units - Online in the Cloud

PROGRAM:

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 program interactively with prompts, or you
can use it from the command line.

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

The units are defined in an external data file. You can use the extensive 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 under Unix, press Ctrl-C or Ctrl-D. Under Windows, press Ctrl-C or Ctrl-Z; with
the latter, you may also need to press Enter.

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 number 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 obvious 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 display 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, simply press Enter at
the 'You want:' prompt. Here is an example:

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

The output from 'units' indicates that the jansky is defined to be equal to a fluxunit
which in turn is defined to be a certain combination of watts, meters, and hertz. The
fully reduced (and in this case somewhat more cryptic) form appears on the far right.

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

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

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

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

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

If you want a list of options you can type '?' at the 'You want:' prompt. The program
will display a list of named units that are conformable with the unit that you entered at
the 'You have:' prompt above. 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 historical 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 expression contains non-alphanumeric characters, you may need to
protect it from interpretation by the shell using single or double quote characters.

If you type

units "2 liters" quarts

then 'units' will print

* 2.1133764
/ 0.47317647

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

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 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 various 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 Imperial 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 values 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 International 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 values
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' prefix. In either case, the simple
familiar relationships among the units are maintained, e.g., 1 'furlong' = 660 'ft', and 1
'USfurlong' = 660 'USft', though the metric equivalents differ slightly between the two
cases. The 'US' prefix or the 'survey' prefix can also be used to obtain the US survey
mile and the value of the US yard prior to 1959, e.g., 'USmile' or 'surveymile' (but not
'USsurveymile'). To get the US value of the statute mile, use either 'USstatutemile' or
'USmile'.

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. Additionally, 'units' supports some extensions, including high priority
multiplication using a space, and a high priority numerical division operator ('|') that
can simplify some expressions.

You multiply units using a space or an asterisk ('*'). The next example 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

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 advantageous. 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 products 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 second 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 meaningful (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
parentheses are needed because the precedence of '^' is higher than that of '/'. Since
'units' cannot represent dimensions with exponents greater than 99, a fully reduced
exponent must have q < 100. When raising a non-dimensionless unit to a power, 'units'
attempts to convert a decimal exponent to a rational number with q < 100. If this is not
possible 'units' displays an error message:

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

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

Sums and Differences of Units
You may sometimes want to add values of different units that are outside 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 message:

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 conversion 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', 'log2', 'exp',
'acos', 'atan' and 'asin'. 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.

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 underscore ('_'). 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 symbol, 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-interactively.

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 precedence, and can be confusing for people who think of units as a
calculator.

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

Historically, the hyphen ('-') has been used in technical publications to indicate
products of units, and the original 'units' program treated it as a multiplication
operator. Because 'units' provides several other ways to obtain unit products, and
because '-' is a subtraction operator in general algebraic expressions, 'units' treats the
binary '-' as a 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 operator it has the same precedence as
multiplication with a space, giving it a higher precedence than division.

When '-' is used as a unary operator it negates its operand. Regardless 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 conversions 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 Nonlinear 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 converting to a temperature rather than
converting a temperature increment.

The 'tempC()' and 'tempF()' definitions are limited to positive absolute 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 circle 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 circleinch. The next example shows two ways to compute
the area of a circle 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 parentheses, 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 numbers, 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
values. Nonlinear unit conversions are described in more detail in Defining 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 typically 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 (';') character:

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 conformable 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 disagreement 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 calculations, 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

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, including 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 interactive prompts to
determine which conversions to perform. See Interactive 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 controlled 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 cannot be reduced. Also display
some other diagnostics about suspicious definitions in the units data file. Only
definitions active in the current locale are checked. You should always run
'units' with this 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 definition. 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 exponential 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 meaningful digits is 15; if you specify a
greater number than your system's maximum, 'units' will print a warning and set the
number to the largest meaningful value. To directly set the maximum value, give an
argument of 'max' (e.g., '-d max'). Be aware, of course, that ``significant'' here
refers only to the display of numbers; if results depend on physical constants not
known to this 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 floating 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 scientific
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
format 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 specification. The '--output-format' option affords the greatest
control of the output appearance, but requires at least rudimentary knowledge of
the 'printf()' format syntax. If you don't want to bother with the 'printf()'
syntax, you can specify greater precision more simply with the '--digits' option or
select exponential format with '--exponential'. The '--output-format' option is
incompatible with the '--exponential' and '--digits' options.

-f filename, --file filename
Instruct 'units' to load the units file filename. You can specify up to 25 units
files on the command line. When you use this 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 conversions 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 statistics 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
conversion, 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 conversion'' line.

-t, --terse
Give terse output when converting units. This option can be used when calling
'units' from another program so that the output 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 additional 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 sometimes
be useful for troubleshooting.

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

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

-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 definitions 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 definitions will be
preserved if you update 'units'.

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

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

might be appropriate for a site-wide supplemental data file. The location 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 standard 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'.) Running '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 without
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 equivalence. Comments
start with a '#' character, which can appear anywhere in a line. The backslash character
('\') acts as a continuation character 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 the comment character '#'.

Unit names must not contain any of the operator characters '+', '-', '*', '/', '|', '^',
';', '~', the comment character '#', or parentheses. 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 definitions, 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, 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 multiplication
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
precedence values and may require parentheses to ensure consistent behavior. To compute
the difference of 'foo' and 'bar' write 'foo+(-bar)' or even 'foo+-bar'.

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 0.0254 m # Inch defined in terms of meters
ft 12 inches # The foot defined in terms of inches
mile 5280 ft # And the mile

A unit that ends with a '-' character is a prefix. If a prefix definition contains any
'/' characters, be sure they are protected by parentheses. 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, temperature conversions
between the Fahrenheit and Celsius scales cannot be done by simply multiplying by
conversion factors.

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

Nonlinear units are represented using a functional notation. It is best to regard this
notation not as a function call but as a way of adding units to a number, much the same
way that writing a linear unit name after a number adds units to that number. Internally,
nonlinear units are defined by a pair of functions that convert to and from linear 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 formal 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 argument conformable with 'K'. For normal nonlinear
units definition, the forward function will always take a dimensionless argument; in
general, the inverse function will need units that match the quantity measured by your
nonlinear unit. Specifying the units enables 'units' to perform error checking on
function arguments, and also to assign units to 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 arguments. 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 powers 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 endpoints given in
brackets. In accord with mathematical convention, square brackets indicate a closed
interval (one that includes its endpoints), 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 decibel (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 specification, and if necessary, the parameter value is
adjusted for comparison 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
definition.

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 original 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 messages.

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 conversions 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 '[' character. After the bracket, you should
indicate the units to be attached to the numbers in the table. No spaces can appear
before the ']' character, 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 performed:

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 piecewise linear unit is
encountered. For example, the relationship between ANSI coated abrasive designation and
mean particle size is non-monotonic 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 confirm that there are no actual errors before
adding the 'noerror' keyword.

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 notation) 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 precision specification that begins with a period (e.g., '.6'). The field width
includes the digits, decimal point, the exponent, thousands separators (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 positive, 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 separator 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 without counting the
digits to the left of the decimal point. If the thousands 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 magnitudes of results. For example, with the format
'%12.6f',

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

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

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

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

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

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

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

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

In this case the displayed value includes a series of digits that represent 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 localization 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 formatting 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 definitions could be accommodated as follows:

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

When 'units' reads the above definitions it will check the environment variable
'INCH_UNIT' and load only the definitions for the appropriate section. If 'INCH_UNIT' is
unset or is not set to one of the four values listed then 'units' will run the last block.
In this case that block uses the '!message' command to display a warning message.
Alternatively 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' command with the
'!locale' command. If you wanted to combine the above example with suitable locales you
could do by preceding the above definition with the following:

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

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

If the variable given after '!var' or '!varnot' is undefined then 'units' prints an error
message and ignores the definitions that follow. Use '!set' to create defaults to prevent
this situation from arising. The '-c' option only checks the definitions that are active
for the current environment and locale, so when adding new definitions take care to check
that all cases give rise to a well defined set of 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 variables; if these
variables do not exist, units finally tries 'USERPROFILE'—typically
'C:\Users\username' (Windows Vista and Windows 7) or
'C:\Documents and Settings\username' (Windows XP).

LC_CTYPE, LANG
Checked to determine the locale if 'units' cannot obtain it from the operating
system. Sections of the 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 conformable 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 environment 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 specify a location for the units data file using either the '-f' option or the
'UNITSFILE' environment variable, and that location does not also contain the
locale map file.

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 distribution.

On systems running Microsoft Windows, the files may be in the same locations if Unix-like
commands are available, a Unix-like file structure is present (e.g., 'C:/usr/local'), and
'units' is compiled from the source distribution. If Unix-like commands are not
available, a more common location is 'C:\Program Files (x86)\GNU\units' (for 64-bit
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' program; 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 beginning 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; otherwise 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 hexadecimal 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 characters 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 outside '!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 characters 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 available. To check if your version of 'units'
includes 'readline', invoke the program with the '--version' option.

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

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

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

If there is a unique way to complete a unitname, 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 history 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 includes currency exchange rates and prices for some precious metals in
the database. Of course, these values change over time, sometimes very rapidly, and
'units' cannot provide real time values. To update the exchange rates run the
'units_cur', which rewrites the files containing the currency rates, typically
'/usr/share/units/currency.units'. This program requires 'python' and the 'unidecode'
package, and 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. Currency exchange rates are taken from Time
Genie (http://www.timegenie.com) and precious metals pricing from Packetizer
(www.packetizer.com). These sites update once per day, so there is no benefit in running
the update script more often than daily. You can run 'units_cur' with a filename
specified on the command line and it will write the data to that file. If you give '-'
for the file it will write to standard output.

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.

!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 environment 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 environment 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.

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