unitsThe units program converts quantities expressed in various scales
to their equivalents in other scales. The units program can
handle multiplicative scale changes as well as nonlinear
conversions such as Fahrenheit to
Celsius.1
Temperature conversions require a special
syntax.
See tempconvert.
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 use the program interactively with prompts, or you can use it from the command line.
unitsTo invoke units for interactive use, type units at your shell prompt. The program will print something like this:
2131 units, 53 prefixes, 24 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 type of units you want to convert
to. To convert to feet, you would type feet. Note that if
the readline library was compiled in then the tab key can be used to
complete unit names. See Readline support, for more information
about readline.
The answer 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 .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 .03048 dekameters.
But the number given the other direction is inexact.
If you try to 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 which 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 return 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 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 dimensionless.
You have: (14 ft lbf) (12 radians/sec)
You want: watts
* 227.77742
/ 0.0043902509
Note that named dimensionaless units are not treated as dimensionless in other contexts. They cannot be used as exponents so for example, meter^radian is not allowed. If you want a list of options you can type ? at the You want: prompt. The program will display a list of named units which are conformable with the unit that you entered at the You have: prompt above. Note that 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.
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 units expression, and type the new units you want.
You will probably need to protect the units expressions from
interpretation by the shell using single 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 (0)
to the calling environment. If units is given non-conformable
units to convert, it will print a message giving the reduced form of
each unit and it will return failure (nonzero) to the calling environment.
When units is invoked 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.
In order to enter more complicated units or fractions, you will need to use operations such as powers, products and division. Powers of units can be specified using the ^ character as shown in the following example, or by simple concatenation: cm3 is equivalent to cm^3. If the exponent is more than one digit, the ^ is required. An exponent like 2^3^2 is evaluated right to left. The ^ operator has the second highest precedence.
You have: cm^3
You want: gallons
* 0.00026417205
/ 3785.4118
You have: arabicfoot * arabictradepound * force
You want: ft lbf
* 0.7296
/ 1.370614
Multiplication of units can be specified by using spaces, or an asterisk
(*). If units is invoked with the --product
option then the hyphen (-) also acts as a multiplication
operator. Division of units is indicated
by the slash (/) or by per.
You have: furlongs per fortnight
You want: m/s
* 0.00016630986
/ 6012.8727
Multiplication has a higher precedence than division and is evaluated left to right, so 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 .5/meter, which is probably not what you would intend if you entered that expression. You can indicate division of numbers with the vertical dash (|). This operator has the highest precedence so the square root of two thirds could be written 2|3^1|2.
You have: 1|2 inch
You want: cm
* 1.27
/ 0.78740157
Parentheses can be used for grouping as desired.
You have: (1/2) kg / (kg/meter)
You want: league
* 0.00010356166
/ 9656.0833
Prefixes are defined separately from base units. In order to get centimeters, the units database defines centi- and c- as prefixes. Prefixes can appear alone with no unit following them. An exponent applies only to the immediately preceding unit and its prefix so that cm^3 or centimeter^3 refer to cubic centimeters but centi*meter^3 refers to hundredths of cubic meters. Only one prefix is permitted per unit, so micromicrofarad will fail, but micro*microfarad will work, as will micro microfarad..
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 which 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 dollars^5.
Outside of the SI system, it is often desirable to add values of
different units together. You may also wish to use units as a
calculator that keeps track of units. Sums of conformable units are written 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 which are added together 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
Historically - has been used for products of units, which complicates
its iterpretation in units. 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. This
behavior can be altered using the --product option which
causes units to treat the binary - operator as a product
operator. Note that when - is a multiplication operator it has
the same precedence as *, but when - is a subtraction operator
it has the lower precedence as the addition operator.
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.
The + character 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 + as part of an exponent if possible.
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. Higher roots can be obtained 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
Nonlinear units are represented using functional notation. They make possible nonlinear unit conversions such temperature. This is different from the linear units that convert temperature differences. Note the difference below. The absolute temperature conversions are handled by units starting with temp, and you must use functional notation. The temperature differences 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 which indicates that x should have units of tempF attached to it. See Nonlinear units. The first conversion shows that if it's 45 degrees Fahrehneit outside it's 7.2 degrees Celsius. The second conversions indicates that a change of 45 degrees Fahrenheit corresponds to a change of 25 degrees Celsius.
Some other examples of nonlinears units are ring size and wire gauge. There are numerous different gauges and ring sizes. See the units database for more details. Note that 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 units database.
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
unitsunits [options] [from-unit [to-unit]]
If the from-unit and to-unit are omitted, then 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 will need
to be quoted to protect them from shell interpretation and to group
them into two arguments. See Command line use.
The following options allow you to read in an alternative units file, check your units file, or change the output format:
units hangs, then the last unit to be printed has a bad
definition. Note that only
definitions active in the current locale are checked.
units to load the units file filename.
If filename is the empty string (-f '')
then the default units file will
be loaded. This enables you to load the default file plus a personal
units file. Up to 25 units files may be specified on the command line.
This option overrides the UNITSFILE environment variable.
units.
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.
units from another program so that the output is easy to
parse.
The conversion information is read from a units data file which
is called units.dat and is probably located in
the /usr/local/share 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 permitivity of vacuum G Gravitational constant mach speed of sound
The database 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 unit 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. British capacity units that differ from their US counterparts, such as the British Imperial gallon, are prefixed with br. Currency is prefixed with its country name: belgiumfranc, britainpound.
The US Survey foot, yard, and mile can be obtained by using the US prefix. These units differ slightly from the international length units. They were in general use until 1959, and are still used for geographic surveys. The acre is officially defined in terms of the US Survey foot. If you want an acre defined according to the international foot, use intacre. The difference between these units is about 4 parts per million. The British also used a slightly different length measure before 1959. These can be obtained with the prefix UK.
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 or a trailing es. If that fails, units
will check for a prefix.
All of the standard metric prefixes are defined.
To find out what units and prefixes are available, read the standard units data file.
All of the units and prefixes that units can convert are defined
in the units data file. If you want to add your own units, you can
supply your own file.
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 file will be sought in the same directory as the
parent file unless a full path is given.
Unit names must not contain any of the operator characters +,
-, *, /, |, ^ or the parentheses.
They cannot begin with a digit or a decimal point (.), nor can
they end with a digit (except for zero).
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 options. You will need to
use the --check-verbose option which prints out each unit as it
checks them. The program will still hang, but the last unit printed
will be the unit which caused the infinite loop.
If you define any units which 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. To compute the difference
of foo and bar write foo+(-bar) or even foo+-bar.
Here is an example of a short units 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 which 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.
Some units conversions of interest are nonlinear; for example, temperature conversions between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conversions 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 which convert to and from linear units in the data file, so that an eventual conversion to primitive units is possible.
Here is an example nonlinear unit definition:
tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
A nonlinear unit definition comprises a unit name, a dummy parameter
name, two functions, and two corresponding units. The functions tell
units how to convert to and from the new unit. In order to
produce valid results, the arguments of these functions need to have
the correct dimensions. To facilitate error checking, you may specify
the dimensions.
The definition begins with the unit name followed immediately (with no
spaces) by a ( character. In parentheses is the name of the
parameter. Next is an optional specification of the units required by
the functions in this definition. In the example above, the
tempF function requires an input argument conformable with
1. For normal nonlinear units definitions the forward
function will always take a dimensionless argument.
The inverse function requires an input argument conformable
with K. In general the inverse function will need units
that match the quantity measured by your nonlinear unit.
The sole purpose of the expression in brackets to enable
units to perform error checking on function arguments.
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.
In order to make conversions to Fahrenheit possible, 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, but then conversions to the unit will be impossible. If the inverse is omitted then 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 print an error if it is not valid there, but this is not a guarantee that your inverse is correct.
If you wish to make synonyms for nonlinear units, you still need to define 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) [1;K] tempF(x); ~tempF(fahrenheit)
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. Note that this definition requires a length as input and produces an area as output, as indicated by the specification in brackets.
circlearea(r) [m;m^2] pi r^2 ; sqrt(circlearea/pi)
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 illegal; 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 preceeding 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. The --check option will print a warning if a
non-monotonic piecewise linear unit is encountered.
Some units have different values in different locations. The localization feature accomodates this by allowing the units database to specify region dependent definitions. A locale region in the units database begins with !locale followed by the name of the locale. The leading ! must appear in the first column of the units database. The locale region is terminated by !endlocale. The following example shows how to define a couple units in a locale.
!locale en_GB
ton brton
gallon brgallon
!endlocale
The current locale is specified
by the LOCALE environment variable. Note that the -c
option only checks the definitions which are active for the current locale.
The units programs uses the following environment variables.
+nn syntax for specifying a line number. The
default pager is more, but less, emacs, or
vi are possible alternatives.
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 the 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 the
? key then units will display a list of all the units which
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.
--check (option for units): Invoking units--check-verbose (option for units): Invoking units--file (option for units): Invoking units--help (option for units): Invoking units--minus (option for units): Invoking units--output-format (option for units): Invoking units--product (option for units): Invoking units--quiet (option for units): Invoking units--silent (option for units): Invoking units--strict (option for units): Invoking units--terse (option for units): Invoking units--verbose (option for units): Invoking units--version (option for units): Invoking units-c (option for units): Invoking units-f (option for units): Invoking units-h (option for units): Invoking units-m (option for units): Invoking units-o (option for units): Invoking units-p (option for units): Invoking units-q (option for units): Invoking units-s (option for units): Invoking units-t (option for units): Invoking units-V (option for units): Invoking units-v (option for units): Invoking unitsunits: Readline support[1] But Fahrenheit to Celsius is linear, you insist. Not so. A transformation T is linear if T(x+y)=T(x)+T(y) and this fails for T(x)=ax+b. This transformation is affine, but not linear.