HELP
I will include
here verbatim the man page for the original units program. You do the rest
this time, right?
UNITS(1)
UNITS(1)
NAME
units - unit conversion program
OVERVIEW
OF `UNITS'
The `units' program converts quantities expressed in vari
ous scales to their equivalents in other scales.
The
`units' program can handle multiplicative scale changes as
well as nonlinear conversions such as Fahrenheit to Cel
sius.
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.
INTERACTING
WITH `UNITS'
To invoke units for interactive use, type `units' at your
shell prompt. The program will print something like this:
2131 units, 53 prefixes, 24 functions
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'.
The answer will be displayed in two ways. The first line
of output, which is marked with a `*' to indicate multi
plication, 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
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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 con
version results with an extra note indicating that recip
rocal 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
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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.
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 mes
sage. 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 defi
nition and comments that may give more details or histori
cal information about the unit.
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 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.
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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.
UNIT
EXPRESSIONS
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.
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,
a hyphen (`-') or an asterisk (`*'). 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 recip
rocal 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 very high precedence,
higher
even than the exponent operator.
You have: 1|2 inch
You want: cm
* 1.27
/ 0.78740157
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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.
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. 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
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* 2.5782804
/ 0.38785542
The expressions which are added together must reduce
to
identical expressions in primitive units, or an error mes
sage will be displayed:
You have: 12 printerspoint + 4 heredium
^
Illegal sum of non-conformable units
Because `-' is used for products, it cannot also be used
to form differences of units. If a `-' appears after `('
or after `+' then it will act as a negation operator. So
you can compute 20 degrees minus 12 minutes by entering
`20 degrees + -12 arcmin'. The `+' character is sometimes
used in exponents like `3.43e+8'. This leads to an ambi
guity in an expression like `3e+2 yC'. The unit `e' is a
small unit of charge, so this can be regarded as equiva
lent 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 dimen
sions 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
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You have: (400 W/m^2 / stefanboltzmann)^(1/4)
You have:
Definition: 289.80882 K
You have: cuberoot(hectare)
^
Unit not a root
Unit functions can be used for nonlinear unit conversions
such as Fahrenheit to Celsius:
You have: tempF(45)
You want: tempC
7.2222222
In this case, think of `tempF(x)' not as a function but as
a notation which indicates that `x' should have units of
`tempF' attached to it. @xref{Defining functions}.
INVOKING
`UNITS'
You invoke `units' like this:
units OPTIONS [FROM-UNIT [TO-UNIT]]
If the FROM-UNIT and TO-UNIT are omitted, then the program
will use interactive prompts to determine which conver
sions to perform. If both FROM-UNIT and TO-UNIT
are
given, `units' will print the result of that single con
version 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 interpreta
tion and to group them into two arguments. @xref{Command
line use}.
The following options allow you to read in an alternative
units file, check your units file, or change the output
format:
-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.
--check-verbose
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'
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hangs, then the last unit to be printed has a bad
definition.
-o format, --output-format format
Use the specified format for numeric output. For
mat is the same as that for the printf function in
the ANSI C standard. For example, if you want more
precision you might use `-o %.15g'.
-f filename, --file filename
Use filename as the units data file rather than the
default units data file. This option overrides the
`UNITSFILE' environment variable.
-h, --help
Print out a summary of the options for `units'.
-q, --quiet, --silent
Suppress prompting of the user for units and the
display of statistics about the number of units
loaded.
-s, --strict
Suppress conversion of units to their reciprocal
units.
-v, --verbose
Give slightly more verbose output when converting
units. When combined with the `-c' option
this
gives the same effect as `--check-verbose'.
-V, --version
Print program version number, tell whether
the
readline library has been included, and give the
location of the default units data file.
UNIT
DEFINITIONS
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:
28 May 2000 8
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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 ele
ments 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, multi
ply by the force conversion unit `force' or use the short
hand `lbf'. (Note that `g' is already taken as the stan
dard 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 inter
national 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' pro
gram 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.
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DEFINING
NEW UNITS
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 char
acter (`) 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.
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 reduc
tion leads to the primitive units, which are marked with
`!' characters. When adding new units, be sure to use the
`-c' option to check that the new units reduce properly.
If you define any units which contain `+' characters,
carefully check them because the `-c' option will not
catch non-conformable sums. 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.
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
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'.
DEFINING
FUNCTIONS
Functions can be useful for performing nonlinear unit con
versions. For example, temperature conversions between
the Fahrenheit and Celsius scales cannot be done by simply
multiplying by conversions factors.
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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 must provide a functional defini
tion that provides the same information.
When using a function to perform a conversion, the func
tion is best regarded as a way of adding units to a num
ber, much the same way that writing a linear unit
name
after a number adds units to that number. But internally,
the unit function is defined as a function which converts
to other units in the data file, so that an eventual con
version to primitive units is possible. It is also neces
sary to specify the inverse conversion from some linear
units to the new units.
Here is an example function definition:
tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
A function definition begins with the function name fol
lowed immediately (with no spaces) by a `(' character. In
parentheses is the name of the parameter. Next
is an
optional specification of what units
this function
requires. In the example above, the `tempF'
function
requires an input argument conformable with
`1'. The
inverse function requires an input argument conformable
with `K'. The sole purpose of the expression in brackets
to enable `units' to perform error checking on function
arguments.
Next the function definition appears. In
the example
above, the `tempF' function is defined by
tempF(x) = (x+(-32)) degF + stdtemp
This means that the `tempF' function regards its argument
as a temperature in Fahrenheit and converts it to an abso
lute temperature.
In order to make conversions to Fahrenheit possible, you
must also specify the inverse. The
inverse will be
`x(tempF)' and its definition appears after a `;' charac
ter. 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 tempera
ture. The inverse can be omitted by leaving out the `;'
character, but then conversions to the unit will be impos
sible.
If you wish to make synonyms for functions, you still need
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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 do
fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)
Sometimes you may be interested in a piecewise linear unit
such as wire gauge. Piecewise linear functions can be
defined by specifying the function's value on a list
of
points. The function will be evaluated using
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 function. The definition of such a function
is
indicated by the embedded `[' character.
After the
bracket, you should indicate the units to be attached to
this function. No spaces can appear before the `]' char
acter, so a definition like `foo[kg meters]' is illegal;
instead write `foo[kg*meters]'. The definition of
the
function consists of a list of pairs optionally separated
by commas. 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'. Defi
nitions line 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 function that is not
strictly monotonic, then the inverse will not be
well
defined. If the inverse is requested for such a function,
`units' will return the smallest inverse.
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ENVIRONMENT
VARIABLES
The `units' programs uses the following environment vari
ables.
PAGER Specifies the pager to use for help and for
dis
playing the conformable units. The help function
browses the units database and calls the
pager
using the `+nn' syntax for specifying a line num
ber. The default pager is `more', but
`less',
`emacs', or `vi' are possible alternatives.
UNITSFILE
Specifies the units database file to use (instead
of the default). This will be overridden by the
`-f' option.
READLINE
SUPPORT
If the `readline' package has been compiled in, then when
`units' is used interactively, numerous command line edit
ing 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 docu
mentation for the readline package. Without any configu
ration, `units' will allow editing in the style of emacs.
Of particular use with `units' are the completion
com
mands.
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.
FILES
/usr/local/share/units.dat - the standard units data file
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AUTHOR
Adrian Mariano (adrian@cam.cornell.edu)
28 May 2000 14
