these:

       pi	   ratio of circumference of a circle to its diameter
       c	   speed of light
       e	   charge on an electron
       force	   acceleration of gravity
       mole	   Avogadro's number
       water	   pressure per unit height of water
       Hg	   pressure per unit height of mercury
       au	   astronomical unit
       k	   Boltzman's constant
       mu0	   permeability of vacuum
       epsilon0	   permittivity of vacuum
       G	   Gravitational constant
       mach	   speed of sound

       The  standard  data  file  includes numerous other constants.  Also in-
       cluded are the densities of various ingredients used in baking so  that
       '2 cups	flour_sifted' can be converted to 'grams'.  This is not an ex-
       haustive list.  Consult the units data file to see the  complete	 list,
       or to see the definitions that are used.

   Atomic Masses of the Elements
       The data file 'elements.units' includes atomic masses for most elements
       and most known isotopes.	 If the mole fractions of constituent isotopes
       are known, an elemental mass is calculated from the sum of the products
       of the mole fractions and the masses of the constituent	isotopes.   If
       the mole fractions are not known, the mass of the most stable isotope--
       if known--is given as the elemental  mass.   For	 radioactive  elements
       with  atomic  numbers 95 or greater, the mass number of the most stable
       isotope is not specified, because the list of studied isotopes is still
       incomplete.  If no stable isotope is known, no elemental mass is given,
       and you will need to choose the most appropriate isotope.

       The data are obtained from the US National Institute for Standards  and
       Technology	(NIST):	     https://physics.nist.gov/cgi-bin/Composi-
       tions/stand_alone.pl?ele=&all=all&ascii=ascii2&isotype=all.	   The
       'elements.units'	 file can be generated from these data using the elem-
       cvt command included with the distribution.

   Currency Exchange Rates and Consumer Price Index
       The data file 'currency.units' includes currency conversion rates;  the
       file  'cpi.units' includes the US Consumer Price Index (CPI), published
       by the US Bureau of Labor Statistics.  The data are updated monthly  by
       the  BLS;  see Updating Currency Exchange Rates and CPI for information
       on updating 'currency.units' and 'cpi.units'.

   English Customary Units
       English customary units differ in various ways among different regions.
       In  Britain  a complex system of volume measurements featured different
       gallons for different materials such as a wine gallon  and  ale	gallon
       that  different	by  twenty percent.  This complexity was swept away in
       1824 by a reform that created an entirely new gallon, the British Impe-
       rial  gallon  defined  as  the  volume occupied by ten pounds of water.
       Meanwhile in the USA the gallon is derived  from	 the  1707  Winchester
       wine  gallon, which is 231 cubic inches.	 These gallons differ by about
       twenty percent.	By default if units runs in  the  'en_GB'  locale  you
       will get the British volume measures.  If it runs in the 'en_US' locale
       you will get the US volume measures.  In other locales the default val-
       ues  are	 the  US  definitions.	If you wish to force different defini-
       tions, then set the environment variable UNITS_ENGLISH to  either  'US'
       or 'GB' to set the desired definitions independent of the locale.

       Before 1959, the value of a yard (and other units of measure defined in
       terms of it) differed slightly among  English-speaking  countries.   In
       1959,  Australia,  Canada,  New Zealand, the United Kingdom, the United
       States, and South  Africa  adopted  the	Canadian  value	 of  1 yard  =
       0.9144 m	 (exactly), which was approximately halfway between the values
       used by the UK and the US; it had the additional	 advantage  of	making
       1 inch  = 2.54 cm (exactly).  This new standard was termed the Interna-
       tional Yard.  Australia, Canada, and the UK then defined all  customary
       lengths	in  terms  of the International Yard (Australia did not define
       the furlong or rod); because many US land surveys were in terms of  the
       pre-1959	 units,	 the US continued to define customary surveyors' units
       (furlong, chain, rod, pole, perch, and link) in terms of	 the  previous
       value  for  the	foot, which was termed the US survey foot.  The US de-
       fined a US survey mile as 5280 US survey feet, and  defined  a  statute
       mile  as a US survey mile.  The US values for these units differed from
       the international values by about 2 ppm.

       The 1959 redefinition of the foot was legally binding in the US but al-
       lowed continued use of the previous definition of the foot for geodetic
       surveying.  It was assumed that this use would be  temporary,  but  use
       persisted, leading to confusion and errors, and it was at odds with the
       intent of uniform standards.  Since January 1, 2023, the US survey foot
       has  been  officially deprecated (85 FR 62698), with its use limited to
       historical and legacy applications.

       The units program has always used the international  values  for	 these
       units; the legacy US values can be obtained by using either the 'US' or
       the 'survey' prefix.  In either case, the simple familiar relationships
       among  the  units  are  maintained, e.g., 1 'furlong' = 660 'ft', and 1
       'USfurlong' = 660 'USft', though the metric equivalents differ slightly
       between the two cases.  The 'US' prefix or the 'survey' prefix can also
       be used to obtain the US survey mile and the value of the US yard prior
       to  1959,  e.g., 'USmile' or 'surveymile' (but not 'USsurveymile').  To
       get the US value of the statute mile,  use  either  'USstatutemile'  or
       'USmile'.   The pre-1959 UK values for these units can be obtained with
       the prefix 'UK'.

       Except for distances that extend over hundreds of miles (such as in the
       US  State  Plane	 Coordinate  System), the differences in the miles are
       usually insignificant:

       You have: 100 surveymile - 100 mile
       You want: inch
	       * 12.672025
	       / 0.078913984

       The US acre was officially defined in terms of the US survey foot,  but
       units  has used a definition based on the international foot; the units
       definition is now the same as the official US value.  If you  want  the
       previous	 US  acre, use 'USacre' and similarly use 'USacrefoot' for the
       previous US version of that unit.  The difference between  these	 units
       is about 4 parts per million.

   Miscellaneous Notes on Unit Definitions
       The  'pound'  is	 a  unit of mass.  To get force, multiply by the force
       conversion unit 'force' or use the shorthand 'lbf'.  (Note that 'g'  is
       already	taken  as  the	standard abbreviation for the gram.)  The unit
       'ounce' is also a unit of mass.	The fluid  ounce  is  'fluidounce'  or
       'floz'.	When British capacity units differ from their US counterparts,
       such as the British Imperial gallon, the unit is defined both ways with
       'br'  and 'us' prefixes.	 Your locale settings will determine the value
       of the unprefixed unit.	Currency is prefixed with  its	country	 name:
       'belgiumfranc', 'britainpound'.

       When  searching for a unit, if the specified string does not appear ex-
       actly as a unit name, then the units  program  will  try	 to  remove  a
       trailing 's', 'es'.  Next units will replace a trailing 'ies' with 'y'.
       If that fails, units will check for a prefix.   The  database  includes
       all  of the standard metric prefixes.  Only one prefix is permitted per
       unit, so 'micromicrofarad' will fail.   However,	 prefixes  can	appear
       alone  with no unit following them, so 'micro*microfarad' will work, as
       will 'micro microfarad'.

       To find out which units and prefixes are available,  read  the  default
       units data files; the main data file is extensively annotated.

UNIT EXPRESSIONS
   Operators
       You can enter more complicated units by combining units with operations
       such as multiplication, division, powers,  addition,  subtraction,  and
       parentheses  for grouping.  You can use the customary symbols for these
       operators when units is invoked with its	 default  options.   Addition-
       ally, units supports some extensions, including high priority multipli-
       cation using a space, and a high priority numerical  division  operator
       ('|') that can simplify some expressions.

       You  multiply units using a space or an asterisk ('*').	The next exam-
       ple shows both forms:

       You have: arabicfoot * arabictradepound * force
       You want: ft lbf
	       * 0.7296
	       / 1.370614

       You can divide units using the slash ('/') or with 'per':

       You have: furlongs per fortnight
       You want: m/s
	       * 0.00016630986
	       / 6012.8727

       You can use parentheses for grouping:

       You have: (1/2) kg / (kg/meter)
       You want: league
	       * 0.00010356166
	       / 9656.0833

       White space surrounding operators is optional, so the previous  example
       could  have  used '(1/2)kg/(kg/meter)'.	As a consequence, however, hy-
       phenated	 spelled-out  numbers  (e.g.,  'forty-two')  cannot  be	 used;
       'forty-two' is interpreted as '40 - 2'.

       Multiplication  using a space has a higher precedence than division us-
       ing a slash and is evaluated left to right; in effect,  the  first  '/'
       character  marks the beginning of the denominator of a unit expression.
       This makes it simple to enter a quotient with several terms in the  de-
       nominator: 'J / mol K'.	The '*' and '/' operators have the same prece-
       dence, and are evaluated left to right; if you multiply with  '*',  you
       must   group   the   terms   in	 the   denominator  with  parentheses:
       'J / (mol * K)'.

       The higher precedence of the space operator may not always be  advanta-
       geous.  For example, 'm/s s/day' is equivalent to 'm / s s day' and has
       dimensions of length per time cubed.  Similarly, '1/2 meter' refers  to
       a  unit	of reciprocal length equivalent to 0.5/meter, perhaps not what
       you would intend if you entered that expression.	 The get a half	 meter
       you  would need to use parentheses: '(1/2) meter'.  The '*' operator is
       convenient for multiplying  a  sequence	of  quotients.	 For  example,
       'm/s * s/day'  is  equivalent  to  'm/day'.  Similarly, you could write
       '1/2 * meter' to get half a meter.

       The units program supports another option for numerical fractions:  you
       can indicate division of numbers with the vertical bar ('|'), so if you
       wanted half a meter you could write '1|2 meter'.	 You  cannot  use  the
       vertical	 bar  to indicate division of non-numerical units (e.g., 'm|s'
       results in an error message).

       Powers of units can be specified using the '^' character, as  shown  in
       the following example, or by simple concatenation of a unit and its ex-
       ponent: 'cm3' is equivalent to 'cm^3'; if the exponent is more than one
       digit, the '^' is required.  You can also use '**' as an exponent oper-
       ator.

       You have: cm^3
       You want: gallons
	       * 0.00026417205
	       / 3785.4118

       Concatenation only  works  with	a  single  unit	 name:	if  you	 write
       '(m/s)2',  units will treat it as multiplication by 2.  When a unit in-
       cludes a prefix,	 exponent  operators  apply  to	 the  combination,  so
       'centimeter3' gives cubic centimeters.  If you separate the prefix from
       the unit with any multiplication operator (e.g., 'centi meter^3'),  the
       prefix  is  treated as a separate unit, so the exponent applies only to
       the unit without the prefix.   The  second  example  is	equivalent  to
       'centi  * (meter^3)', and gives a hundredth of a cubic meter, not a cu-
       bic centimeter.	The units program is limited internally to products of
       99 units; accordingly, expressions like 'meter^100' or 'joule^34' (rep-
       resented internally as 'kg^34 m^68 / s^68') will fail.

       The '|' operator has the highest	 precedence,  so  you  can  write  the
       square  root of two thirds as '2|3^1|2'.	 The '^' operator has the sec-
       ond highest precedence, and is evaluated right to left, as usual:

       You have: 5 * 2^3^2
       You want:
	       Definition: 2560

       With a dimensionless base unit, any dimensionless exponent is  meaning-
       ful (e.g., 'pi^exp(2.371)').  Even though angle is sometimes treated as
       dimensionless, exponents cannot have dimensions of angle:

       You have: 2^radian
			^
       Exponent not dimensionless

       If the base unit is not dimensionless, the exponent must be a  rational
       number  p/q,  and  the  dimension  of the unit must be a power of q, so
       'gallon^2|3' works but 'acre^2|3' fails.	 An exponent using  the	 slash
       ('/') operator (e.g., 'gallon^(2/3)') is also acceptable; the parenthe-
       ses are needed because the precedence of '^' is	higher	than  that  of
       '/'.   Since  units  cannot represent dimensions with exponents greater
       than 99, a fully reduced exponent must have q < 100.   When  raising  a
       non-dimensionless  unit to a power, units attempts to convert a decimal
       exponent to a rational number with q < 100.  If this  is	 not  possible
       units displays an error message:

       You have: ft^1.234
       Base unit not dimensionless; rational exponent required

       A  decimal  exponent  must match its rational representation to machine
       precision, so 'acre^1.5' works but 'gallon^0.666' does not.

   Sums and Differences of Units
       You may sometimes want to add values of different units that  are  out-
       side the SI.  You may also wish to use units as a calculator that keeps
       track of units.	Sums of conformable units are  written	with  the  '+'
       character, and differences with the '-' character.

       You have: 2 hours + 23 minutes + 32 seconds
       You want: seconds
	       * 8612
	       / 0.00011611705

       You have: 12 ft + 3 in
       You want: cm
	       * 373.38
	       / 0.0026782366

       You have: 2 btu + 450 ft lbf
       You want: btu
	       * 2.5782804
	       / 0.38785542

       The  expressions	 that are added or subtracted must reduce to identical
       expressions in primitive units, or an error message will be displayed:

       You have: 12 printerspoint - 4 heredium
					     ^
       Invalid sum of non-conformable units

       If you add two values of vastly different  scale	 you  may  exceed  the
       available  precision of floating point (about 15 digits). The effect is
       that the addition of the smaller value makes no change  to  the	larger
       value; in other words, the smaller value is treated as if it were zero.

       You have: lightyear + cm

       No warning is given, however.  As usual, the precedence for '+' and '-'
       is lower than that of the other operators.  A fractional quantity  such
       as  2 1/2 cups can be given as '(2+1|2) cups'; the parentheses are nec-
       essary because multiplication has higher precedence than addition.   If
       you omit the parentheses, units attempts to add '2' and '1|2 cups', and
       you get an error message:

       You have: 2+1|2 cups
			  ^
       Invalid sum or difference of non-conformable units

       The expression could also be correctly written as '(2+1/2)  cups'.   If
       you  write  '2 1|2  cups' the space is interpreted as multiplication so
       the result is the same as '1 cup'.

       The  '+'	 and  '-'  characters  sometimes  appears  in  exponents  like
       '3.43e+8'.  This leads to an ambiguity in an expression like '3e+2 yC'.
       The unit 'e' is a small unit of charge, so  this	 can  be  regarded  as
       equivalent  to  '(3e+2)	yC'  or '(3 e)+(2 yC)'.	 This ambiguity is re-
       solved by always interpreting '+' and '-' as part  of  an  exponent  if
       possible.

   Numbers as Units
       For  units,  numbers are just another kind of unit.  They can appear as
       many times as you like and in any order in a unit expression.  For  ex-
       ample,  to  find	 the  volume of a box that is 2 ft by 3 ft by 12 ft in
       steres, you could do the following:

       You have: 2 ft 3 ft 12 ft
       You want: stere
	       * 2.038813
	       / 0.49048148
       You have: $ 5 / yard
       You want: cents / inch
	       * 13.888889
	       / 0.072

       And the second example shows how the dollar sign in the	units  conver-
       sion can precede the five.  Be careful:	units will interpret '$5' with
       no space as equivalent to 'dollar^5'.

   Built-in Functions
       Several built-in functions are provided: 'sin', 'cos',  'tan',  'asin',
       'acos',	'atan',	 'sinh',  'cosh',  'tanh',  'asinh', 'acosh', 'atanh',
       'exp', 'ln',  'log',  'abs',  'round',  'floor',	 'ceil',  'factorial',
       'Gamma',	 'lnGamma',  'erf',  and 'erfc'; the function 'lnGamma' is the
       natural logarithm of the 'Gamma' function.

       The 'sin', 'cos', and 'tan' functions require  either  a	 dimensionless
       argument or an argument with dimensions of angle.

       You have: sin(30 degrees)
       You want:
	       Definition: 0.5
       You have: sin(pi/2)
       You want:
	       Definition: 1
       You have: sin(3 kg)
			 ^
       Unit not dimensionless

       The  other  functions on the list require dimensionless arguments.  The
       inverse trigonometric functions return arguments with dimensions of an-
       gle.

       The  'ln'  and 'log' functions give natural log and log base 10 respec-
       tively.	To obtain logs for any integer base, enter  the	 desired  base
       immediately  after  'log'.   For	 example,  to get log base 2 you would
       write 'log2' and to get log base 47 you could write 'log47'.

       You have: log2(32)
       You want:
	       Definition: 5
       You have: log3(32)
       You want:
	       Definition: 3.1546488
       You have: log4(32)
       You want:
	       Definition: 2.5
       You have: log32(32)
       You want:
	       Definition: 1
       You have: log(32)
       You want:
	       Definition: 1.50515
       You have: log10(32)
       You want:
	       Definition: 1.50515

       If you wish to  take  roots  of	units,	you  may  use  the  'sqrt'  or
       'cuberoot'  functions.	These functions require that the argument have
       the appropriate root.  You can obtain higher roots by using  fractional
       exponents:

       You have: sqrt(acre)
       You want: feet
	       * 208.71074
	       / 0.0047913202
       You have: (400 W/m^2 / stefanboltzmann)^(1/4)
       You have:
	       Definition: 289.80882 K
       You have: cuberoot(hectare)
				 ^
       Unit not a root

   Previous Result
       You  can	 insert the result of the previous conversion using the under-
       score ('_').  It is useful when you want to convert the same  input  to
       several different units, for example

       You have: 2.3 tonrefrigeration
       You want: btu/hr
	       * 27600
	       / 3.6231884e-005
       You have: _
       You want: kW
	       * 8.0887615
	       / 0.12362832

       Suppose	you  want to do some deep frying that requires an oil depth of
       2 inches.  You have 1/2 gallon of oil, and want to know the largest-di-
       ameter  pan  that will maintain the required depth.  The nonlinear unit
       'circlearea' gives the radius of the circle (see Other Nonlinear Units,
       for  a more detailed description) in SI units; you want the diameter in
       inches:

       You have: 1|2 gallon / 2 in
       You want: circlearea
	       0.10890173 m
       You have: 2 _
       You want: in
	       * 8.5749393
	       / 0.1166189

       In most cases, surrounding white space is optional, so the previous ex-
       ample  could  have used '2_'.  If '_' follows a non-numerical unit sym-
       bol, however, the space is required:

       You have: m_
		  ^
       Parse error

       You can use the '_' symbol any number of times; for example,

       You have: m
       You want:
	       Definition: 1 m
       You have: _ _
       You want:
	       Definition: 1 m^2

       Using '_' before a conversion has been performed (e.g., immediately af-
       ter invocation) generates an error:

       You have: _
		 ^
       No previous result; '_' not set

       Accordingly,  '_'  serves no purpose when units is invoked non-interac-
       tively.

       If units is invoked with the '--verbose' option (see  Invoking  Units),
       the value of '_' is not expanded:

       You have: mile
       You want: ft
	       mile = 5280 ft
	       mile = (1 / 0.00018939394) ft
       You have: _
       You want: m
	       _ = 1609.344 m
	       _ = (1 / 0.00062137119) m

       You  can give '_' at the 'You want:' prompt, but it usually is not very
       useful.

   Complicated Unit Expressions
       The units program is especially helpful in ensuring accuracy and dimen-
       sional consistency when converting lengthy unit expressions.  For exam-
       ple, one form of the Darcy-Weisbach fluid-flow equation is

	    Delta P = (8 / pi)^2 (rho fLQ^2) / d^5,

       where Delta P is the pressure drop, rho is the mass density, f  is  the
       (dimensionless)	friction factor, L is the length of the pipe, Q is the
       volumetric flow rate, and d is the pipe diameter.  You  might  want  to
       have the equation in the form

	    Delta P = A1 rho fLQ^2 / d^5

       that  accepted  the  user's normal units; for typical units used in the
       US, the required conversion could be something like

       You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5)
       You want: psi
	       * 43.533969
	       / 0.022970568

       The parentheses allow individual terms in the expression to be  entered
       naturally,  as they might be read from the formula.  Alternatively, the
       multiplication could be done with the '*' rather	 than  a  space;  then
       parentheses are needed only around 'ft^3/s' because of its exponent:

       You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5
       You want: psi
	       * 43.533969
	       / 0.022970568

       Without	parentheses, and using spaces for multiplication, the previous
       conversion would need to be entered as

       You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5
       You want: psi
	       * 43.533969
	       / 0.022970568

   Variables Assigned at Run Time
       Unit definitions are fixed once units has finished  reading  the	 units
       data  file(s), but at run time you can assign unit expressions to vari-
       ables whose names begin with an underscore, using the syntax

       _name = <unit expression>

       This can help manage a long calculation by saving intermediate  quanti-
       ties  as	 variables  that you can use later.  For example, to determine
       the shot-noise-limited signal-to-noise ratio (SNR) of an imaging system
       using a helium-neon laser, you could do

       You have: _lambda = 632.8 nm	       # laser wavelength
       You have: _nu = c / _lambda	       # optical frequency
       You have: _photon_energy = h * _nu
       You have: _power = 550 uW
       You have: _photon_count = _power * 500 ns / _photon_energy
       You have: _snr = sqrt(_photon_count)
       You have: _snr
       You want:
	       Definition: sqrt(_photon_count) = 29597.922

       Except  for  beginning with an underscore, runtime variables follow the
       same naming rules as units.  Because names beginning with '_'  are  re-
       served  for  these variables and unit names cannot begin with '_', run-
       time variables can never hide unit definitions.	Runtime variables  are
       undefined  until	 you make an assignment to them, so if you give a name
       beginning with an underscore and no assignment has been made,  you  get
       an error message.

       When  you  assign a unit expression to a runtime variable, units checks
       the expression to determine whether it is valid, but the resulting def-
       inition	is  stored  as	a text string, and is not reduced to primitive
       units.  The text will be processed anew each time you use the  variable
       in a conversion or calculation.	This means that if your definition de-
       pends on other runtime variables (or the special variable '_'), the re-
       sult  of	 calculating  with  your  variable will change if any of those
       variables change.  A dependence need not be direct.

       Continuing the example of the laser above, suppose you  have  done  the
       calculation  as shown.  You now wonder what happens if you switch to an
       argon laser:

       You have: _lambda = 454.6 nm
       You have: _snr
       You want:
	       Definition: sqrt(_photon_count) = 25086.651

       If you then change the power:

       You have: _power = 1 mW
       You have: _snr
       You want:
	       Definition: sqrt(_photon_count) = 33826.834

       Instead of having to reenter or edit a lengthy expression when you per-
       form  another  calculation,  you need only enter values that change; in
       this respect, runtime variables are similar to a spreadsheet.

       The more times a variable appears in an expression that depends on  it,
       the  greater  the benefit of having a calculation using that expression
       reflect changes to that variable.  For example, the length of  a	 side-
       real day at a given latitude and declination of the Sun is given by

	    L = acos((sin h - sin <phi> sin <delta>) /
			   (cos <phi> cos <delta>))

       where  L	 is  the day length, h is the altitude, <phi> is the latitude,
       and <delta> is the Sun's declination.

       The length of a solar day is obtained from a sidereal day by  multiply-
       ing by

       siderealday / day

       By  convention,	the Sun's altitude at rise or set is -50' to allow for
       atmospheric refraction and the semidiameter of its disk.	 At the summer
       solstice, the Sun's declination is approximately 23.44<degree>; to find
       the length of the longest day of the year for a latitude of 55<degree>,
       you could do

       You have: _alt = -50 arcmin
       You have: _lat = 55 deg
       You have: _decl = 23.44 deg
       You have: _num = sin(_alt) - sin(_lat) sin(_decl)
       You have: _denom = cos(_lat) cos(_decl)
       You have: _sday = 2 (acos(_num / _denom) / circle) 24 hr
       You have: _day = _sday siderealday / day
       You have: _day
       You want: hms
	       17 hr + 19 min + 34.895151 sec

       At   the	 winter	 solstice,  the	 Sun's	declination  is	 approximately
       -23.44<degree>, so you could calculate the length of the	 shortest  day
       of the year using:

       You have: _decl = -23.44 deg
       You have: _day
       You want: hms
	       7 hr + 8 min + 40.981084 sec

       Latitude	 and declination each appear twice in the expression for _day;
       the result in the examples above is updated by changing only the	 value
       of the declination.

       It's  important to remember that evaluation of runtime variables is de-
       layed, so you cannot make an assignment that is self-referential.   For
       example, the following does not work:

       You have: _decl = 23.44 deg
       You have: _decl = -_decl
       You have: _decl
       Circular unit definition

       A runtime variable must be assigned before it can be used in an assign-
       ment; in the first of the three	examples  above,  giving  the  general
       equation	 before the values for _alt, _lat, and _decl had been assigned
       would result in an error message.

   Backwards Compatibility: '*' and '-'
       The original units assigned multiplication a higher precedence than di-
       vision  using the slash.	 This differs from the usual precedence rules,
       which give multiplication and division equal  precedence,  and  can  be
       confusing for people who think of units as a calculator.

       The star operator ('*') included in this units program has, by default,
       the same precedence as division, and hence follows the usual precedence
       rules.	For  backwards	compatibility  you  can	 invoke units with the
       '--oldstar' option.  Then '*' has a higher  precedence  than  division,
       and the same precedence as multiplication using the space.

       Historically,  the hyphen ('-') has been used in technical publications
       to indicate products of units, and the original units  program  treated
       it  as a multiplication operator.  Because units provides several other
       ways to obtain unit products, and because '-' is a subtraction operator
       in general algebraic expressions, units treats the binary '-' as a sub-
       traction operator by default.   For  backwards  compatibility  use  the
       '--product' option, which causes units to treat the binary '-' operator
       as a product operator.  When '-' is a multiplication  operator  it  has
       the  same precedence as multiplication with a space, giving it a higher
       precedence than division.

       When '-' is used as a unary operator it negates its  operand.   Regard-
       less  of the units options, if '-' appears after '(' or after '+', then
       it will act as a negation operator.  So you can always compute  20  de-
       grees minus 12 minutes by entering '20 degrees + -12 arcmin'.  You must
       use this construction when you define new units because you cannot know
       what options will be in force when your definition is processed.

NONLINEAR UNIT CONVERSIONS
       Nonlinear  units	 are represented using functional notation.  They make
       possible nonlinear unit conversions such as temperature.

   Temperature Conversions
       Conversions between temperatures are different from linear  conversions
       between	temperature  increments--see  the example below.  The absolute
       temperature conversions are handled by units starting with 'temp',  and
       you  must  use  functional notation.  The temperature-increment conver-
       sions are done using units starting with 'deg' and they do not  require
       functional notation.

       You have: tempF(45)
       You want: tempC
	       7.2222222
       You have: 45 degF
       You want: degC
	       * 25
	       / 0.04

       Think  of 'tempF(x)' not as a function but as a notation that indicates
       that x should have units of 'tempF' attached to it.  See Defining  Non-
       linear  Units.	The  first  conversion	shows  that if it's 45 degrees
       Fahrenheit outside, it's 7.2 degrees Celsius.   The  second  conversion
       indicates  that	a  change  of  45  degrees Fahrenheit corresponds to a
       change of 25 degrees Celsius.  The conversion from 'tempF(x)' is to ab-
       solute temperature, so that

       You have: tempF(45)
       You want: degR
	       * 504.67
	       / 0.0019814929

       gives the same result as

       You have: tempF(45)
       You want: tempR
	       * 504.67
	       / 0.0019814929

       But  if	you  convert  'tempF(x)' to 'degC', the output is probably not
       what you expect:

       You have: tempF(45)
       You want: degC
	       * 280.37222
	       / 0.0035666871

       The result is the temperature in K, because 'degC' is defined  as  'K',
       the kelvin. For consistent results, use the 'tempX' units when convert-
       ing to a temperature rather than converting a temperature increment.

       The 'tempC()' and 'tempF()' definitions are limited to  positive	 abso-
       lute  temperatures,  and giving a value that would result in a negative
       absolute temperature generates an error message:

       You have: tempC(-275)
			   ^
       Argument of function outside domain

   US Consumer Price Index
       units includes the US Consumer Price Index published by the  US	Bureau
       of  Labor  Statistics.	Several functions that use this value are pro-
       vided: 'cpi', 'cpi_now', 'inflation_since', and 'dollars_in'.

       The 'cpi' function gives the CPI for a specified decimal year.  A deci-
       mal year is given as the year plus the fractional part of the year; be-
       cause of leap years and the different lengths of months, calculating an
       exact  value  for  the fractional part can be tedious, but for the pur-
       poses of CPI, an approximate value is usually adequate.	 For  example,
       1 January  2000	is  2000.0,  1 April  2000  is 2000.25, 1 July 2000 is
       2000.4986, and 1 October 2000 is 2000.75.  Note also that the CPI  data
       update monthly; values in between months are linearly interpolated.

       In the middle of 1975, the CPI was

       You have: cpi(1975.5)
       You want:
	       Definition: 53.6

       The value of the CPI for the previous month is usually published toward
       the the month; the latest value of the CPI is available with 'cpi_now'.
       On 7 January 2024, the value was

       You have: cpi_now
       You want:
	       Definition: UScpi_now = 307.051

       This  means that the CPI was 307.015 on 1 December 2023.	 The 'cpi_now'
       variable can only present the most recent data available, so it can lag
       the  current CPI by several weeks.  The decimal year of the last update
       is available with 'cpi_lastdate'.

       The 'inflation_since' function provides a convenient way	 to  determine
       the  inflation factor from a specified decimal year to the latest value
       in the CPI table.  For example, on 7 January 2024:

       You have: inflation_since(1970)
       You want:
	       Definition: 8.1445889

       In other words, goods that cost 1 US$ in 1970 would cost	 8.14  US$  on
       1 December 2023.

       The  'inflation_since' function can be used to determine an annual rate
       of inflation.  The earliest US CPI data are from about 1913.1; the  ap-
       proximate time between then and 7 January 2024 is 110.9 years.  The ap-
       proximate annual inflation rate for that period is then

       You have: inflation_since(1913.1)^1|110.9 - 1
       You want: %
	       * 3.1548115
	       / 0.31697614

       The inflation rate for any time period can be found from the  ratio  of
       the CPI at the end of the period to that of the beginning:

       You have: (cpi(1982)/cpi(1972))^1|10 - 1
       You want: %
	       * 8.6247033
	       / 0.11594602

       The period 1972-1982 was indeed one of high inflation.

       The  'dollars_in' function is similar to 'inflation_since' but its out-
       put is in US$ rather than dimensionless:

       You have: dollars_in(1970)
       You want:
	       Definition: 8.1445889 US$

       A typical use might be

       You have: 250 dollars_in(1970)
       You want: $
	       * 2036.1472
	       / 0.00049112362

       Because 'dollars_in' includes the units, you should not include them at
       the  'You have:'	 prompt.  You can also use 'dollars_in' to convert be-
       tween two specified years:

       You have: 250 dollars_in(1970)
       You want: dollars_in(1950)
	       * 156.49867
	       / 0.0063898305

       which shows that 250 US$ in 1970 would have equivalent purchasing power
       to 156 US$ in 1950.

   Other Nonlinear Units
       Some  other  examples  of  nonlinear  units are numerous different ring
       sizes and wire gauges, the grit sizes used for abrasives,  the  decibel
       scale,  shoe  size, scales for the density of sugar (e.g., baume).  The
       standard data file also supplies units for computing the area of a cir-
       cle  and	 the volume of a sphere.  See the standard units data file for
       more details.  Wire gauges with multiple	 zeroes	 are  signified	 using
       negative	 numbers where two zeroes is '-1'.  Alternatively, you can use
       the synonyms 'g00', 'g000', and so on that are defined in the  standard
       units data file.

       You have: wiregauge(11)
       You want: inches
	       * 0.090742002
	       / 11.020255
       You have: brwiregauge(g00)
       You want: inches
	       * 0.348
	       / 2.8735632
       You have: 1 mm
       You want: wiregauge
	       18.201919
       You have: grit_P(600)
       You want: grit_ansicoated
	       342.76923

       The  last  example shows the conversion from P graded sand paper, which
       is the European standard and may be marked "P600" on the back,  to  the
       USA standard.

       You  can	 compute  the  area  of	 a  circle  using  the nonlinear unit,
       'circlearea'.  You can also do this  using  the	circularinch  or  cir-
       cleinch.	 The next example shows two ways to compute the area of a cir-
       cle with a five inch radius and one way to  compute  the	 volume	 of  a
       sphere with a radius of one meter.

       You have: circlearea(5 in)
       You want: in2
	       * 78.539816
	       / 0.012732395
       You have: 10^2 circleinch
       You want: in2
	       * 78.539816
	       / 0.012732395
       You have: spherevol(meter)
       You want: ft3
	       * 147.92573
	       / 0.0067601492

       The inverse of a nonlinear conversion is indicated by prefixing a tilde
       ('~') to the nonlinear unit name:

       You have: ~wiregauge(0.090742002 inches)
       You want:
	       Definition: 11

       You can give a nonlinear unit definition without an argument or	paren-
       theses, and press Enter at the 'You want:' prompt to get the definition
       of a nonlinear unit; if the definition is not valid for all  real  num-
       bers,  the range of validity is also given.  If the definition requires
       specific units this information is also displayed:

       You have: tempC
	       Definition: tempC(x) = x K + stdtemp
			   defined for x >= -273.15
       You have: ~tempC
	       Definition: ~tempC(tempC) = (tempC +(-stdtemp))/K
			   defined for tempC >= 0 K
       You have: circlearea
	       Definition: circlearea(r) = pi r^2
			   r has units m

       To see the definition of the inverse use the  '~'  notation.   In  this
       case  the  parameter  in	 the functional definition will usually be the
       name of the unit.  Note that the inverse for 'tempC' shows that it  re-
       quires  units  of 'K' in the specification of the allowed range of val-
       ues.  Nonlinear unit conversions are described in more detail in Defin-
       ing Nonlinear Units.

UNIT LISTS: CONVERSION TO SUMS OF UNITS
       Outside	of  the SI, it is sometimes desirable to convert a single unit
       to a sum of units--for example, feet to feet plus inches.  The  conver-
       sion from sums of units was described in Sums and Differences of Units,
       and is a simple matter of adding the units with the '+' sign:

       You have: 12 ft + 3 in + 3|8 in
       You want: ft
	       * 12.28125
	       / 0.081424936

       Although you can similarly write a sum of units to convert to, the  re-
       sult will not be the conversion to the units in the sum, but rather the
       conversion to the particular sum that you have entered:

       You have: 12.28125 ft
       You want: ft + in + 1|8 in
	       * 11.228571
	       / 0.089058524

       The unit expression given at the 'You want:' prompt  is	equivalent  to
       asking  for conversion to multiples of '1 ft + 1 in + 1|8 in', which is
       1.09375 ft, so the conversion in the previous example is equivalent to

       You have: 12.28125 ft
       You want: 1.09375 ft
	       * 11.228571
	       / 0.089058524

       In converting to a sum of units like miles, feet and inches, you	 typi-
       cally  want  the largest integral value for the first unit, followed by
       the largest integral value for the next, and the remainder converted to
       the  last  unit.	  You can do this conversion easily with units using a
       special syntax for lists of units.  You must list the desired units  in
       order  from largest to smallest, separated by the semicolon (';') char-
       acter:

       You have: 12.28125 ft
       You want: ft;in;1|8 in
	       12 ft + 3 in + 3|8 in

       The conversion always gives integer coefficients on the	units  in  the
       list, except possibly the last unit when the conversion is not exact:

       You have: 12.28126 ft
       You want: ft;in;1|8 in
	       12 ft + 3 in + 3.00096 * 1|8 in

       The order in which you list the units is important:

       You have: 3 kg
       You want: oz;lb
	       105 oz + 0.051367866 lb
       You have: 3 kg
       You want: lb;oz
	       6 lb + 9.8218858 oz

       Listing ounces before pounds produces a technically correct result, but
       not a very useful one.  You must list the units in descending order  of
       size in order to get the most useful result.

       Ending  a  unit	list with the separator ';' has the same effect as re-
       peating the last unit on the list, so 'ft;in;1|8 in;' is equivalent  to
       'ft;in;1|8 in;1|8 in'.  With the example above, this gives

       You have: 12.28126 ft
       You want: ft;in;1|8 in;
	       12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in

       in  effect  separating  the integer and fractional parts of the coeffi-
       cient for the last unit.	 If you instead prefer to round the last coef-
       ficient to an integer you can do this with the '--round' ('-r') option.
       With the previous example, the result is

       You have: 12.28126 ft
       You want: ft;in;1|8 in
	       12 ft + 3 in + 3|8 in (rounded down to nearest 1|8 in)

       When you use the '-r' option, repeating the last unit on the  list  has
       no  effect  (e.g.,  'ft;in;1|8  in;1|8  in' is equivalent to 'ft;in;1|8
       in'), and hence neither does ending a list with a ';'.  With  a	single
       unit and the '-r' option, a terminal ';' does have an effect: it causes
       units to treat the single unit as a list and produce  a	rounded	 value
       for the single unit.  Without the extra ';', the '-r' option has no ef-
       fect on single unit conversions.	 This example shows the	 output	 using
       the '-r' option:

       You have: 12.28126 ft
       You want: in
	       * 147.37512
	       / 0.0067854058
       You have: 12.28126 ft
       You want: in;
	       147 in (rounded down to nearest in)

       Each  unit  that appears in the list must be conformable with the first
       unit on the list, and of course the listed units must also be  conform-
       able with the unit that you enter at the 'You have:' prompt.

       You have: meter
       You want: ft;kg
		    ^
       conformability error
	       ft = 0.3048 m
	       kg = 1 kg
       You have: meter
       You want: lb;oz
       conformability error
	       1 m
	       0.45359237 kg

       In the first case, units reports the disagreement between units appear-
       ing on the list.	 In the second case, units  reports  disagreement  be-
       tween  the unit you entered and the desired conversion.	This conforma-
       bility error is based on the first unit on the unit list.

       Other common candidates for conversion to sums of units are angles  and
       time:

       You have: 23.437754 deg
       You want: deg;arcmin;arcsec
	   23 deg + 26 arcmin + 15.9144 arcsec
       You have: 7.2319 hr
       You want: hr;min;sec
	   7 hr + 13 min + 54.84 sec

       Some applications for unit lists may be less obvious.  Suppose that you
       have a postal scale and wish to ensure that it's accurate at 1 oz,  but
       have only metric calibration weights.  You might try

       You have: 1 oz
       You want: 100 g;50 g; 20 g;10 g;5 g;2 g;1 g;
	       20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g

       You might then place one each of the 20 g, 5 g, 2 g, and 1 g weights on
       the scale and hope that it indicates close to

       You have: 20 g + 5 g + 2 g + 1 g
       You want: oz;
	       0.98767093 oz

       Appending ';' to 'oz' forces a one-line display that includes the unit;
       here the integer part of the result is zero, so it is not displayed.

       If a non-empty list item differs vastly in scale from the quantity from
       which the list is to be converted, you may exceed the available	preci-
       sion  of floating point (about 15 digits), in which case you will get a
       warning, e.g.,

       You have: lightyear
       You want: mile;100 inch;10 inch;mm;micron
	       5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision limit)

   Cooking Measure
       In North America, recipes for cooking typically measure ingredients  by
       volume,	and use units that are not always convenient multiples of each
       other.  Suppose that you have a recipe for 6 and you  wish  to  make  a
       portion	for  1.	  If the recipe calls for 2 1/2 cups of an ingredient,
       you might wish to know the measurements in terms of  measuring  devices
       you have available, you could use units and enter

       You have: (2+1|2) cup / 6
       You want: cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp
	       1|3 cup + 1 tbsp + 1 tsp

       By  default,  if	 a unit in a list begins with fraction of the form 1|x
       and its multiplier is an integer, the fraction is given as the  product
       of the multiplier and the numerator; for example,

       You have: 12.28125 ft
       You want: ft;in;1|8 in;
	       12 ft + 3 in + 3|8 in

       In  many	 cases, such as the example above, this is what is wanted, but
       sometimes it is not.  For example, a cooking recipe for	6  might  call
       for  5 1/4 cup of an ingredient, but you want a portion for 2, and your
       1-cup measure is not available; you might try

       You have: (5+1|4) cup / 3
       You want: 1|2 cup;1|3 cup;1|4 cup
	       3|2 cup + 1|4 cup

       This result might be fine for a baker who has a 1 1/2-cup measure  (and
       recognizes  the	equivalence),  but  it may not be as useful to someone
       with more limited set of measures, who does want to do additional  cal-
       culations,  and only wants to know "How many 1/2-cup measures to I need
       to add?"	 After all, that's what was actually asked.  With the '--show-
       factor' option, the factor will not be combined with a unity numerator,
       so that you get

       You have: (5+1|4) cup / 3
       You want: 1|2 cup;1|3 cup;1|4 cup
	       3 * 1|2 cup + 1|4 cup

       A user-specified fractional unit with a numerator other than 1 is never
       overridden,  however--if a unit list specifies '3|4 cup;1|2 cup', a re-
       sult equivalent to 1 1/2 cups will always be shown  as  '2  *  3|4 cup'
       whether or not the '--show-factor' option is given.

   Unit List Aliases
       A unit list such as

       cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp

       can  be	tedious	 to enter.  The units program provides shorthand names
       for some common combinations:

       hms	   time: hours, minutes, seconds
       dms	   angle: degrees, minutes, seconds
       time	   time: years, days, hours, minutes and seconds
       usvol	   US cooking volume: cups and smaller
       uswt	   US weight: pounds and ounces
       ftin	   length: feet, inches and 1/8 inches
       inchfine	   length: inches subdivided to 1/64 inch

       Using these shorthands, or unit list aliases, you can do the  following
       conversions:

       You have: anomalisticyear
       You want: time
	       1 year + 25 min + 3.4653216 sec
       You have: 1|6 cup
       You want: usvol
	       2 tbsp + 2 tsp

       You  can	 define	 your  own  unit  list aliases; see Defining Unit List
       Aliases.

       You cannot combine a unit list alias with other units: it  must	appear
       alone at the 'You want:' prompt.

       You  can	 display the definition of a unit list alias by entering it at
       the 'You have:' prompt:

       You have: dms
	       Definition: unit list, deg;arcmin;arcsec

       When you specify compact output with '--compact', '--terse' or '-t' and
       perform	conversion  to a unit list, units lists the conversion factors
       for each unit in the list, separated by semicolons.

       You have: year
       You want: day;min;sec
       365;348;45.974678

       Unlike the case of regular output, zeros are included  in  this	output
       list:

       You have: liter
       You want: cup;1|2 cup;1|4 cup;tbsp
       4;0;0;3.6280454

ALTERNATIVE UNIT SYSTEMS
   CGS Units
       The  SI--an  extension  of  the MKS (meter-kilogram-second) system--has
       largely supplanted the older CGS (centimeter-gram-second)  system,  but
       CGS  units  are	still  used in a few specialized fields, especially in
       physics where they lead to a  more  elegant  formulation	 of  Maxwell's
       equations.   Conversions	 between SI and CGS involving mechanical units
       are straightforward, involving powers of 10 (e.g., 1 m = 100 cm).  Con-
       versions	 involving  electromagnetic  units  are	 more complicated, and
       units supports four different systems of CGS units: electrostatic units
       (ESU),  electromagnetic units (EMU), the Gaussian system and the Heavi-
       side-Lorentz system.  The differences between these systems arise  from
       different choices made for proportionality constants in electromagnetic
       equations.  Coulomb's law gives electrostatic force between two charges
       separated by a distance delim $$ r:

	    F = k_C q_1 q_2 / r^2.

       Ampere's	 law  gives  the electromagnetic force per unit length between
       two current-carrying conductors separated by a distance r:

	    F/l = 2 k_A I_1 I_2 / r.

       The two constants, k_C and k_A, are related by the square of the	 speed
       of light: k_A = k_C / c^2.

       In  the SI, the constants have dimensions, and an additional base unit,
       the ampere, measures electric current.  The CGS systems do  not	define
       new  base  units,  but  express	charge and current as derived units in
       terms of mass, length, and time.	 In the ESU system, the	 constant  for
       Coulomb's  law  is  chosen to be unity and dimensionless, which defines
       the unit of charge.  In the EMU system, the constant for	 Ampere's  law
       is  chosen  to be unity and dimensionless, which defines a unit of cur-
       rent.  The Gaussian system usually uses the ESU units  for  charge  and
       current; it chooses another constant so that the units for the electric
       and magnetic fields are the same.  The Heaviside-Lorentz system is "ra-
       tionalized"  so	that factors of 4{pi} do not appear in Maxwell's equa-
       tions.  The SI system is similarly rationalized, but the other CGS sys-
       tems  are  not.	 In  the  Heaviside-Lorentz (HLU) system the factor of
       4{pi} appears in Coulomb's law instead; this system  differs  from  the
       Gaussian system by factors of the square root of 4{pi}

       The  dimensions of electrical quantities in the various CGS systems are
       different from the SI dimensions for the same units; strictly,  conver-
       sions between these systems and SI are not possible.  But units in dif-
       ferent systems relate to the same physical quantities, so  there	 is  a
       correspondence  between	these  units.	The  units program defines the
       units so that you can convert between corresponding units in the	 vari-
       ous systems.

       The  CGS definitions involve cm^(1/2) and g^(1/2), which is problematic
       because units does not normally support fractional roots of base units.
       The  '--units'  ('-u') option allows selection of a CGS unit system and
       works around this restriction by introducing base units for the	square
       roots  of length and mass: 'sqrt_cm' and 'sqrt_g'.  The centimeter then
       becomes 'sqrt_cm^2' and the gram, 'sqrt_g^2'.  This allows working from
       equations  using the units in the CGS system, and enforcing dimensional
       conformity  within  that	 system.   Recognized  CGS  arguments  to  the
       '--units' option are 'gauss[ian]', 'esu', 'emu', 'lhu'; the argument is
       case insensitive.  You can also give 'si' which just enforces  the  de-
       fault  SI  mode and displays '(SI)' at the 'You have:' prompt to empha-
       size the units mode.  Some other types of units are also	 supported  as
       described  below.   Giving  an unrecognized system generates a warning,
       and units uses SI units.

       The changes resulting from the '--units' option are actually controlled
       by  the UNITS_SYSTEM environment variable.  If you frequently work with
       one of the supported CGS units systems, you may	set  this  environment
       variable	 rather	 than  giving the '--units' option at each invocation.
       As usual, an option given on the command line overrides the setting  of
       the  environment variable. For example, if you would normally work with
       Gaussian units but might occasionally  work  with  SI,  you  could  set
       UNITS_SYSTEM  to	 'gaussian'  and specify SI with the '--units' option.
       Unlike the argument to the '--units' option, the value of  UNITS_SYSTEM
       is  case	 sensitive,  so	 setting  a value of 'EMU' will have no effect
       other than to give an error message and set SI units.

       The CGS definitions appear as  conditional  settings  in	 the  standard
       units  data  file,  which  you  can consult for more information on how
       these units are defined, or on how to define an alternate units system.

       The ESU system derives the  electromagnetic  units  from	 its  unit  of
       charge,	the  statcoulomb,  which  is  defined from Coulomb's law.  The
       statcoulomb equals dyne^(1/2) cm, or cm^(3/2) g^(1/2) s^(-1).  The unit
       of  current, the statampere, is statcoulomb sec, analogous to the rela-
       tionship in SI.	Other electrical units are then derived	 in  a	manner
       similar	to  that  for SI units; the units use the SI names prefixed by
       'stat-', e.g., 'statvolt' or 'statV'.  The prefix 'st-' is also	recog-
       nized (e.g., 'stV').

       The  EMU system derives the electromagnetic units from its unit of cur-
       rent, the abampere, which is defined in terms  of  Ampere's  law.   The
       abampere is equal to dyne^(1/2), or cm^(1/2) g^(1/2) s^(-1).  delim off
       The unit of charge, the abcoulomb, is abampere sec, again analogous  to
       the SI relationship.  Other electrical units are then derived in a man-
       ner similar to that for SI units; the units use the SI  names  prefixed
       by  'ab-',  e.g.,  'abvolt' or 'abV'.  The magnetic field units include
       the gauss, the oersted and the maxwell.

       The Gaussian units system, which was also known as the  Symmetric  Sys-
       tem,  uses  the	same charge and current units as the ESU system (e.g.,
       'statC', 'statA'); it differs by defining the magnetic field so that it
       has the same units as the electric field.  The resulting magnetic field
       units are the same ones used in the EMU system: the gauss, the  oersted
       and the maxwell.

       The  Heaviside-Lorentz  system  appears to lack named units.  We define
       five basic units, 'hlu_charge', 'hlu_current', 'hlu_volt', 'hlu_efield'
       and  'hlu_bfield' for conversions with this system.  It is important to
       remember that with all of the CGS systems, the units may look the  same
       but mean something different.  The HLU system and Gaussian systems both
       measure magnetic field using the same CGS dimensions, but the amount of
       magnetic field with the same units is different in the two systems.

       The  CGS	 systems define units that measure the same thing but may have
       conflicting dimensions.	Furthermore, the dimensions of the electromag-
       netic  CGS  units  are  never  compatible  with SI.  But if you measure
       charge in two different systems you have	 measured  the	same  physical
       thing,  so there is a correspondence between the units in the different
       systems, and units supports conversions	between	 corresponding	units.
       When  running  with  SI, units defines all of the CGS units in terms of
       SI.  When you select a CGS system, units defines the SI units  and  the
       other CGS system units in terms of the system you have selected.

       (Gaussian) You have: statA
		  You want: abA
	       * 3.335641e-11
	       / 2.9979246e+10
       (Gaussian) You have: abA
		  You want: sqrt(dyne)
       conformability error
	       2.9979246e+10 sqrt_cm^3 sqrt_g / s^2
	       1 sqrt_cm sqrt_g / s

       In  the	above  example, units converts between the current units statA
       and abA even though the abA, from the EMU system, has incompatible  di-
       mensions.   This	 works because in Gaussian mode, the abA is defined in
       terms of the statA, so it does not have the correct definition for EMU;
       consequently, you cannot convert the abA to its EMU definition.

       One  challenge  of  conversion is that because the CGS system has fewer
       base units, quantities that have different dimensions in	 SI  may  have
       the  same  dimension  in	 a CGS system.	And yet, they may not have the
       same conversion factor.	For example, the unit for the E	 field	and  B
       fields  are the same in the Gaussian system, but the conversion factors
       to SI are quite different.  This means that correct conversion is  only
       possible	 if  you  keep	track of what quantity is being measured.  You
       cannot convert statV/cm to SI without indicating which  type  of	 field
       the unit measures.  To aid in dimensional analysis, units defines vari-
       ous dimension units such as 'LENGTH', 'TIME', and 'CHARGE'  to  be  the
       appropriate  dimension  in  SI.	The electromagnetic dimensions such as
       'B_FIELD' or 'E_FIELD' may be useful aids both for conversion  and  di-
       mensional  analysis in CGS.  You can convert them to or from CGS in or-
       der to perform SI conversions that in some cases will not work directly
       due  to	dimensional  incompatibilities.	  This	example	 shows how the
       Gaussian system uses the same units for all of the fields, but they all
       have different conversion factors with SI.

       (Gaussian) You have: statV/cm
		  You want: E_FIELD
	       * 29979.246
	       / 3.335641e-05
       (Gaussian) You have: statV/cm
		  You want: B_FIELD
	       * 0.0001
	       / 10000
       (Gaussian) You have: statV/cm
		  You want: H_FIELD
	       * 79.577472
	       / 0.012566371
       (Gaussian) You have: statV/cm
		  You want: D_FIELD
	       * 2.6544187e-07
	       / 3767303.1

       The next example shows that the oersted cannot be converted directly to
       the SI unit of magnetic field, A/m, because  the	 dimensions  conflict.
       We  cannot  redefine the ampere to make this work because then it would
       not convert with the statampere.	 But you can still do this  conversion
       as shown below.

       (Gaussian) You have: oersted
		  You want: A/m
       conformability error
	       1 sqrt_g / s sqrt_cm
	       29979246 sqrt_cm sqrt_g / s^2
       (Gaussian) You have: oersted
		  You want: H_FIELD
	       * 79.577472
	       / 0.012566371

   Natural Units
       Like the CGS units, "natural" units are an alternative to the SI system
       used primarily physicists in different fields, with  different  systems
       tailored to different fields of study.  These systems are "natural" be-
       cause the base measurements are defined using  physical	constants  in-
       stead  of  arbitrary  values such as the meter or second.  In different
       branches of physics, different physical constants are more fundamental,
       which has given rise to a variety of incompatible natural unit systems.

       The  supported  systems	are the "natural" units (which seem to have no
       better name) used in high energy	 physics  and  cosmology,  the	Planck
       units,  often  used by scientists working with gravity, and the Hartree
       atomic units are favored by those working  in  physical	chemistry  and
       condensed matter physics.

       You  can select the various natural units using the '--units' option in
       the same way that you select the CGS units.  The "natural"  units  come
       in  two types, a rationalized system derived from the Heaviside-Lorentz
       units and an unrationalized system derived from	the  Gaussian  system.
       You  can select these using 'natural' and 'natural-gauss' respectively.
       For conversions in SI mode, several unit names starting with  'natural'
       are  available.	 This "natural" system is defined by setting {hbar}, c
       and the Boltzman constant to 1.	Only a single base unit	 remains:  the
       electron volt.

       The  Planck  units exist in a variety of forms, and units supports two.
       Both supported forms are rationalized, in that factors of 4{pi} do  not
       appear  in  Maxwell's equations.	 However, Planck units can also differ
       based on how the gravitational constant is  treated.   This  system  is
       similar to the natural units in that c, {hbar}, and Boltzman's constant
       are set to 1, but in this system, Newton's gravitational constant, G is
       also  fixed.   In  the  "reduced"  Planck  system,  delim $$ 8{pi}G = 1
       whereas in the unreduced system G = 1.  The reduced  system  eliminates
       factors of 8{pi} delim off from the Einstein field equations for gravi-
       tation, so this is similar to the process of forming rationalized units
       to  simplify  Maxwell's	equations.  To obtain the unreduced system use
       the name 'planck' and  for  the	reduced	 Planck	 units,	 'planck-red'.
       Units  such as 'planckenergy' and 'planckenergy_red' enable you to con-
       vert the unreduced and reduced Planck energy unit in  SI	 mode  between
       the  various systems.  In Planck units, all measurements are dimension-
       less.

       The final natural unit system is the Hartree atomic  units.   Like  the
       Planck  units, all measurements in the Hartree units are dimensionless,
       but this system is defined by defined from completely different	physi-
       cal  constants:	the  electron  mass,  Planck's	constant, the electron
       charge, and the Coulomb constant are the defining physical  quantities,
       which  are  all set to unity.  To invoke this system with the '--units'
       option use the name 'hartree'.

   Prompt Prefix
       If a unit system is specified with the '--units' option,	 the  selected
       system's	 name  is  prepended  to the 'You have:' prompt as a reminder,
       e.g.,

       (Gaussian) You have: stC
		  You want:
	       Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s

       You can suppressed the prefix by including a line

       !prompt

       with no argument in a site or personal units data file.	The prompt can
       be  conditionally suppressed by including such a line within '!var' ...
       '!endvar' constructs, e.g.,

       !var UNITS_SYSTEM gaussian gauss
       !prompt
       !endvar

       This might be appropriate if you normally use Gaussian units  and  find
       the prefix distracting but want to be reminded when you have selected a
       different CGS system.

LOGGING CALCULATIONS
       The '--log' option allows you to save the results of calculations in  a
       file;  this  can be useful if you need a permanent record of your work.
       For example, the fluid-flow conversion in Complicated Unit Expressions,
       is lengthy, and if you were to use it in designing a piping system, you
       might want a record of it for the project  file.	  If  the  interactive
       session

       # Conversion factor A1 for pressure drop
       # dP = A1 rho f L Q^2/d^5
       You have: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units
       You want: psi
	       * 43.533969
	       / 0.022970568

       were logged, the log file would contain

       ### Log started Fri Oct 02 15:55:35 2015
       # Conversion factor A1 for pressure drop
       # dP = A1 rho f L Q^2/d^5
       From: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5)   # Input units
       To:   psi
	       * 43.533969
	       / 0.022970568

       The time is written to the log file when the file is opened.

       The  use	 of  comments can help clarify the meaning of calculations for
       the log.	 The log includes conformability errors between the  units  at
       the  'You have:' and 'You want:' prompts, but not other errors, includ-
       ing lack of conformability of items in sums  or	differences  or	 among
       items  in  a unit list.	For example, a conversion between zenith angle
       and elevation angle could involve

       You have: 90 deg - (5 deg + 22 min + 9 sec)
					  ^
       Invalid sum or difference of non-conformable units
       You have: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
       You want: dms
	       84 deg + 37 arcmin + 51 arcsec
       You have: _
       You want: deg
	       * 84.630833
	       / 0.011816024
       You have:

       The log file would contain

       From: 90 deg - (5 deg + 22 arcmin + 9 arcsec)
       To:   deg;arcmin;arcsec
	       84 deg + 37 arcmin + 51 arcsec
       From: _
       To:   deg
	       * 84.630833
	       / 0.011816024

       The initial entry error (forgetting  that  minutes  have	 dimension  of
       time,  and  that	 arcminutes must be used for dimensions of angle) does
       not appear in the output.  When converting to a unit list alias,	 units
       expands the alias in the log file.

       The  'From:'  and  'To:'	 tags  are written to the log file even if the
       '--quiet' option is given.  If the log file exists when	units  is  in-
       voked, the new results are appended to the log file.  The time is writ-
       ten to the log file each time the file is opened.  The  '--log'	option
       is ignored when units is used non-interactively.

INVOKING UNITS
       You invoke units like this:

       units [options] [from-unit [to-unit]]

       If the from-unit and to-unit are omitted, the program will use interac-
       tive prompts to determine which conversions to perform.	 See  Interac-
       tive  Use.   If	both from-unit and to-unit are given, units will print
       the result of that single conversion and then exit.  If only  from-unit
       appears	on the command line, units will display the definition of that
       unit and exit.  Units specified on the command  line  may  need	to  be
       quoted to protect them from shell interpretation and to group them into
       two arguments.  Note also that the '--quiet' option is enabled  by  de-
       fault  if  you specify from-unit on the command line.  See Command Line
       Use.

       The default behavior of units can be changed by various	options	 given
       on the command line.  In most cases, the options may be given in either
       short form (a single '-' followed by a single character) or  long  form
       ('--'  followed	by  a word or hyphen-separated words).	Short-form op-
       tions are cryptic but require less typing;  long-form  options  require
       more  typing  but  are more explanatory and may be more mnemonic.  With
       long-form options you need only enter sufficient characters to uniquely
       identify the option to the program.  For example, '--out %f' works, but
       '--o %f' fails because units has other long options beginning with 'o'.
       However,	 '--q'	works because '--quiet' is the only long option begin-
       ning with 'q'.

       Some options require arguments to specify a  value  (e.g.,  '-d 12'  or
       '--digits 12').	 Short-form  options that do not take arguments may be
       concatenated (e.g., '-erS' is equivalent to '-e -r -S'); the  last  op-
       tion in such a list may be one that takes an argument (e.g., '-ed 12').
       With short-form options, the space between an option and	 its  argument
       is optional (e.g., '-d12' is equivalent to '-d 12').  Long-form options
       may not be concatenated, and the space between a long-form  option  and
       its  argument is required.  Short-form and long-form options may be in-
       termixed on the command line.  Options may be given in any  order,  but
       when incompatible options (e.g., '--output-format' and '--exponential')
       are given in combination, behavior is controlled	 by  the  last	option
       given.  For example, '-o%.12f -e' gives exponential format with the de-
       fault eight significant digits).

       The following options are available:

       -c, --check
	      Check that all units and prefixes defined in  units  data	 files
	      reduce  to  primitive  units.   Display a list of all units that
	      cannot be reduced and a list of units with circular definitions.
	      Also display some other diagnostics about suspicious definitions
	      in the units data file.  Only definitions active in the  current
	      locale  are  checked.  You should always run units with this op-
	      tion after modifying a units data file.

	      Some errors may hide other errors, so you should run units  with
	      this option again after correcting any errors, and keep doing so
	      until there are no errors.

       --check-verbose, --verbose-check
	      Like the '--check' option, this option displays a list of	 units
	      that cannot be reduced.  But it also lists the units as they are
	      checked.	Because the '--check' option now catches circular unit
	      definitions that previously caused units to hang, this option is
	      no longer necessary.  It is retained only for compatibility with
	      previous versions.

       -d ndigits, --digits ndigits
	      Set  the number of significant digits in the output to the value
	      specified (which must  be	 greater  than	zero).	 For  example,
	      '-d 12' sets the number of significant digits to 12.  With expo-
	      nential output units displays one digit to the left of the deci-
	      mal  point  and eleven digits to the right of the decimal point.
	      On most systems, the maximum  number  of	internally  meaningful
	      digits is 15; if you specify a greater number than your system's
	      maximum, units will print a warning and set the  number  to  the
	      largest  meaningful  value.   To directly set the maximum value,
	      give an argument of max (e.g., '-d max').	 Be aware, of  course,
	      that  "significant"  here refers only to the display of numbers;
	      if results depend on physical constants not known to this preci-
	      sion,  the physically meaningful precision may be less than that
	      shown.  The '--digits' option conflicts with the	'--output-for-
	      mat' option.

       -e, --exponential
	      Set  the	numeric output format to exponential (i.e., scientific
	      notation), like that used in the Unix units  program.   The  de-
	      fault precision is eight significant digits (seven digits to the
	      right of the decimal  point);  this  can	be  changed  with  the
	      '--digits'  option.   The	 '--exponential' option conflicts with
	      the '--output-format' option.

       -o format, --output-format format
	      This option affords complete control  over  the  numeric	output
	      format using the specified format. The format is a single float-
	      ing point numeric format for the printf function in the  C  pro-
	      gramming	language.   All compilers support the format types 'g'
	      and 'G' to specify significant digits, 'e' and  'E'  for	scien-
	      tific  notation,	and  'f' for fixed-point decimal.  The ISO C99
	      standard introduced the 'F' type for fixed-point decimal and the
	      'a'  and	'A'  types for hexadecimal floating point; these types
	      are allowed with compilers that support them.  The default  for-
	      mat   is	'%.8g';	 for  greater  precision,  you	could  specify
	      '-o %.15g'. See Numeric Output Format and the documentation  for
	      printf  for  more detailed descriptions of the format specifica-
	      tion.  The '--output-format' option affords the greatest control
	      of  the  output  appearance,  but	 requires at least rudimentary
	      knowledge of the printf format syntax.  If  you  don't  want  to
	      bother with the printf syntax, you can specify greater precision
	      more simply with the '--digits'  option  or  select  exponential
	      format  with  '--exponential'.   The '--output-format' option is
	      incompatible with the '--exponential' and '--digits' options.

       -f filename, --file filename
	      Instruct units to load the units file filename.  You can specify
	      up to 25 units files on the command line.	 When you use this op-
	      tion, units will load only the files you	list  on  the  command
	      line;  it will not load the standard file or your personal units
	      file unless you explicitly list them.  If filename is the	 empty
	      string ('-f ""'), the default main units file (or that specified
	      by UNITSFILE) will be loaded in addition to any others specified
	      with '-f'.

       -L logfile, --log logfile
	      Save  the	 results of calculations in the file logfile; this can
	      be useful if it is important to have a record  of	 unit  conver-
	      sions  or	 other calculations that are to be used extensively or
	      in a critical activity such as a program or design project.   If
	      logfile  exits,  the new results are appended to the file.  This
	      option is ignored when units  is	used  non-interactively.   See
	      Logging  Calculations  for  a more detailed description and some
	      examples.

       -H filename, --history filename
	      Instruct units to save history to filename, so that a record  of
	      your  commands is available for retrieval across different units
	      invocations.  To prevent the history from being saved set	 file-
	      name  to	the empty string ('-H ""').  This option has no effect
	      if readline is not available.

       -h, --help
	      Print out a summary of the options for units.

       -m, --minus
	      Causes '-' to be interpreted as a subtraction operator.  This is
	      the default behavior.

       -p, --product
	      Causes  '-'  to be interpreted as a multiplication operator when
	      it has two operands.  It will act as a negation operator when it
	      has  only	 one  operand: '(-3)'.	By default '-' is treated as a
	      subtraction operator.

       --oldstar
	      Causes '*' to have the old-style	precedence,  higher  than  the
	      precedence of division so that '1/2*3' will equal '1/6'.

       --newstar
	      Forces '*' to have the new (default) precedence that follows the
	      usual rules of algebra: the precedence of '*' is the same as the
	      precedence of '/', so that '1/2*3' will equal '3/2'.

       -r, --round
	      When  converting to a combination of units given by a unit list,
	      round the value of the last unit in the list to the nearest  in-
	      teger.

       -S, --show-factor
	      When  converting	to a combination of units specified in a list,
	      always show a non-unity factor before a unit that begins with  a
	      fraction with a unity denominator.  By default, if the unit in a
	      list begins with fraction of the form 1|x and its multiplier  is
	      an integer other than 1, the fraction is given as the product of
	      the multiplier and the numerator (e.g., '3|8 in' rather than  '3
	      *	 1|8 in').  In some cases, this is not what is wanted; for ex-
	      ample, the results for a cooking recipe might show '3 * 1|2 cup'
	      as '3|2 cup'.  With the '--show-factor' option, a result equiva-
	      lent to 1.5 cups will display  as	 '3  *	1|2 cup'  rather  than
	      '3|2 cup'.   A  user-specified  fractional unit with a numerator
	      other than 1 is never overridden, however--if a unit list speci-
	      fies  '3|4  cup;1|2 cup', a result equivalent to 1 1/2 cups will
	      always be shown as '2 * 3|4 cup' whether or not the '--show-fac-
	      tor' option is given.

       --conformable
	      In  non-interactive  mode,  show	all units conformable with the
	      original unit expression.	 Only one unit expression is  allowed;
	      if you give more than one, units will exit with an error message
	      and return failure.

       -v, --verbose
	      Give slightly more verbose output when converting	 units.	  When
	      combined	with  the  '-c'	 option	 this gives the same effect as
	      '--check-verbose'.  When combined with  '--version'  produces  a
	      more detailed output, equivalent to the '--info' option.

       -V, --version
	      Print  the program version number, tell whether the readline li-
	      brary has been included, tell whether UTF-8 support has been in-
	      cluded;  give the locale, the location of the default main units
	      data file, and the location of the personal units data file; in-
	      dicate if the personal units data file does not exist.

	      When given in combination with the '--terse' option, the program
	      prints only the version number and exits.

	      When given in combination with the '--verbose' option, the  pro-
	      gram, the '--version' option has the same effect as the '--info'
	      option below.

       -I, --info
	      Print the information given with the  '--version'	 option,  show
	      the  pathname  of	 the  units  program,  show  the status of the
	      UNITSFILE and MYUNITSFILE environment variables, and  additional
	      information  about how units locates the related files.  On sys-
	      tems running Microsoft Windows, the status  of  the  UNITSLOCALE
	      environment  variable  and  information about the related locale
	      map are also given.  This option is usually of interest only  to
	      developers  and  administrators,	but it can sometimes be useful
	      for troubleshooting.

	      Combining the '--version' and '--verbose' options has  the  same
	      effect as giving '--info'.

       -U, --unitsfile
	      Print the location of the default main units data file and exit;
	      if the file cannot be found, print "Units data file not found".

       -u units-system, --units units-system
	      Specify a CGS units system or natural units  system.   The  sup-
	      ported  units  systems  are: gauss[ian], esu, emu, hlu, natural,
	      natural-gauss, hartree, planck, planck-red, and si. See Alterna-
	      tive  Unit Systems for further information about these unit sys-
	      tems.

       -l locale, --locale locale
	      Force a specified locale such as 'en_GB' to get British  defini-
	      tions  by	 default.   This  overrides the locale determined from
	      system settings or environment variables. See Locale for	a  de-
	      scription of locale format.

       -n, --nolists
	      Disable conversion to unit lists.

       -s, --strict
	      Suppress conversion of units to their reciprocal units.  For ex-
	      ample, units will normally  convert  hertz  to  seconds  because
	      these  units  are	 reciprocals of each other.  The strict option
	      requires that units be strictly conformable to perform a conver-
	      sion,  and will give an error if you attempt to convert hertz to
	      seconds.

       -1, --one-line
	      Give only one line of output (the forward	 conversion);  do  not
	      print  the  reverse  conversion.	 If a reciprocal conversion is
	      performed, then units will still print the  "reciprocal  conver-
	      sion" line.

       -t, --terse
	      Print only a single conversion factor without any clutter, or if
	      you request a definition, prints just the definition  (including
	      its units).  This option can be used when calling units from an-
	      other program so that the output is easy to parse.  The  command
	      units  --terse  mile m produces the output '1690.344'.  This op-
	      tion has the  combined  effect  of  these	 options:   '--strict'
	      '--quiet'	 '--one-line' '--compact'.  When combined with '--ver-
	      sion' it produces a display showing only the  program  name  and
	      version number.

       --compact
	      Give  compact  output  featuring only the conversion factor; the
	      multiplication and division signs are not shown, and there is no
	      leading  whitespace.   If	 you  convert to a unit list, then the
	      output is a semicolon separated list of factors.	This turns off
	      the '--verbose' option.

       -q, --quiet, --silent
	      Suppress	the  display  of  statistics about the number of units
	      loaded, any messages printed by  the  units  database,  and  the
	      prompting	 of  the  user for units.  This option does not affect
	      how units displays the results.  This option is turned on by de-
	      fault  if you invoke units with a unit expression on the command
	      line.

SCRIPTING WITH UNITS
       Despite its numerous options,  units  cannot  cover  every  conceivable
       unit-conversion task.  For example, suppose we have found some mysteri-
       ous scale, but cannot figure out the units in which  it	is  reporting.
       We  reach into our pocket, place a 3.75-gram coin on the scale, and ob-
       serve the scale reading '0.120'.	  How  do  we  quickly	determine  the
       units?	Or  we	might wonder if a unit has any "synonyms," i.e., other
       units with the same value.

       The capabilities of units are easily extended  with  simple  scripting.
       Both  questions above involve conformable units; on a system with Unix-
       like utilities, conversions to conformable units could be shown	accom-
       plished with the following script:

       #!/bin/sh
       progname=`basename $0 .sh`
       umsg="Usage: $progname [<number>] unit"
       if [ $# -lt 1 ]
       then
	   echo "$progname: missing quantity to convert"
	   echo "$umsg"
	   exit 1
       fi
       for unit in `units --conformable "$*" | cut -f 1 -d ' '`
       do
	   echo "$*"   # have -- quantity to convert
	   echo $unit  # want -- conformable unit
       done | units --terse --verbose

       When  units is invoked with no non-option arguments, it reads have/want
       pairs, on alternating lines, from its standard input, so the  task  can
       be  accomplished	 with  only two invocations of units.  This avoids the
       computational overhead of needlessly reprocessing  the  units  database
       for  each  conformable unit, as well as the inherent system overhead of
       process invocation.

       By itself, the script is not very useful.  But it could be used in com-
       bination	 with  other commands to address specific tasks.  For example,
       running the script through a simple output filter could help solve  the
       scale problem above.  If the script is named conformable, running

       $ conformable 3.75g | grep 0.120

       gives

	       3.75g = 0.1205653 apounce
	       3.75g = 0.1205653 fineounce
	       3.75g = 0.1205653 ozt
	       3.75g = 0.1205653 tradewukiyeh
	       3.75g = 0.1205653 troyounce

       So we might conclude that the scale is calibrated in troy ounces.

       We might run

       $ units --verbose are
	       Definition: 100 m^2 = 100 m^2

       and wonder if 'are' has any synonyms, value.  To find out, we could run

       $ conformable are | grep "= 1 "
	       are = 1 a
	       are = 1 are

OUTPUT STYLES
       The  output  can be tweaked in various ways using command line options.
       With no options, the output looks like this

       $ units
       Currency exchange rates from FloatRates (USD base) on 2023-07-08
       3612 units, 109 prefixes, 122 nonlinear units
       You have: 23ft
       You want: m
	       * 7.0104
	       / 0.14264521
       You have: m
       You want: ft;in
	       3 ft + 3.3700787 in

       This is arguably a bit cryptic; the '--verbose' option makes clear what
       the output means:

       $ units --verbose
       Currency exchange rates from FloatRates (USD base) on 2023-07-08
       3612 units, 109 prefixes, 122 nonlinear units
       You have: 23 ft
       You want: m
	       23 ft = 7.0104 m
	       23 ft = (1 / 0.14264521) m
       You have: meter
       You want: ft;in
	       meter = 3 ft + 3.3700787 in

       The  '--quiet'  option  suppresses  the	clutter	 displayed  when units
       starts, as well as the prompts to the user.  This option is enabled  by
       default when you give units on the command line.

       $ units --quiet
       23 ft
       m
	       * 7.0104
	       / 0.14264521
       $ units 23ft m
	       * 7.0104
	       / 0.14264521

       The  remaining style options allow you to display only numerical values
       without the tab or the multiplication and division signs, or to display
       just a single line showing the forward conversion:

       $ units --compact 23ft m
       7.0104
       0.14264521
       $ units --compact m 'ft;in'
       3;3.3700787
       $ units --one-line 23ft m
	       * 7.0104
       $ units --one-line 23ft 1/m
	       reciprocal conversion
	       * 0.14264521
       $ units --one-line 23ft kg
       conformability error
	       7.0104 m
	       1 kg

       Note  that  when converting to a unit list, the '--compact' option dis-
       plays a semicolon separated list of results.  Also be  aware  that  the
       'one-line' option doesn't live up to its name if you execute a recipro-
       cal conversion or if you get a conformability error.  The  former  case
       can be prevented using the '--strict' option, which suppresses recipro-
       cal conversions.	 Similarly you can suppress unit list conversion using
       '--nolists'.  It is impossible to prevent the three line error output.

       $ units --compact --nolists m 'ft;in'
       Error in 'ft;in': Parse error
       $ units --one-line --strict 23ft 1/m

       The  various style options can be combined appropriately.  The ultimate
       combination  is	the  '--terse'	option,	 which	combines   '--strict',
       '--quiet', '--one-line', and '--compact' to produce the minimal output,
       just a single number for regular conversions and a semicolon  separated
       list for conversion to unit lists.  This will likely be the best choice
       for programs that want to call units and then process its result.

       $ units --terse 23ft m
       7.0104
       $ units --terse m 'ft;in'
       3;3.3700787
       $ units --terse 23ft 1/m
       conformability error
       7.0104 m
       1 / m
       $ units --terse '1 mile'
       1609.344 m
       $ units --terse mile
       5280 ft = 1609.344 m

ADDING YOUR OWN DEFINITIONS
   Units Data Files
       The units and prefixes that units can convert are defined in the	 units
       data  file,  typically  '/usr/share/units/definitions.units'.   If  you
       can't find this file, run units --version to  get  information  on  the
       file  locations for your installation.  Although you can extend or mod-
       ify this data file if you have appropriate user privileges,  it's  usu-
       ally better to put extensions in separate files so that the definitions
       will be preserved if you update units.

       You can include additional data files in the units database  using  the
       '!include' command in the standard units data file. For example

       !include	   /usr/local/share/units/local.units

       might be appropriate for a site-wide supplemental data file.  The loca-
       tion of the '!include' statement in the standard units data file is im-
       portant;	 later definitions replace earlier ones, so any definitions in
       an included file will override definitions before the '!include' state-
       ment in the standard units data file.  With normal invocation, no warn-
       ing is given about redefinitions; to ensure that you don't have an  un-
       intended	 redefinition,	run units -c after making changes to any units
       data file.

       If you want to add your own units in addition to or in place  of	 stan-
       dard  or	 site-wide supplemental units data files, you can include them
       in the '.units' file in your home directory.  If this file exists it is
       read  after  the	 standard  units data file, so that any definitions in
       this file will replace definitions of the same units  in	 the  standard
       data  file or in files included from the standard data file.  This file
       will not be read if any units files are specified on the command	 line.
       (Under Windows the personal units file is named 'unitdef.units'.)  Run-
       ning units -V will display the location and name of your personal units
       file.

       The units program first tries to determine your home directory from the
       HOME environment variable.  On systems running  Microsoft  Windows,  if
       HOME  does  not	exist, units attempts to find your home directory from
       HOMEDRIVE, HOMEPATH and USERPROFILE.  You can specify an arbitrary file
       as your personal units data file with the MYUNITSFILE environment vari-
       able; if this variable exists, its value is used without searching your
       home directory.	The default units data files are described in more de-
       tail in Data Files.

   Defining New Units and Prefixes
       A unit is specified on a single line by giving its name and an  equiva-
       lence.	Comments start with a '#' character, which can appear anywhere
       in a line.  The backslash character ('\') acts as a continuation	 char-
       acter if it appears as the last character on a line, making it possible
       to spread definitions out over several lines if desired.	 A file can be
       included	 by giving the command '!include' followed by the file's name.
       The '!' must be the first character on the  line.   The	file  will  be
       sought  in the same directory as the parent file unless you give a full
       path.  The name of the file to be included cannot contain spaces or the
       comment character '#'.

       Unit  names cannot begin or end with an underscore ('_'), a comma (',')
       or a decimal point ('.').  Names must not contain any of	 the  operator
       characters  '+', '-', '*', '/', '|', '^', ';', '~', the comment charac-
       ter '#', or parentheses.	 To facilitate copying and pasting from	 docu-
       ments, several typographical characters are converted to operators: the
       figure dash (U+2012), minus ('-'; U+2212), and en  dash	('-';  U+2013)
       are  converted  to  the	operator  '-';	the  multiplication sign ('x';
       U+00D7), N-ary times operator (U+2A09), dot operator ('.'; U+22C5), and
       middle  dot  ('.'; U+00B7) are converted to the operator '*'; the divi-
       sion sign ('/'; U+00F7) is converted to the operator '/'; and the frac-
       tion slash (U+2044) is converted to the operator '|'; accordingly, none
       of these characters can appear in unit names.

       Names cannot begin with a digit, and if a name ends in  a  digit	 other
       than zero or one, the digit must be preceded by a string beginning with
       an underscore,  and  afterwards	consisting  only  of  digits,  decimal
       points,	or commas.  For example, 'foo_2', 'foo_2,1', or 'foo_3.14' are
       valid names but 'foo2' or 'foo_a2' are invalid.	The underscore is nec-
       essary  because	without it, units cannot determine whether 'foo2' is a
       unit name or represents 'foo^2'.	 Zero and one are  exceptions  because
       units never interprets them as exponents.

       You could define nitrous oxide as

       N2O     nitrogen 2  + oxygen

       but would need to define nitrogen dioxide as

       NO_2    nitrogen + oxygen 2

       Be careful to define new units in terms of old ones so that a reduction
       leads to the primitive units, which are marked  with  '!'   characters.
       Dimensionless  units are indicated by using the string '!dimensionless'
       for the unit definition.

       When adding new units, be sure to use the '-c' option to check that the
       new  units  reduce  properly and that there are no circular definitions
       that lead to endless loops.  Because some errors may hide other errors,
       you  should  run	 units with the '-c' option again after correcting any
       errors, and keep doing so until no errors are displayed.

       If you define any units that contain '+' characters  in	their  defini-
       tions, carefully check them because the '-c' option will not catch non-
       conformable sums.  Be careful with the '-' operator as well.  When used
       as  a binary operator, the '-' character can perform addition or multi-
       plication depending on the options used to  invoke  units.   To	ensure
       consistent  behavior  use  '-'  only  as a unary negation operator when
       writing units definitions.  To multiply two units leave a space or  use
       the  '*'	 operator with care, recalling that it has two possible prece-
       dence values and may require parentheses to ensure consistent behavior.
       To compute the difference of 'foo' and 'bar' write 'foo+(-bar)' or even
       'foo+-bar'.

       You may wish to intentionally redefine a unit.  When you do  this,  and
       use the '-c' option, units displays a warning message about the redefi-
       nition.	You can suppress these warnings by redefining a unit  using  a
       '+'  at the beginning of the unit name.	Do not include any white space
       between the '+' and the redefined unit name.

       Here is an example of a short data file that defines some basic units:

       m       !	       # The meter is a primitive unit
       sec     !	       # The second is a primitive unit
       rad     !dimensionless  # A dimensionless primitive unit
       micro-  1e-6	       # Define a prefix
       minute  60 sec	       # A minute is 60 seconds
       hour    60 min	       # An hour is 60 minutes
       inch    72 m	       # Inch defined incorrectly terms of meters
       ft      12 inches       # The foot defined in terms of inches
       mile    5280 ft	       # And the mile
       +inch   0.0254 m	       # Correct redefinition, warning suppressed

       A unit that ends with a '-' character is a prefix.  If a prefix defini-
       tion  contains any '/' characters, be sure they are protected by paren-
       theses.	If you define 'half- 1/2', then 'halfmeter' would  be  equiva-
       lent to '1 / (2 meter)'.

   Defining Nonlinear Units
       Some  unit conversions of interest are nonlinear; for example, tempera-
       ture conversions between the Fahrenheit and Celsius  scales  cannot  be
       done by simply multiplying by conversion factors.

       When  you  give a linear unit definition such as 'inch 2.54 cm' you are
       providing information that units uses to convert values in inches  into
       primitive  units of meters.  For nonlinear units, you give a functional
       definition that provides the same information.

       Nonlinear units are represented using a	functional  notation.	It  is
       best  to	 regard	 this  notation not as a function call but as a way of
       adding units to a number, much the same way that writing a linear  unit
       name  after  a number adds units to that number.	 Internally, nonlinear
       units are defined by a pair of functions that convert to and from  lin-
       ear  units in the database, so that an eventual conversion to primitive
       units is possible.

       Here is an example nonlinear unit definition:

       tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
		   (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

       A nonlinear unit definition comprises a unit name, a  formal  parameter
       name, two functions, and optional specifications for units, the domain,
       and the range (the domain of the inverse function).  The functions tell
       units  how  to  convert to and from the new unit.  To produce valid re-
       sults, the arguments of these functions need to have the correct dimen-
       sions and be within the domains for which the functions are defined.

       The  definition begins with the unit name followed immediately (with no
       spaces) by a '(' character.  In the parentheses is the name of the for-
       mal parameter.  Next is an optional specification of the units required
       by the  functions  in  the  definition.	 In  the  example  above,  the
       'units=[1;K]'  specification  indicates	that  the 'tempF' function re-
       quires an input argument conformable with '1' (i.e.,  the  argument  is
       dimensionless),	and  that the inverse function requires an input argu-
       ment conformable with 'K'.  For normal nonlinear units definition,  the
       forward function will always take a dimensionless argument; in general,
       the inverse function will need units that match the  quantity  measured
       by  your nonlinear unit.	 Specifying the units enables units to perform
       error checking on function arguments, and also to assign units  to  do-
       main and range specifications, which are described later.

       Next  the  function  definitions	 appear.   In  the  example above, the
       'tempF' function is defined by

       tempF(x) = (x+(-32)) degF + stdtemp

       This gives a rule for converting 'x' in the  units  'tempF'  to	linear
       units  of absolute temperature, which makes it possible to convert from
       tempF to other units.

       To enable conversions to Fahrenheit, you must give a rule for  the  in-
       verse  conversions.   The inverse will be 'x(tempF)' and its definition
       appears after a ';' character.  In our example, the inverse is

       x(tempF) = (tempF+(-stdtemp))/degF + 32

       This inverse definition takes an absolute temperature as	 its  argument
       and  converts  it  to  the  Fahrenheit temperature.  The inverse can be
       omitted by leaving out the ';' character and  the  inverse  definition,
       but  then conversions to the unit will not be possible.	If the inverse
       definition is omitted, the '--check' option will display a warning.  It
       is up to you to calculate and enter the correct inverse function to ob-
       tain proper conversions; the '--check' option tests the inverse at  one
       point  and  prints an error if it is not valid there, but this is not a
       guarantee that your inverse is correct.

       With some definitions, the units may vary.  For example, the definition

       square(x)       x^2

       can have any arbitrary units, and can  also  take  dimensionless	 argu-
       ments.	In such a case, you should not specify units.  If a definition
       takes a root of its arguments, the definition is valid only  for	 units
       that yield such a root.	For example,

       squirt(x)       sqrt(x)

       is valid for a dimensionless argument, and for arguments with even pow-
       ers of units.

       Some definitions may not be valid for all real numbers.	In such cases,
       units can handle errors better if you specify an appropriate domain and
       range.  You specify the domain and range as shown below:

       baume(d) units=[1;g/cm^3] domain=[0,130.5] range=[1,10] \
		(145/(145-d)) g/cm^3 ; (baume+-g/cm^3) 145 / baume

       In this example the domain is specified after 'domain=' with  the  end-
       points  given  in  brackets.   In  accord with mathematical convention,
       square brackets indicate a closed interval (one that includes its  end-
       points),	 and  parentheses indicate an open interval (one that does not
       include its endpoints).	An interval can be open or closed  on  one  or
       both  ends; an interval that is unbounded on either end is indicated by
       omitting the limit on that end.	For example, a quantity to which deci-
       bel  (dB) is applied may have any value greater than zero, so the range
       is indicated by '(0,)':

       decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel)

       If the domain or range is given, the second endpoint  must  be  greater
       than the first.

       The domain and range specifications can appear independently and in any
       order along with the units specification.  The values  for  the	domain
       and range endpoints are attached to the units given in the units speci-
       fication, and if necessary, the parameter value is adjusted for compar-
       ison  with  the	endpoints.   For  example,  if	a  definition includes
       'units=[1;ft]' and 'range=[3,)', the range will be taken as 3 ft to in-
       finity.	 If the function is passed a parameter of '900 mm', that value
       will be adjusted to 2.9527559 ft, which is outside the specified range.
       If  you	omit  the units specification from the previous example, units
       can not tell whether you intend the lower endpoint to be 3 ft or	 3 mi-
       crofurlongs,  and can not adjust the parameter value of 900 mm for com-
       parison.	 Without units, numerical values other than zero  or  plus  or
       minus  infinity	for domain or range endpoints are meaningless, and ac-
       cordingly they are not allowed.	 If  you  give	other  values  without
       units,  then  the  definition will be ignored and you will get an error
       message.

       Although the units, domain, and range specifications are optional, it's
       best  to	 give  them when they are applicable; doing so allows units to
       perform better error checking and give  more  helpful  error  messages.
       Giving the domain and range also enables the '--check' option to find a
       point in the domain to use for its point check of your inverse  defini-
       tion.

       You can make synonyms for nonlinear units by providing both the forward
       and inverse functions; inverse functions can be obtained using the  '~'
       operator.  So to create a synonym for 'tempF' you could write

       fahrenheit(x) units=[1;K] tempF(x); ~tempF(fahrenheit)

       This  is	 useful	 for creating a nonlinear unit definition that differs
       slightly from an existing definition without having to repeat the orig-
       inal functions.	For example,

       dBW(x)	  units=[1;W] range=[0,) dB(x) W ;  ~dB(dBW/W)

       If  you	wish  a synonym to refer to an existing nonlinear unit without
       modification, you can do so more simply by adding the synonym with  ap-
       pended  parentheses  as	a new unit, with the existing nonlinear unit--
       without parentheses--as the definition.	So to  create  a  synonym  for
       'tempF' you could write

       fahrenheit()  tempF

       The definition must be a nonlinear unit; for example, the synonym

       fahrenheit()  meter

       will result in an error message when units starts.

       You  may occasionally wish to define a function that operates on units.
       This can be done using a nonlinear unit definition.  For	 example,  the
       definition  below  provides conversion between radius and the area of a
       circle.	This definition requires a length as  input  and  produces  an
       area as output, as indicated by the 'units=' specification.  Specifying
       the range as the nonnegative numbers can	 prevent  cryptic  error  mes-
       sages.

       circlearea(r) units=[m;m^2] range=[0,)	pi r^2 ; sqrt(circlearea/pi)

   Defining Piecewise Linear Units
       Sometimes you may be interested in a piecewise linear unit such as many
       wire gauges.  Piecewise linear units can be defined by specifying  con-
       versions	 to  linear  units  on	a list of points.  Conversion at other
       points will be done by linear interpolation.  A partial	definition  of
       zinc gauge is

       zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1

       In  this example, 'zincgauge' is the name of the piecewise linear unit.
       The definition of such a unit is indicated by the embedded '['  charac-
       ter.   After  the bracket, you should indicate the units to be attached
       to the numbers in the table.  No spaces can appear before the ']' char-
       acter,  so a definition like 'foo[kg meters]' is invalid; instead write
       'foo[kg*meters]'.  The definition of the unit consists  of  a  list  of
       pairs optionally separated by commas.  This list defines a function for
       converting from the piecewise linear unit to linear units.   The	 first
       item  in	 each  pair  is	 the function argument; the second item is the
       value of the function at that  argument	(in  the  units	 specified  in
       brackets).  In this example, we define 'zincgauge' at five points.  For
       example, we set 'zincgauge(1)' equal to '0.002 in'.   Definitions  like
       this  may  be  more readable  if written using  continuation characters
       as

       zincgauge[in] \
	    1 0.002  \
	   10 0.02   \
	   15 0.04   \
	   19 0.06   \
	   23 0.1

       With the preceding definition, the following  conversion	 can  be  per-
       formed:

       You have: zincgauge(10)
       You want: in
	   * 0.02
	   / 50
       You have: .01 inch
       You want: zincgauge
	   5

       If  you	define a piecewise linear unit that is not strictly monotonic,
       then the inverse will not be well defined.  If the inverse is requested
       for such a unit, units will return the smallest inverse.

       After  adding  nonlinear	 units	definitions,  you  should normally run
       'units --check' to check for errors.  If the  'units'  keyword  is  not
       given,  the '--check' option checks a nonlinear unit definition using a
       dimensionless argument, and then checks using an arbitrary  combination
       of units, as well as the square and cube of that combination; a warning
       is given if any of these tests fail.  For example,

       Warning: function 'squirt(x)' defined as 'sqrt(x)'
		failed for some test inputs:
		squirt(7(kg K)^1): Unit not a root
		squirt(7(kg K)^3): Unit not a root

       Running 'units --check' will print a warning if a non-monotonic	piece-
       wise linear unit is encountered.	 For example, the relationship between
       ANSI coated abrasive designation and mean particle  size	 is  non-mono-
       tonic in the vicinity of 800 grit:

       ansicoated[micron] \
	    . . .
	   600 10.55 \
	   800 11.5 \
	   1000 9.5 \

       Running 'units --check' would give the error message

       Table 'ansicoated' lacks unique inverse around entry 800

       Although	 the  inverse is not well defined in this region, it's not re-
       ally an error.  Viewing such error messages  can	 be  tedious,  and  if
       there  are  enough  of them, they can distract from true errors.	 Error
       checking for nonlinear unit definitions can be suppressed by giving the
       'noerror' keyword; for the examples above, this could be done as

       squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt^2
       ansicoated[micron] noerror \
	    . . .

       Use  the	 'noerror'  keyword  with  caution.  The safest approach after
       adding a nonlinear unit definition is to run 'units --check'  and  con-
       firm  that  there are no actual errors before adding the 'noerror' key-
       word.

   Defining Unit List Aliases
       Unit list aliases are treated differently from  unit  definitions,  be-
       cause they are a data entry shorthand rather than a true definition for
       a new unit.  A unit list alias definition begins with  '!unitlist'  and
       includes	 the  alias  and the definition;  for example, the aliases in-
       cluded in the standard units data file are

       !unitlist   hms	   hr;min;sec
       !unitlist   time	   year;day;hr;min;sec
       !unitlist   dms	   deg;arcmin;arcsec
       !unitlist   ftin	   ft;in;1|8 in
       !unitlist   usvol   cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
			   tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp

       Unit list aliases are only for unit lists, so the definition  must  in-
       clude  a	 ';'.	Unit  list aliases can never be combined with units or
       other unit list aliases, so the definition of 'time' shown above	 could
       not have been shortened to 'year;day;hms'.

       As  usual,  be  sure  to	 run  'units --check' to ensure that the units
       listed in unit list aliases are conformable.

NUMERIC OUTPUT FORMAT
       By default, units shows results to eight significant  digits.  You  can
       change this with the '--exponential', '--digits', and '--output-format'
       options.	 The first sets an exponential format (i.e., scientific	 nota-
       tion) like that used in the original Unix units program, the second al-
       lows you to specify a different number of significant digits,  and  the
       last  allows  you to control the output appearance using the format for
       the printf function in the C programming language.  If you only want to
       change  the  number of significant digits or specify exponential format
       type, use the '--digits' and '--exponential' options.   The  '--output-
       format'	option	affords the greatest control of the output appearance,
       but requires at least rudimentary knowledge of the printf  format  syn-
       tax. See Invoking Units for descriptions of these options.

   Format Specification
       The  format  specification recognized with the '--output-format' option
       is a subset of that for printf.	The format specification has the  form
       %[flags][width][.precision]type;	 it  must begin with '%', and must end
       with a floating-point type specifier: 'g' or 'G' to specify the	number
       of  significant digits, 'e' or 'E' for scientific notation, and 'f' for
       fixed-point decimal.  The ISO C99  standard  added  the	'F'  type  for
       fixed-point  decimal and the 'a' and 'A' types for hexadecimal floating
       point; these types are allowed with compilers that support them.	  Type
       length modifiers (e.g., 'L' to indicate a long double) are inapplicable
       and are not allowed.

       The default format for units is	'%.8g';	 for  greater  precision,  you
       could specify '-o %.15g'.  The 'g' and 'G' format types use exponential
       format whenever the exponent would  be  less  than  -4,	so  the	 value
       0.000013	 displays as '1.3e-005'.  These types also use exponential no-
       tation when the exponent is greater than or equal to the precision,  so
       with  the default format, the value 5 x 10^7 displays as '50000000' and
       the value 5 x 10^8 displays as '5e+008'.	  If  you  prefer  fixed-point
       display,	 you might specify '-o %.8f'; however, small numbers will dis-
       play very few significant digits, and values less than 5 x  10^-8  will
       show nothing but zeros.

       The  format  specification may include one or more optional flags: '+',
       ' ' (space), '#', '-', or '0' (the  digit  zero).   The	digit-grouping
       flag ''' is allowed with compilers that support it.  Flags are followed
       by an optional value for the minimum field width, and an optional  pre-
       cision specification that begins with a period (e.g., '.6').  The field
       width includes the digits, decimal point, the exponent, thousands sepa-
       rators (with the digit-grouping flag), and the sign if any of these are
       shown.

   Flags
       The '+' flag causes the output to have a sign ('+' or '-').  The	 space
       flag ' ' is similar to the '+' flag, except that when the value is pos-
       itive, it is prefixed with a space rather than a plus sign;  this  flag
       is ignored if the '+' flag is also given.  The '+' or ' ' flag could be
       useful if conversions might include positive and negative results,  and
       you  wanted  to	align the decimal points in exponential notation.  The
       '#' flag causes the output value to contain  a  decimal	point  in  all
       cases;  by  default,  the output contains a decimal point only if there
       are digits (which can be trailing zeros) to the	right  of  the	point.
       With  the  'g' or 'G' types, the '#' flag also prevents the suppression
       of trailing zeros.  The digit-grouping flag ''' shows a thousands sepa-
       rator  in  digits to the left of the decimal point.  This can be useful
       when displaying large numbers in fixed-point decimal; for example, with
       the format '%f',

       You have: mile
       You want: microfurlong
	       * 8000000.000000
	       / 0.000000

       the  magnitude of the first result may not be immediately obvious with-
       out counting the digits to the left of the decimal point.  If the thou-
       sands  separator	 is  the comma (','), the output with the format '%'f'
       might be

       You have: mile
       You want: microfurlong
	       * 8,000,000.000000
	       / 0.000000

       making the magnitude readily apparent.	Unfortunately,	few  compilers
       support the digit-grouping flag.

       With  the  '-' flag, the output value is left aligned within the speci-
       fied field width.  If a field width greater than	 needed	 to  show  the
       output  value is specified, the '0' (zero) flag causes the output value
       to be left padded  with	zeros  until  the  specified  field  width  is
       reached; for example, with the format '%011.6f',

       You have: troypound
       You want: grain
	       * 5760.000000
	       / 0000.000174

       The '0' flag has no effect if the '-' (left align) flag is given.

   Field Width
       By default, the output value is left aligned and shown with the minimum
       width necessary for the specified (or default) precision.  If  a	 field
       width greater than this is specified, the value shown is right aligned,
       and padded on the left with enough  spaces  to  provide	the  specified
       field  width.  A width specification is typically used with fixed-point
       decimal to have columns of numbers align at the decimal point; this ar-
       guably is less useful with units than with long columnar output, but it
       may nonetheless assist in quickly assessing the relative magnitudes  of
       results.	 For example, with the format '%12.6f',

       You have: km
       You want: in
	       * 39370.078740
	       /     0.000025
       You have: km
       You want: rod
	       *   198.838782
	       /     0.005029
       You have: km
       You want: furlong
	       *     4.970970
	       /     0.201168

   Precision
       The  meaning  of	 "precision"  depends on the format type.  With 'g' or
       'G', it specifies the number of significant digits (like the '--digits'
       option); with 'e', 'E', 'f', or 'F', it specifies the maximum number of
       digits to be shown after the decimal point.

       With the 'g' and 'G' format types, trailing zeros  are  suppressed,  so
       the  results  may sometimes have fewer digits than the specified preci-
       sion (as indicated above, the '#' flag causes trailing zeros to be dis-
       played).

       The  default precision is 6, so '%g' is equivalent to '%.6g', and would
       show the output to six significant digits.   Similarly,	'%e'  or  '%f'
       would show the output with six digits after the decimal point.

       The  C printf function allows a precision of arbitrary size, whether or
       not all of the digits are meaningful.  With most compilers, the maximum
       internal	 precision  with units is 15 decimal digits (or 13 hexadecimal
       digits).	 With the '--digits' option, you are limited  to  the  maximum
       internal	 precision; with the '--output-format' option, you may specify
       a precision greater than this, but it may not be meaningful.   In  some
       cases,  specifying  excess  precision can result in rounding artifacts.
       For example, a pound is	exactly	 7000  grains,	but  with  the	format
       '%.18g', the output might be

       You have: pound
       You want: grain
	       * 6999.9999999999991
	       / 0.00014285714285714287

       With the format '%.25g' you might get the following:

       You have: 1/3
       You want:
	       Definition: 0.333333333333333314829616256247

       In  this case the displayed value includes a series of digits that rep-
       resent the underlying binary floating-point approximation  to  1/3  but
       are not meaningful for the desired computation.	In general, the result
       with excess precision is system dependent.  The precision affects  only
       the  display  of numbers; if a result relies on physical constants that
       are not known to the specified  precision,  the	number	of  physically
       meaningful digits may be less than the number of digits shown.

       See  the documentation for printf for more detailed descriptions of the
       format specification.

       The '--output-format' option is incompatible with  the  '--exponential'
       or  '--digits'  options; if the former is given in combination with ei-
       ther of the latter, the format is controlled by the last option given.

LOCALIZATION
       Some units have different values in different locations.	 The localiza-
       tion feature accommodates this by allowing a units data file to specify
       definitions that depend on the user's locale.

   Locale
       A locale is a subset of a user's environment that indicates the	user's
       language	 and country, and some attendant preferences, such as the for-
       matting of dates.  The units program attempts to determine  the	locale
       from  the POSIX setlocale function; if this cannot be done, units exam-
       ines the environment variables LC_CTYPE and LANG.  On POSIX systems,  a
       locale is of the form language_country, where language is the two-char-
       acter code from ISO 639-1 and country is the  two-character  code  from
       ISO 3166-1; language is lower case and country is upper case. For exam-
       ple, the POSIX locale for the United Kingdom is en_GB.

       On systems running Microsoft Windows, the value returned	 by  setlocale
       is different from that on POSIX systems; units attempts to map the Win-
       dows value  to  a  POSIX	 value	by  means  of  a  table	 in  the  file
       'locale_map.txt'	 in  the  same directory as the other data files.  The
       file includes entries for many combinations of  language	 and  country,
       and   can   be	extended   to	include	  other	  combinations.	   The
       'locale_map.txt' file comprises two tab-separated columns;  each	 entry
       is of the form

	    Windows-locale   POSIX-locale

       where  POSIX-locale is as described above, and Windows-locale typically
       spells out both the language and country.  For example, the  entry  for
       the United States is

       English_United States   en_US

       You  can	 force	units to run in a desired locale by using the '-l' op-
       tion.

       In order to create unit definitions for a particular locale you begin a
       block  of  definitions  in a unit datafile with '!locale' followed by a
       locale name.  The '!' must be the first character  on  the  line.   The
       units  program  reads the following definitions only if the current lo-
       cale matches.  You end the block of localized units with	 '!endlocale'.
       Here is an example, which defines the British gallon.

       !locale en_GB
       gallon	    4.54609 liter
       !endlocale

   Additional Localization
       Sometimes  the  locale  isn't sufficient to determine unit preferences.
       There could be regional preferences, or a company could	have  specific
       preferences.   Though  probably	uncommon, such differences could arise
       with the choice of English customary units outside of  English-speaking
       countries.   To	address this, units allows specifying definitions that
       depend on environment variable settings.	 The environment variables can
       be  controlled based on the current locale, or the user can set them to
       force a particular group of definitions.

       A conditional block of definitions in a units data file begins with ei-
       ther  '!var' or '!varnot' following by an environment variable name and
       then a space separated list of values.  The leading '!' must appear  in
       the  first  column  of  a units data file, and the conditional block is
       terminated by '!endvar'.	 Definitions in blocks beginning  with	'!var'
       are  executed  only if the environment variable is exactly equal to one
       of the listed values.  Definitions in blocks beginning  with  '!varnot'
       are executed only if the environment variable does not equal any of the
       list values.

       The inch has long been a customary measure of length  in	 many  places.
       The word comes from the Latin uncia meaning "one twelfth," referring to
       its relationship with the foot.	By the 20th century, the inch was  of-
       ficially	 defined  in  English-speaking countries relative to the yard,
       but until 1959, the yard differed slightly among those  countries.   In
       France  the  customary  inch, which was displaced in 1799 by the meter,
       had a different length based on a french foot.  These customary defini-
       tions could be accommodated as follows:

       !var INCH_UNIT usa
       yard	     3600|3937 m
       !endvar
       !var INCH_UNIT canada
       yard	     0.9144 meter
       !endvar
       !var INCH_UNIT uk
       yard	     0.91439841 meter
       !endvar
       !var INCH_UNIT canada uk usa
       foot	     1|3 yard
       inch	     1|12 foot
       !endvar
       !var INCH_UNIT france
       foot	     144|443.296 m
       inch	     1|12 foot
       line	     1|12 inch
       !endvar
       !varnot INCH_UNIT usa uk france canada
       !message Unknown value for INCH_UNIT
       !endvar

       When  units  reads  the above definitions it will check the environment
       variable INCH_UNIT and load only the definitions	 for  the  appropriate
       section.	 If INCH_UNIT is unset or is not set to one of the four values
       listed, then units will run the last block.  In this  case  that	 block
       uses  the  '!message'  command  to display a warning message.  Alterna-
       tively that block could set default values.

       In order to create default values that are overridden by user  settings
       the  data  file	can  use the '!set' command, which sets an environment
       variable only if it is not already set;	these settings	are  only  for
       the  current  units  invocation	and do not persist.  So if the example
       above were preceded by '!set INCH_UNIT france', then  this  would  make
       'france'	 the  default  value  for  INCH_UNIT.  If the user had set the
       variable in the environment before invoking units, then units would use
       the user's value.

       To link these settings to the user's locale you combine the '!set' com-
       mand with the '!locale' command.	 If you wanted to  combine  the	 above
       example with suitable locales you could do by preceding the above defi-
       nition with the following:

       !locale en_US
       !set INCH_UNIT usa
       !endlocale
       !locale en_GB
       !set INCH_UNIT uk
       !endlocale
       !locale en_CA
       !set INCH_UNIT canada
       !endlocale
       !locale fr_FR
       !set INCH_UNIT france
       !endlocale
       !set INCH_UNIT france

       These definitions set the overall default for INCH_UNIT to 'france' and
       set default values for four locales appropriately.  The overall default
       setting comes last so that it only applies when INCH_UNIT was  not  set
       by one of the other commands or by the user.

       If  the	variable  given	 after	'!var' or '!varnot' is undefined, then
       units prints an error message and ignores the definitions that  follow.
       Use  '!set'  to create defaults to prevent this situation from arising.
       The '-c' option only checks the definitions that	 are  active  for  the
       current	environment  and  locale,  so when adding new definitions take
       care to check that all cases give rise to a well defined set of defini-
       tions.

ENVIRONMENT VARIABLES
       The units program uses the following environment variables:

       HOME   Specifies	 the  location	of  your home directory; it is used by
	      units to find a personal units data file '.units'.   On  systems
	      running  Microsoft  Windows, the file is 'unitdef.units', and if
	      HOME does not exist, units tries to determine your  home	direc-
	      tory  from  the HOMEDRIVE and HOMEPATH environment variables; if
	      these   variables	  do   not   exist,   units   finally	 tries
	      USERPROFILE--typically  'C:\Users\username'  (Windows  Vista and
	      Windows 7) or 'C:\Documents and Settings\username' (Windows XP).

       LC_CTYPE, LANG
	      Checked to determine the locale if units cannot obtain  it  from
	      the  operating  system.  Sections of the default main units data
	      file are specific to certain locales.

       MYUNITSFILE
	      Specifies your personal units data file.	If this	 variable  ex-
	      ists,  units  uses its value rather than searching your home di-
	      rectory for '.units'.  The  personal  units  file	 will  not  be
	      loaded if any data files are given using the '-f' option.

       PAGER  Specifies	 the pager to use for help and for displaying the con-
	      formable units.  The help function browses  the  units  database
	      and calls the pager using the '+n'n syntax for specifying a line
	      number.  The default pager is more; PAGER can be used to specify
	      alternatives such as less, pg, emacs, or vi.

       UNITS_ENGLISH
	      Set  to  either  'US' or 'GB' to choose United States or British
	      volume definitions, overriding the default from your locale.

       UNITSFILE
	      Specifies the units data file to use (instead of	the  default).
	      You  can	only specify a single units data file using this envi-
	      ronment variable.	 If units data files are given using the  '-f'
	      option,  the  file  specified by UNITSFILE will be not be loaded
	      unless the '-f'  option  is  given  with	the  empty  string  (-
	      'units -f ""').

       UNITSLOCALEMAP
	      Windows  only; this variable has no effect on Unix-like systems.
	      Specifies the units locale map file to use (instead of  the  de-
	      fault).	This  variable seldom needs to be set, but you can use
	      it to ensure that the locale map file will be found if you spec-
	      ify a location for the units data file using either the '-f' op-
	      tion or the UNITSFILE environment variable,  and	that  location
	      does not also contain the locale map file.

       UNITS_SYSTEM
	      This  environment variable is used in the default main data file
	      to select CGS measurement systems.  Currently supported  systems
	      are    'esu',    'emu',	 'gauss[ian]',	  'hlu',    'natural',
	      'natural-gauss', 'planck',  'planck-red',	 'hartree'  and	 'si'.
	      The default is 'si'.

DATA FILES
       The  units  program  uses  four default data files: the main data file,
       'definitions.units';   the   atomic    masses	of    the    elements,
       'elements.units'; currency exchange rates, 'currency.units', and the US
       Consumer Price Index, 'cpi.units'.  The last three files are loaded  by
       means  of  '!include' directives in the main file (see Database Command
       Syntax).	 The program can also use an optional personal units data file
       '.units' ('unitdef.units' under Windows) located in the user's home di-
       rectory.	 The personal units data file is described in more  detail  in
       Units Data Files.

       On   Unix-like  systems,	 the  data  files  are	typically  located  in
       '/usr/share/units' if units is provided with the operating  system,  or
       in  '/usr/local/share/units'  if units is compiled from the source dis-
       tribution.  Note that the currency file 'currency.units' is a  symbolic
       link to another location.

       On  systems running Microsoft Windows, the files may be in the same lo-
       cations if Unix-like commands are available, a Unix-like file structure
       is  present  (e.g.,  'C:/usr/local'),  and  units  is compiled from the
       source distribution.  If Unix-like commands are not available,  a  more
       common  location is 'C:\Program Files (x86)\GNU\units' (for 64-bit Win-
       dows installations) or 'C:\Program Files\GNU\units' (for 32-bit instal-
       lations).

       If    units    is    obtained	from	the    GNU    Win32    Project
       (http://gnuwin32.sourceforge.net/),   the   files   are	 commonly   in
       'C:\Program Files\GnuWin32\share\units'.

       If  the default main units data file is not an absolute pathname, units
       will look for the file in the directory that contains  the  units  pro-
       gram;  if  the  file is not found there, units will look in a directory
       ../share/units relative to the directory with the units program.

       You  can	  determine   the   location   of   the	  files	  by   running
       'units --version'.  Running 'units --info' will give you additional in-
       formation about the files, how units will attempt to find them, and the
       status of the related environment variables.

UNICODE SUPPORT
       The standard units data file is in Unicode, using UTF-8 encoding.  Most
       definitions use only ASCII characters (i.e., code points U+0000 through
       U+007F); definitions using non-ASCII characters appear in blocks begin-
       ning with '!utf8' and ending with '!endutf8'.

       The non-ASCII definitions are loaded only if the platform and  the  lo-
       cale  support UTF-8.  Platform support is determined when units is com-
       piled; the locale is checked at every invocation of units.  To  see  if
       your version of units includes Unicode support, invoke the program with
       the '--version' option.

       When Unicode support is available, units checks every line within UTF-8
       blocks in all of the units data files for invalid or non-printing UTF-8
       sequences; if such sequences occur, units ignores the entire line.   In
       addition	 to  checking  validity, units determines the display width of
       non-ASCII characters to ensure proper positioning  of  the  pointer  in
       some  error messages and to align columns for the 'search' and '?' com-
       mands.

       As of early 2019, Microsoft Windows provides limited support for	 UTF-8
       in  console  applications, and accordingly, units does not support Uni-
       code on Windows.	 The UTF-16 and UTF-32 encodings are not supported  on
       any platforms.

       If  Unicode support is available and definitions that contain non-ASCII
       UTF-8 characters are added to a	units  data  file,  those  definitions
       should  be  enclosed  within '!utf8' ... '!endutf8' to ensure that they
       are only loaded when Unicode support is available.  As usual,  the  '!'
       must  appear as the first character on the line.	 As discussed in Units
       Data Files, it's usually best to put such definitions  in  supplemental
       data  files linked by an '!include' command or in a personal units data
       file.

       When Unicode support is not available, units makes no assumptions about
       character encoding, except that characters in the range 00-7F hexadeci-
       mal correspond to ASCII encoding.  Non-ASCII characters are simply  se-
       quences of bytes, and have no special meanings; for definitions in sup-
       plementary units data files, you can use any encoding  consistent  with
       this  assumption.  For example, if you wish to use non-ASCII characters
       in definitions when running units under Windows, you can use a  charac-
       ter  set	 such  as Windows "ANSI" (code page 1252 in the US and Western
       Europe); if this is done, the console code page must be set to the same
       encoding	 for  the  characters  to  display properly.  You can even use
       UTF-8, though some messages may be improperly aligned, and  units  will
       not  detect  invalid  UTF-8  sequences.	If you use UTF-8 encoding when
       Unicode support is not available, you should place any definitions with
       non-ASCII  characters outside '!utf8' ... '!endutf8' blocks--otherwise,
       they will be ignored.

       Except for code examples, typeset material  usually  uses  the  Unicode
       symbols	for mathematical operators.  To facilitate copying and pasting
       from such sources, several typographical characters  are	 converted  to
       the  ASCII  operators  used  in	units: the figure dash (U+2012), minus
       ('-'; U+2212), and en dash ('-'; U+2013) are converted to the  operator
       '-';  the  multiplication  sign	('x';  U+00D7),	 N-ary	times operator
       (U+2A09), dot operator ('.'; U+22C5), and middle dot ('.'; U+00B7)  are
       converted  to the operator '*'; the division sign ('/'; U+00F7) is con-
       verted to the operator '/'; and the fraction  slash  (U+2044)  is  con-
       verted to the operator '|'.

READLINE SUPPORT
       If  the	readline package has been compiled in, then when units is used
       interactively, numerous command line editing  features  are  available.
       To check if your version of units includes readline, invoke the program
       with the '--version' option.

       For complete information about readline, consult the documentation  for
       the  readline  package.	 Without  any  configuration, units will allow
       editing in the style of emacs.  Of particular use with  units  are  the
       completion commands.

       If you type a few characters and then hit ESC followed by ?, then units
       will display a list of all the units that  start	 with  the  characters
       typed.	For example, if you type metr and then request completion, you
       will see something like this:

       You have: metr
       metre		 metriccup	   metrichorsepower  metrictenth
       metretes		 metricfifth	   metricounce	     metricton
       metriccarat	 metricgrain	   metricquart	     metricyarncount
       You have: metr

       If there is a unique way to complete a unit name, you can hit  the  TAB
       key  and units will provide the rest of the unit name.  If units beeps,
       it means that there is no unique completion.  Pressing the  TAB	key  a
       second time will print the list of all completions.

       The readline library also keeps a history of the values you enter.  You
       can move through this history using the up and down arrows.   The  his-
       tory  is	 saved	to the file '.units_history' in your home directory so
       that it will persist across multiple units invocations.	If you wish to
       keep  work  for	a  certain project separate you can change the history
       filename using the '--history' option.  You could, for example, make an
       alias  for  units to units --history .units_history so that units would
       save separate history in the current directory.	 The  length  of  each
       history	file is limited to 5000 lines.	Note also that if you run sev-
       eral concurrent copies of units each one will save its new  history  to
       the history file upon exit.

UPDATING CURRENCY EXCHANGE RATES AND CPI
   Currency Exchange Rates
       The units program database includes currency exchange rates and prices
       for some precious metals.  Of course, these values change over time,
       sometimes very rapidly, and units cannot provide real-time values.  To
       update the exchange rates, run units_cur, which rewrites the file con-
       taining the currency rates, typically '/var/lib/units/currency.units'
       or '/usr/local/com/units/currency.units' on a Unix-like system or
       'C:\Program Files (x86)\GNU\units\definitions.units' on a Windows sys-
       tem.

       This program requires Python 3 (https://www.python.org).	  The  program
       must  be	 run with suitable permissions to write the file.  To keep the
       rates updated automatically, run it using a cron	 job  on  a  Unix-like
       system, or a similar scheduling program on a different system.

       Reliable	 free  sources of currency exchange rates have been annoyingly
       ephemeral.  The program currently supports several sources:

	*  ExchangeRate-API.com (https://www.exchangerate-api.com).
	   The default currency server.	 Allows open  access  without  an  API
	   key,	 with unlimited API requests.  Rates update once a day, the US
	   dollar ('USD') is the default base currency,	 and  you  can	choose
	   your	 base  currency with the '-b' option described below.  You can
	   optionally sign up for an API key to access paid benefits  such  as
	   faster data update rates.

	*  FloatRates (https://www/floatrates.com).
	   The US dollar ('USD') is the default base currency.	You can change
	   the base currency with the '-b' option described below.   Allowable
	   base	 currencies  are  listed  on the FloatRates website.  Exchange
	   rates update daily.

	*  The European Central Bank (https://www.ecb.europa.eu).
	   The base currency is always the euro ('EUR').  Exchange  rates  up-
	   date	 daily.	  This source offers a more limited list of currencies
	   than the others.

	*  Fixer (https://fixer.io).
	   Registration for a free API key is required.	 With a free API  key,
	   base	 currency  is the euro; exchange rates are updated hourly, the
	   service has a limit of 1,000 API calls per month, and  SSL  encryp-
	   tion (https protocol) is not available.  Most of these restrictions
	   are eliminated or reduced with paid plans.

	*  open exchange rates (https://openexchangerates.org).
	   Registration for a free API key is required.	 With a free API  key,
	   the	base  currency	is  the	 US dollar; exchange rates are updated
	   hourly, and there is a limit of 1,000 API calls per month.  Most of
	   these restrictions are eliminated or reduced with paid plans.

       The  default source is FloatRates; you can select a different one using
       '-s' option described below.

       Precious	 metals	 pricing  is  obtained	from  Packetizer   (www.packe-
       tizer.com).  This site updates once per day.

   US Consumer Price Index
       The  units program includes the US Consumer Price Index (CPI) published
       by the US Bureau of Labor Statistics: specifically, the Consumer	 Price
       Index   for  All	 Urban	Consumers  (CPI-U),  Series  CUUR0000SA0.  The
       units_cur command updates the CPI and saves the result  in  'cpi.units'
       in  the	same  location as 'currency.units'.  The data are obtained via
       the BLS Public Data API (https://www.bls.gov/developers/).   This  data
       updates	once a month.  When units_cur runs it will only attempt to up-
       date the CPI data if the current CPI  data  file	 is  from  a  previous
       month, or if the current date is after the 18th of the month.

   Invoking units_cur
       You invoke units_cur like this:

       units_cur [options] [currency_file] [cpi_file]

       By default, the output is written to the default currency and CPI files
       described above; this is usually what you want, because this  is	 where
       units  looks  for  the  files.	If you wish, you can specify different
       filenames on the command line and units_cur  will  write	 the  data  to
       those files.  If you give '-' for a file it will write to standard out-
       put.

       The following options are available:

       -h, --help
	      Print a summary of the options for units_cur.

       -V, --version
	      Print the units_cur version number.

       -v, --verbose
	      Give slightly more verbose output when attempting to update cur-
	      rency exchange rates.

       -s source, --source source
	      Specify  the  source for currency exchange rates; currently sup-
	      ported values are 'floatrates' (for FloatRates),	'eubank'  (for
	      the   European   Central	 Bank),	  'fixer'   (for  Fixer),  and
	      'openexchangerates' (for open exchange rates); the last two  re-
	      quire an API key to be given with the '-k' option.

       -b base, --base base
	      Set  the	base  currency (when allowed by the site providing the
	      data).  base should be  a	 3-letter  ISO	currency  code,	 e.g.,
	      'USD'.   The  specified  currency will be the primitive currency
	      unit used by units.  You may find it convenient to specify  your
	      local  currency.	 Conversions may be more accurate and you will
	      be able to convert to your currency by simply hitting  Enter  at
	      the  'You want:'	prompt.	  This option is ignored if the source
	      does not allow specifying the base  currency.   (Currently  only
	      floatrates supports this option.)

       -k key, --key key
	      Set the API key to key for currency sources that require it.

       --blskey BLSkey
	      Set the US Bureau of Labor Statistics (BLS) key for fetching CPI
	      data.  Without a BLS key you should be able  to  fetch  the  CPI
	      data  exactly  one  time	per day.  If you want to use a key you
	      must request a personal key from BLS.

DATABASE COMMAND SYNTAX
       unit definition
	      Define a regular unit.

       prefix- definition
	      Define a prefix.

       funcname(var)   noerror	  units=[in-units,out-units]	domain=[x1,x2]
       range=[y1,y2] definition(var) ; inverse(funcname)
	      Define  a	 nonlinear  unit  or unit function.  The four optional
	      keywords noerror, 'units=', 'range=' and 'domain=' can appear in
	      any order.  The definition of the inverse is optional.

       tabname[out-units] noerror pair-list
	      Define  a piecewise linear unit.	The pair list gives the points
	      on the table listed in ascending order.  The noerror keyword  is
	      optional.

       !endlocale
	      End a block of definitions beginning with '!locale'

       !endutf8
	      End a block of definitions begun with '!utf8'

       !endvar
	      End a block of definitions begun with '!var' or '!varnot'

       !include file
	      Include the specified file.

       !locale value
	      Load  the	 following  definitions	 only  of the locale is set to
	      value.

       !message text
	      Display text when the database is read unless the	 quiet	option
	      ('-q')  is enabled.  If you omit text, then units will display a
	      blank line.  Messages will also appear in the log file.

       !prompt text
	      Prefix the 'You have:' prompt with the specified text.   If  you
	      omit text, then any existing prefix is canceled.

       !set variable value
	      Sets  the environment variable, variable, to the specified value
	      only if it is not already set.

       !unitlist alias definition
	      Define a unit list alias.

       !utf8  Load the following definitions only if  units  is	 running  with
	      UTF-8 enabled.

       !var envar value-list
	      Load  the block of definitions that follows only if the environ-
	      ment variable envar is set to one of the values  listed  in  the
	      space-separated  value  list.  If envar is not set, units prints
	      an error message and ignores the block of definitions.

       !varnot envar value-list
	      Load the block of definitions that follows only if the  environ-
	      ment  variable  envar  is set to value that is not listed in the
	      space-separated value list.  If envar is not set,	 units	prints
	      an error message and ignores the block of definitions.

FILES
       /usr/local/share/units/definitions.units	 --  the  standard  units data
       file

AUTHOR
       units was written by Adrian Mariano



			       16 February 2024			      UNITS(1)
