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## unitconv

Conversion of units of measurement.

## TOC »

- Outdated egg!
- unitconv
- Usage
- Documentation
- Procedures and Macros
- Predefined Quantities
- Predefined Units
- SI Unit Prefixes
- IEC Standard Prefixes
- Time Multiples
- Angles
- Units of Length
- Units of Area and Volume
- Units of Mass
- Units of Time
- Units of Acceleration
- Units of Frequency
- Units of Force
- Units of Power
- Units of Energy
- Units of Current
- Units of Electric Charge
- Units of Electric Potential
- Units of Resistance
- Units of Capacitance
- Units of Conductance
- Units of Inductance
- Units of Substance
- Units of density
- Units of concentration
- Units of temperature
- Units of information
- Units of information rate

- Arithmetic Operations with Units

- About this egg

## Usage

(require-extension unitconv)

## Documentation

The `unitconv` library is an implementation of unit conversion routines based on the paper by Gordon S. Novak:

Conversion of Units of Measurement. IEEE Trans. on Software Engineering, vol. 21, no. 8 (Aug. 1995), pp. 651-661.

(Available online at http://www.cs.utexas.edu/users/novak/units95.html).

Correctness of unit conversion is established by the technique of dimensional analysis: the source and goal units must have the same dimensions. Following Novak, this extension defines a dimension as an 8-vector of integral powers of the following base quantities:

(define-base-quantity Unity 0) (define-base-quantity Length dimvals[0]) (define-base-quantity Time dimvals[1]) (define-base-quantity Temperature dimvals[2]) (define-base-quantity Mass dimvals[3]) (define-base-quantity Current dimvals[4]) (define-base-quantity Luminosity dimvals[5]) (define-base-quantity Substance dimvals[6]) (define-base-quantity Currency dimvals[7]) (define-base-quantity Information dimvals[8])

The unit conversion routine uses dimension integers to check that the requested unit conversion is legitimate. For example, the conversion from kilograms to meters illegal. Consequently, the dimensionality of each unit must be specified when the unit is declared.

;; Syntax is (define-unit name quantity factor abbreviation ...) ;; define units of length (define-unit meter Length 1.0 m meters) (define-unit inch Length 0.0254 in inches) ;; define units of mass and time (define-unit kilogram Mass 1.0 kg kilograms) (define-unit second Time 1.0 s seconds) ;; define two new derived quantities: acceleration and force (define-quantity Acceleration (/ Length (** Time 2))) (define-quantity Force (* Mass Acceleration)) ;; define a unit of force (define-unit newton Force (/ (* kilogram meter) (* second second)) nt newtons)

Now only conversion between units of the same dimensionality is permitted:

(unit-convert meter inch 1) -> 39.3700787401575 (unit-convert meter inch 2 3 4) -> (78.740157480315 118.110236220472 157.48031496063) (unit-convert meter kilogram 1) Error: (unitconv) unit-convert : given units are of different dimensions: source= #(unit meter (m meters) [Length] 1.0) ; dest= #(unit kilogram (kg kilograms) [Mass] 1.0)

### Procedures and Macros

`unit-convert:`procedureConverts the given numeric values expressed in unit

`SRC`to their equivalents in unit`DEST`.Arguments

`SRC, DEST`are records of type`unit`. See the definitions below for information about the units that are defined by this extension, as well as for information about creating new units.

`unit-equal?:`procedureReturns true if the two units have the same dimension and factor, false otherwise.

`(define-quantity name expr)`syntaxDefines a derivative quantity

`NAME`.`EXPR`is an S-expression with the following syntax:quantity-expr ::= base-quantity | derived-quantity | (* quantity-expr quantity-expr) | (* quantity-expr integer) | (/ quantity-expr quantity-expr) | (/ quantity-expr integer) | (** quantity-expr integer)

where

`base-quantity`- one of the predefined base quantities
`derived-quantity`- a quantity created by
`define-quantity` `**`- exponentiation operator

`(define-unit name dims factor . abbrevs)`syntaxDefines a variable

`NAME`that holds a unit definition of a unit with the given dimension and factor.`DIMS`can be either one of the base quantities (see next section) or a derivative quantity created by`define-quantity`.

`(define-prefix-unit unit prefix . abbrevs)`syntaxDefines a variable whose name is the concatenated

`PREFIX`and`UNIT`and that holds a unit definition of the given unit and prefix.

### Predefined Quantities

#### Base Quantities

`Unity`(dimensionless)`Length``Time``Temperature``Mass``Current``Luminosity``Substance``Currency``Information`

#### Derived Quantities

**Geometry**`Area``(** Length 2)``Volume``(** Length 3)`**Mechanics**`Velocity``(/ Length Time)``Acceleration``(/ Length (** Time 2))``Force``(* Mass Acceleration)``Pressure``(/ Force Area)``Energy``(* Force Length)``Power``(/ Energy Time)`**Electricity**`Charge``(* Current Time)``Potential``(/ Energy Charge)``Capacitance``(/ Charge Potential)``Resistance``(/ Potential Current)``Conductance``(/ Current Potential)``Inductance``(/ (* Potential Time) Current)`**Chemistry**`Concentration``(/ Substance Volume)``Density``(/ Mass Volume)`**Optics**`Luminance``(/ Luminosity Area)`**Other**`Frequency``(/ Unity Time)``Rate``(/ Information Time)`

### Predefined Units

#### SI Unit Prefixes

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

yocto | Unity | 1e-24 | |

zepto | Unity | 1e-21 | |

atto | Unity | 1e-18 | |

femto | Unity | 1e-15 | |

pico | Unity | 1e-12 | |

nano | Unity | 1e-09 | |

micro | Unity | 1e-06 | |

milli | Unity | 0.001 | |

centi | Unity | 0.01 | |

deci | Unity | 0.1 | |

deca | Unity | 10.0 | |

hecto | Unity | 100.0 | |

kilo | Unity | 1000.0 | |

mega | Unity | 1000000.0 | |

giga | Unity | 1000000000.0 | |

tera | Unity | 1000000000000.0 | |

peta | Unity | 1e+15 | |

exa | Unity | 1e+18 | |

zetta | Unity | 1e+21 | |

yotta | Unity | 1e+24 |

#### IEC Standard Prefixes

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

kibi | Unity | 1024 | |

mebi | Unity | 1048576 | |

gibi | Unity | 1073741824.0 | |

tebi | Unity | 1099511627776.0 | |

pebi | Unity | 1.12589990684262e+15 | |

exbi | Unity | 1.15292150460685e+18 | |

zebi | Unity | 1.18059162071741e+21 | |

yobi | Unity | 1.20892581961463e+24 |

#### Time Multiples

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

twelve | Unity | 12 | |

sixty | Unity | 60 |

#### Angles

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

Name | Quantity | Factor | Abbreviation(s) |

radian | Unity | 1.0 | (rad radians) |

degree | Unity | (/ pi 180) | (deg degrees) |

#### Units of Length

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

meter | Length | 1.0 | (m meters) |

inch | Length | 0.0254 | (in inches) |

foot | Length | 0.3048 | (ft feet) |

angstrom | Length | 1e-10 | (ang angstroms) |

parsec | Length | 3.083e+16 | (parsecs) |

#### Units of Area and Volume

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

square-meter | Area | (* meter meter) | (m^2 m2 meter-squared meters-squared square-meters) |

square-inch | Area | (* inch inch) | (in^2 inch-squared inches-squared square-inches) |

square-micron | Area | (* micrometer micrometer) | (um^2 micrometer-squared micrometers-squared micron-squared microns-squared square-microns) |

square-millimeter | Area | (* millimeter millimeter) | (mm^2 millimeter-squared millimeters-squared square-millimeters) |

cubic-meter | Volume | (* meter (* meter meter)) | (m^3 meter-cubed meters-cubed cubic-meters) |

liter | Volume | (* 0.001 cubic-meter) | (L litre liters) |

#### Units of Mass

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

kilogram | Mass | 1.0 | (kg kilograms) |

gram | Mass | 0.001 | (g grams) |

pound | Mass | (* gram 453.59237) | (lb pounds) |

slug | Mass | (* pound 32.17405) | (slugs) |

atomic-mass-unit | Mass | 1.6605402e-27 | (amu atomic-mass-units) |

#### Units of Time

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

second | Time | 1.0 | (s seconds) |

hour | Time | (* sixty (* sixty second)) | (h hrs hours) |

#### Units of Acceleration

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

meters-per-second-squared | Acceleration | (/ meter (* second second)) | (m/s2 m/s^2 m/sec2 m/sec^2) |

#### Units of Frequency

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

hertz | Frequency | 1.0 | (hz) |

#### Units of Force

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

newton | Force | (/ (* kilogram meter) (* second second)) | (nt newtons) |

pound-force | Force | (/ (* slug foot) (* second second)) | (lbf) |

#### Units of Power

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

watt | Power | (/ (* kilogram meter meter) (* second second second)) | (W watts) |

horsepower | Power | (* 550 (/ (* foot pound-force) second)) | (hp) |

#### Units of Energy

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

joule | Energy | (* newton meter) | (J joules) |

electron-volt | Energy | (* 1.60217733e-19 joule) | (ev electron-volts) |

kilowatt-hour | Energy | (* kilo (* watt hour)) | (kwh kilowatt-hours) |

calorie | Energy | (* 4.184 joule) | (cal calories) |

erg | Energy | (* 1e-07 joule) | (ergs) |

british-thermal-unit | Energy | (* 1055.056 joule) | (btu btus) |

#### Units of Current

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

ampere | Current | 1.0 | (A amp amps amperes) |

#### Units of Electric Charge

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

coulomb | Charge | (* ampere second) | (C coulombs) |

#### Units of Electric Potential

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

volt | Potential | (/ (* kilogram meter meter) (* ampere second second second)) | (V volts) |

#### Units of Resistance

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

ohm | Resistance | (/ volt ampere) | (ohms) |

#### Units of Capacitance

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

farad | Capacitance | (/ coulomb volt) | (F farads) |

#### Units of Conductance

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

siemens | Conductance | (/ ampere volt) | (S mho) |

#### Units of Inductance

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

henry | Inductance | (/ (* meter meter kilogram) (* ampere ampere second second)) | (H) |

#### Units of Substance

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

mole | Substance | 1.0 | (mol moles) |

#### Units of density

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

rho | Density | (/ kilogram cubic-meter) |

#### Units of concentration

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

molarity | Concentration | (/ mole liter) | (M mol/L) |

parts-per-million | Concentration | (/ milligram kilogram) | (ppm) |

#### Units of temperature

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

degK | Temperature | 1.0 | (K) |

#### Units of information

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

bit | Information | 1 | (b bits shannon shannons Sh) |

byte | Information | 8 | (B bytes) |

nat | Information | 1.44269504088896 | (nats nit nits nepit nepits) |

ban | Information | 3.32192809488736 | (bans hartley hartleys Hart Harts dit dits) |

#### Units of information rate

Name | Quantity | Factor | Abbreviation(s) |
---|---|---|---|

bits-per-second | Rate | (/ bit second) | (bps) |

bytes-per-second | Rate | (/ byte second) | (Bps) |

### Arithmetic Operations with Units

The `with-units` library contains procedures for arithmetic operations on quantities with units. A quantity with unit information is created by procedure `val-with-units`:

(use unitconv with-units) (val-with-units 10 m) -> #(10 #(unit meter (m meters) [Length] 1.0))

The following operations are available for operations on quantities with units:

`u:value`- Returns the value of the given quantity.
`u:units`- Returns the unit of the given quantity.
`u:equal?`- Returns true if the units of the given quantities are equal, false otherwise.
`u:zero?``u:=``u:negate``u:invert``u:+ u:- u:* u:/``u:sqrt``u:sin``u:cos``u:expt`

## About this egg

### Author

### Version history

- 2.6
- Bugfixes in unit* and unit/
- 2.3
- Added definitions for centimeter and centimeter-squared
- 2.2
- Removed redundant definition of define-unit (reported by felix)
- 2.1
- Documentation converted to wiki format
- 2.0
- Added unit arithmetic (with-units)
- 1.8
- Exporting all prefixed units; added info on information units [Joshua Griffith]
- 1.7
- Exporting the Rate quantity
- 1.6
- Exporting the IEC standard prefixes
- 1.5
- Ported to Chicken 4
- 1.4
- The predefined quantities have been put into unit-definitions.scm
- 1.3
- Bug fix in unit-convert
- 1.2
- Changed unit-convert to return a single numeric value given a single conversion argument
- 1.1
- Added information units [patch by Joshua Griffith]
- 1.0
- Initial release

### License

Copyright 2007-2015 Ivan Raikov and the University of California, Irvine. This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. A full copy of the GPL license can be found at <http://www.gnu.org/licenses/>.