UNITS(1)		    General Commands Manual		      UNITS(1)



NAME
       units -- unit conversion and calculation program

SYNOPSIS
       'units' [options] [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.

       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-pur-
       pose  scientific  calculator  that keeps track of units in its calcula-
       tions.  You can form  arbitrary	complex  mathematical  expressions  of
       dimensions  including sums, products, quotients, powers, and even roots
       of dimensions.  Thus you can ensure accuracy  and  dimensional  consis-
       tency  when  working  with long expressions that involve many different
       units that may combine in complex ways; for an illustration,  see  Com-
       plicated Unit Expressions.

       The units are defined in an external data file.	You can use the exten-
       sive data file that comes with this 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 file.

       You can change the default behavior of  'units'	with  various  options
       given  on the command line. See Invoking Units for a description of the
       available 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 www.timegenie.com on 2014-03-05
	  2860 units, 109 prefixes, 85 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 complete unit names. See Readline  Support	for  more  information
       about  'readline'.  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
       dimensions,  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 combina-
       tion of watts, meters, and hertz.  The fully reduced (and in this  case
       somewhat more cryptic) form appears on the far right.

       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  con-
       formable  with  the  unit  that	you  entered at the 'You have:' prompt
       above.  Conformable 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.	(You can generally  quit  out  of  the
       page 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 expres-
       sion contains non-alphanumeric characters, you may need to  protect  it
       from  interpretation  by the shell using single or double quote charac-
       ters.

       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.

       If  the	conversion  is	successful,  then  '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.

       When you invoke 'units' with only one argument, it will print  out  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	a  units  data	file  that  is
       called	 'definitions.units'   and   is   usually   located   in   the
       '/usr/share/units' directory.  If you  invoke  'units'  with  the  '-V'
       option,	it  will  print  the  location of this file.  The default file
       includes definitions for all familiar units, abbreviations  and	metric
       prefixes.  It also includes many obscure or archaic units.  Many common
       spelled-out numbers (e.g., 'seventeen') are recognized.

       Many constants of nature are defined, including these:

	  pi	      ratio of circumference to 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 atomic masses for all of  the  elements
       and numerous other constants.  Also included are the densities of vari-
       ous ingredients used in baking so that  '2 cups	flour_sifted'  can  be
       converted  to  'grams'.	 This  is not an exhaustive list.  Consult the
       units data file to see the complete list, or  to  see  the  definitions
       that are used.

       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
       exactly 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  standard
       units data file, which is extensively annotated.

   English Customary Units
       English	customary  units  differ in various ways in 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 definitions
       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, and link) in terms of the previous value for the
       foot, which was termed the US survey foot.  The US defined 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 differ from the international val-
       ues by about 2 ppm.

       The  'units' program uses the international values for these units; the
       US values can be obtained by using either the 'US' or the 'survey' pre-
       fix.  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'.

       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  pre-1959 UK values for these units can be obtained with the prefix
       'UK'.

       In the US, the acre is officially defined in terms  of  the  US	survey
       foot,  but  'units'  uses a definition based on the international foot.
       If you want the	official  US  acre  use  'USacre'  and	similarly  use
       'USacrefoot'  for the official US version of that unit.	The difference
       between these units is about 4 parts per million.

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	multi-
       plication  using a space, and a high priority numerical division opera-
       tor ('|') 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,
       hyphenated  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
       using  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
       denominator: 'J / mol K'.  The '*' and  '/'  operators  have  the  same
       precedence,  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
       exponent:  'cm3'  is equivalent to 'cm^3'; if the exponent is more than
       one digit, the '^' is required.	You can also use '**' as  an  exponent
       operator.

	  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
       includes  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
       cubic  centimeter.   The 'units' program is limited internally to prod-
       ucts  of  99  units;  accordingly,  expressions	like  'meter^100'   or
       'joule^34' (represented 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  deci-
       mal  exponent to a rational number with q < 100.  If this is not possi-
       ble '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
						^
	  Illegal sum of non-conformable units

       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 necessary 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 mes-
       sage:

	  You have: 2+1|2 cups
			     ^
	  Illegal 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
       resolved 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
       example,  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',  'ln',
       'log',  'exp', 'acos', 'atan', 'asin', 'cosh', 'sinh', 'tanh', 'acosh',
       'asinh', and 'atanh'.  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
       angle.

       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-
       diameter 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
       example could have used '2_'.  If '_' follows a non-numerical unit sym-
       bol, however, the space is required:

	  You have: m_
		     ^
	  Parse error

       When '_' is followed by a digit, the operation is multiplication rather
       than exponentiation, so that '_2', is equivalent to '_ * 2' rather than
       '_^2'.

       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
       after 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
       dimensional consistency when converting lengthy unit expressions.   For
       example, 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.  It might be desired
       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

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

       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 subtraction 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 oper-
       ator  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
       degrees	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
       absolute 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
			      ^

   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
       requires 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
       conversion 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
       result 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
       repeating  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
       coefficient for the last unit.  If you instead prefer to round the last
       coefficient 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
       effect 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
       appearing  on  the list.  In the second case, 'units' reports disagree-
       ment between the unit you entered and  the  desired  conversion.   This
       conformability 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

       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
       result equivalent to 1 1/2 cups will always be shown as '2  *  3|4 cup'
       whether or not the '--show-factor' option is given.

       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.

       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	      hours, minutes, seconds
	  dms	      angle: degrees, minutes, seconds
	  time	      years, days, hours, minutes and seconds
	  usvol       US cooking volume: cups and smaller

       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  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

USING 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  three  different systems of CGS units: electrostatic
       units (ESU), electromagnetic units (EMU), and the Gaussian 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  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.

   Specifying CGS Units
       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 sys-
       tem and works around this restriction by introducing base units for the
       square  roots of length and mass: 'sqrt_cm' and 'sqrt_g'.  The centime-
       ter 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 arguments to the
       '--units' option are 'gauss[ian]', 'esu', 'emu', and 'si'; the argument
       is case insensitive.  The default mode for 'units'  is  SI  units;  the
       only  effect  of  giving  'si'  with the '--units' option is to prepend
       '(SI)' to the 'You have:' prompt.  Giving an unrecognized system gener-
       ates 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 environ-
       ment variable rather than giving the '--units' option at  each  invoca-
       tion.  As usual, an option given on the command line overrides the set-
       ting 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.

   CGS Units Systems
       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.

   Conversions Between Different Systems
       The CGS systems define units that measure the same thing but  may  have
       conflicting   dimensions.    Furthermore,   the	 dimensions   of   the
       electromagnetic 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 correspond-
       ing 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
       dimensions.  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
       various 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	dimen-
       sional  analysis  in CGS.  You can convert them to or from CGS in order
       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

   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)
					     ^
	  Illegal 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
       invoked, the new results are appended to the log  file.	 The  time  is
       written	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.  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
       options	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
       beginning 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
       option 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  intermixed 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 con-
       trolled by the last option  given.   For  example,  '-o%.12f -e'  gives
       exponential format with the default eight significant digits).

       The following options are available:

       -c, --check
	      Check that all units and prefixes defined in the units data file
	      reduce to primitive units.  Print a list of all units that  can-
	      not  be reduced.	Also display some other diagnostics about sus-
	      picious definitions in the units data  file.   Only  definitions
	      active in the current locale are checked.  You should always run
	      'units' with this option after modifying a units data file.

       --check-verbose, --verbose-check
	      Like the '--check' option, this option prints a  list  of  units
	      that cannot be reduced.  But to help find unit  definitions that
	      cause endless loops, it lists the units as they are checked.  If
	      'units'  hangs, then the last unit to be printed has a bad defi-
	      nition.  Only definitions  active  in  the  current  locale  are
	      checked.

       -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
	      decimal  point  and  eleven  digits  to the right of the decimal
	      point.  On most systems, the maximum number of internally  mean-
	      ingful  digits  is 15; if you specify a greater number than your
	      system's maximum, 'units' will print a warning and set the  num-
	      ber  to the largest meaningful value.  To directly set the maxi-
	      mum 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 precision, the physically meaningful precision may
	      be less than that shown.	The '--digits' option  conflicts  with
	      the '--output-format' option.

       -e, --exponential
	      Set  the	numeric output format to exponential (i.e., scientific
	      notation), like that used in  the  Unix  'units'	program.   The
	      default  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
	      programming  language.   All  compilers support the format types
	      'g' and 'G' to specify significant digits, 'e' and 'E' for  sci-
	      entific  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 specifi-
	      cation.  The '--output-format' option affords the greatest  con-
	      trol 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 pre-
	      cision more simply with the '--digits' option or select exponen-
	      tial  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 spec-
	      ify up to 25 units files on the command line.  When you use this
	      option, '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 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  filename 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'.

       --compact
	      Give  compact output featuring only the conversion factor.  This
	      turns off the '--verbose' option.

       -q, --quiet, --silent
	      Suppress prompting of the user for units and the display of sta-
	      tistics about the number of units loaded.

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

       -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
	      integer.

       -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
	      example, the results for	a  cooking  recipe  might  show  '3  *
	      1|2 cup'	as  '3|2 cup'.	 With  the  '--show-factor'  option, a
	      result equivalent 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  specifies  '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-factor' option is given.

       -s, --strict
	      Suppress	conversion  of	units  to their reciprocal units.  For
	      example, '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
	      Give  terse  output  when  converting units.  This option can be
	      used when calling 'units' from another program so that the  out-
	      put  is  easy  to parse.	This option has the combined effect of
	      these options: '--strict'  '--quiet'  '--one-line'  '--compact'.
	      When  combined  with  '--version'  it produces a display showing
	      only the program name and version number.

       -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'
	      library has been included, tell whether UTF-8 support  has  been
	      included;  give  the  locale,  the location of the default units
	      data file, and the location of the  personal  units  data  file;
	      indicate 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 program, 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 addi-
	      tional information about how 'units' locates the related	files.
	      On   systems  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 some-
	      times 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 units data file and  exit;  if
	      the file cannot be found, print ``Units data file not found''.

       -u (gauss[ian]|esu|emu), --units (gauss[ian]|esu|emu)
	      Specify a CGS units system: Gaussian, ESU, or EMU.

       -l locale, --locale locale
	      Print  the  information  given with the '--version' option, show
	      the Force a specified locale such as 'en_GB' to get British def-
	      initions	by default.  This overrides the locale determined from
	      system settings or environment  variables.   See	Locale	for  a
	      description of locale format.

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
       modify  this  data  file  if you have appropriate user privileges, it's
       usually better to put extensions in separate files so that the  defini-
       tions 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
       important; later definitions replace earlier ones, so  any  definitions
       in  an  included  file  will override definitions before the '!include'
       statement in the standard units data file.  With normal invocation,  no
       warning	is given about redefinitions; to ensure that you don't have an
       unintended 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  variable; if this variable exists, its value is used with-
       out searching your home directory.  The default units  data  files  are
       described in more detail 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 must not contain any of the operator	characters  '+',  '-',
       '*',  '/',  '|', '^', ';', '~', the comment character '#', or parenthe-
       ses.  They cannot begin or end with an underscore ('_'), a comma  (',')
       or  a  decimal  point  ('.').   The figure dash (U+2012), typographical
       minus (`-'; U+2212), and en dash (`-'; U+2013)  are  converted  to  the
       operator  '-',  so  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,  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.   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.  If you create a loop in the units defini-
       tions, then 'units' will hang when invoked with the '-c'  option.   You
       will  need  to  use the '--check-verbose' option, which prints out each
       unit as it is checked.  The program will still hang, but the last  unit
       printed will be the unit that caused the infinite loop.

       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
       redefinition.   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 equivalent
       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  func-
       tional 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
       results,  the  arguments  of  these  functions need to have the correct
       dimensions 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
       requires 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 per-
       form error checking on function arguments, and also to assign units  to
       domain 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
       inverse 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
       obtain 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
       infinity.   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 microfurlongs,  and  can not adjust the parameter value of 900 mm
       for comparison.	Without units, numerical values  other	than  zero  or
       plus  or  minus infinity for domain or range endpoints are meaningless,
       and accordingly 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
       appended  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
       really 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,
       because	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
       included 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
       include	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
       allows 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 syntax. 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
       notation  when  the exponent is greater than or equal to the precision,
       so with the default format, the value 5e7 displays  as  '50000000'  and
       the value 5e8 displays as '5e+008'.  If you prefer fixed-point display,
       you might specify '-o %.8f'; however, small numbers will  display  very
       few  significant  digits, and values less than 0.5e-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
       specified  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
       arguably is less useful with 'units' than with  long  columnar  output,
       but  it may nonetheless assist in quickly assessing the relative magni-
       tudes 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 max-
       imum internal precision with 'units' is 15 decimal digits (or 13  hexa-
       decimal	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 arti-
       facts.	For example, a pound is exactly 7000 grains, but with the for-
       mat '%.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
       either  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'
       examines the environment variables 'LC_CTYPE'  and  'LANG'.   On  POSIX
       systems,  a locale is of the form language'_'country, where language is
       the two-character 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 example, 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
       Windows 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'
       option.

       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
       locale  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  controled  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
       either  '!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
       officially  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 val-
       ues listed then 'units' will run the last block.   In  this  case  that
       block uses the '!message' command to display a warning message.	Alter-
       natively 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  fol-
       low.   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
       definitions.

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
	      directory  from the 'HOMEDRIVE' and 'HOMEPATH' environment vari-
	      ables; 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 standard units data file
	      are specific to certain locales.

       MYUNITSFILE
	      Specifies your personal  units  data  file.   If	this  variable
	      exists,  'units'	uses its value rather than searching your home
	      directory 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
	      default).  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'
	      option or the 'UNITSFILE' environment variable, and  that  loca-
	      tion does not also contain the locale map file.

       UNITS_SYSTEM
	      This  environment  variable is used in the standard data file to
	      select CGS measurement systems.  Currently supported systems are
	      'esu', 'emu', 'gauss[ian]', and 'si'.  The default is 'si'.

DATA FILES
       The  'units'  program  uses two default data files: 'definitions.units'
       and 'currency.units'.  The program can also use	an  optional  personal
       units data file '.units' ('unitdef.units' under Windows) located in the
       user's home directory.  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
       locations if Unix-like commands are available, a Unix-like file	struc-
       ture  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
       Windows	installations)	or  'C:\Program Files\GNU\units'  (for	32-bit
       installations).

       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  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
       information 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'.

       When 'units' starts, it checks the locale to  determine	the  character
       set.  If 'units' is compiled with Unicode support and definitions; oth-
       erwise these definitions are ignored.  When Unicode support is  active,
       'units'	will  check  every  line  of  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 '?'  commands.

       At present, 'units' does not support Unicode under  Microsoft  Windows.
       The UTF-16 and UTF-32 encodings are not supported on any systems.

       If  definitions	that contain non-ASCII 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 active, '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
       sequences of bytes, and have no special meanings;  for  definitions  in
       supplementary  units  data  files,  you can use any encoding consistent
       with this assumption.  For example, if you wish to use non-ASCII  char-
       acters in definitions when running 'units' under Windows, you can use a
       character set such as Windows ``ANSI'' (code page 1252 in  the  US  and
       Western	Europe).   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
       active, you should place any definitions with non-ASCII characters out-
       side '!utf8' ...  '!endutf8' blocks--otherwise, they will be ignored.

       Typeset	material  other  than  code  examples usually uses the Unicode
       minus (U+2212) rather than the  ASCII  hyphen-minus  operator  (U+002D)
       used in 'units'; the figure dash (U+2012) and en dash (U+2013) are also
       occasionally used.  To allow such material to be copied and pasted  for
       interactive  use or in units data files, 'units' converts these charac-
       ters to U+002D before further processing.  Because  of  this,  none  of
       these characters can appear in unit names.

READLINE SUPPORT
       If  the	'readline'  package has been compiled in, then when 'units' is
       used interactively, numerous command line editing features  are	avail-
       able.   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  char-
       acters typed.  For example, if you type 'metr' and then request comple-
       tion, 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
       several concurrent copies of 'units' each one will save its new history
       to the history file upon exit.

UPDATING 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
       containing 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 system.

       This program requires Python (https://www.python.org); either version 2
       or  3  will work.  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:

	*  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 update daily.
	   This source offers a more limited list of currencies than the  oth-
	   ers.

	*  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 encryption (https protocol) is not	avail-
	   able.   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 cur-
	   rency 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.

       You invoke 'units_cur' like this:

	  units_cur [options] [outfile]

       By default,  the  output  is  written  to  the  default	currency  file
       described  above;  this is usually what you want, because this is where
       'units' looks for the file.  If you wish, you can specify  a  different
       filename  on  the  command  line and 'units_cur' will write the data to
       that file.  If you give '-' for the 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
	      require 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 sources that require it.

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.

GNU FREE DOCUMENTATION LICENSE
FILES
       /usr/local/share/units/definitions.units  --  the  standard  units data
       file

AUTHOR
				20 October 2018 		      UNITS(1)
