Module dimensioned::unit_systems::ucum [] [src]

The Unified Code for Units of Measure (UCUM)

This is an attempt to define a unit system for The Unified Code for Units of Measure. It does not perfectly match the specification in the ways mentioned below.

The UCUM specification uses NIST values from 1980 for experimentally determined constants. For some of these, we use the 2014 values instead, which can be found here.

There are a few classifications of units that UCUM defines but that it does not make sense to define here, and so we do not. They are as follows:

  • Units defined in terms of characters that we can't use. For example, the symbol for minutes as measure of angle is given by a single quote, '.

  • Units that require conversions that involve more than multiplication. These include some temperature units (such as degrees Celcius) and logrithmic units (such as decibels).


While the UCUM specification aims to minimize conflicts, there are still some. Units that may conflict are indicated by the UCUM spec by square brackets. When there is a conflict, for the unit in square brackets, we name it with a trailing underscore. For example, the speed of light conflicts with coulomb, so we use C_ for the speed of light.

A note on derived units:

Mass is involved in a great many units. As the SI unit of mass is the kilogram, there are many units defined in terms of tffhe kilogram. To create a derived unit in dimensioned, it must have a value of 1.0. Since UCUM uses the gram and not the kilogram as a base unit, that leads to many common derived units being off by a factor of 1000. As a result, you will see many derived units with prefixes, such as MilliNewton and KiloFarad. The constants for the more common units (N and F for the two mentioned) are still defined, but if you need to refer to their types (such as in function signatures), this is something to bear in mind.

Following, we list all of the base units, derived units, and constants that are defined in this unit system.

Base Units

Constant Unit Print Token Dimensionn
M Meter m Length
S Second s Time
G Gram g Mass
RAD Radian rad
K Kelvin K Temperature
C Coulomb C Charge
CD Candela cd LuminousIntensity

Derived Units

Constant Unit Unit Definition Dimension
SR Steradian Radian * Radian
HZ Hertz Unitless / Second Frequency
MILLIN MilliNewton Gram * Meter / Second / Second Force
MILLIPA MilliPascal MilliNewton / Meter / Meter Pressure
MILLIJ MilliJoule MilliNewton * Meter Energy
MILLIW MilliWatt MilliJoule / Second Power
A Ampere Coulomb / Second Current
MILLIV MilliVolt MilliJoule / Coulomb ElectricPotential
KILOF KiloFarad Coulomb / MilliVolt Capacitance
MILLIOHM MilliOhm MilliVolt / Ampere Resistance
KILOSIE KiloSiemens Unitless / MilliOhm Conductance
MILLIWB MilliWeber MilliVolt * Second MagneticFlux
MILLIT MilliTesla MilliWeber / Meter / Meter
MILLIH MilliHenry MilliWeber / Ampere Inductance
LM Lumen Candela * Steradian
LX Lux Lumen / Meter / Meter
BQ Becquerel Unitless / Second
GY Gray MilliJoule / Gram
SV Sievert MilliJoule / Gram
S2 Second2 Second * Second
S3 Second3 Second2 * Second
M2 Meter2 Meter * Meter Area
M3 Meter3 Meter2 * Meter Volume
PM PerMeter Unitless / Meter ReciprocalLength
MPS MeterPerSecond Meter / Second Velocity
MPS2 MeterPerSecond2 Meter / Second2 Acceleration
MPS3 MeterPerSecond3 Meter / Second3 Jerk
M2PS Meter2PerSecond Meter2 / Second
M2PS2 Meter2PerSecond2 Meter2 / Second2
APM AmperePerMeter Ampere / Meter
CPM2 CandelaPerMeter2 Candela / Meter2
CPG CoulombPerGram Coulomb / Gram
GPM GramPerMeter Gram / Meter
GPM4S GramPerMeter4Second Gram / Meter3 / Meter / Second
MILLIJS MilliJouleSecond MilliJoule * Second
MILLIJPK MilliJoulePerKelvin MilliJoule / Kelvin
KILOFPM KiloFaradPerMeter KiloFarad / Meter
MILLINPA2 MilliNewtonPerAmpere2 MilliNewton / Ampere / Ampere
M3PGS2 Meter3PerGramSecond2 Meter3 / Gram / Second2
MILLIPS MilliPascalSecond MilliPascal * Second
M3PSG Meter3PerSecondGram Meter3 / Second / Gram


Name Constant Value Unit Dimension
Centimeter CM CENTI * M Meter Length
Astronomic unit ASU 149597.870691e6 * M Meter Length
Parsec PRS 3.085678e16 * M Meter Length
Light-year LY C_ * ANN_J Meter Length
International inch IN_I 2.54 * CM Meter Length
International foot FT_I 12.0 * IN_I Meter Length
International yard YD_I 3.0 * FT_I Meter Length
International mile MI_I 5280.0 * FT_I Meter Length
International fathom FTH_I 6.0 * FT_I Meter Length
International nautical mile NMI_I 1852.0 * M Meter Length
International mil MIL_I 1.0e-3 * IN_I Meter Length
International hand HD_I 4.0 * IN_I Meter Length
US foot FT_US 1200.0 / 3937.0 * M Meter Length
US yard YD_US 3.0 * FT_US Meter Length
US inch IN_US FT_US / 12.0 Meter Length
US rod RD_US 16.5 * FT_US Meter Length
US Gunter's chain CH_US 4.0 * RD_US Meter Length
US Gunter's chain LK_US CH_US / 100.0 Meter Length
US Ramden's chain RCH_US 100.0 * FT_US Meter Length
US Link for Ramden's chain RLK_US RCH_US / 100.0 Meter Length
US fathom FTH_US 6.0 * FT_US Meter Length
US furlong FUR_US 40.0 * RD_US Meter Length
US mile MI_US 8.0 * FUR_US Meter Length
US mil MIL_US 1.0e-3 * IN_US Meter Length
British inch IN_BR 2.539998 * CM Meter Length
British foot FT_BR 12.0 * IN_BR Meter Length
British rod RD_BR 16.5 * FT_BR Meter Length
British Gunter's chain CH_BR 4.0 * RD_BR Meter Length
British link for Gunter's chain LK_BR CH_BR / 100.0 Meter Length
British fathom FTH_BR 6.0 * FT_BR Meter Length
British pace PC_BR 2.5 * FT_BR Meter Length
British yard YD_BR 3.0 * FT_BR Meter Length
British mile MI_BR 5280.0 * FT_BR Meter Length
British nautical mile NMI_BR 6080.0 * FT_BR Meter Length
Line LNE IN_I / 12.0 Meter Length
Point PNT LNE / 6.0 Meter Length
Pica PCA 12.0 * PNT Meter Length
Printer's point PNT_PR 0.013837 * IN_I Meter Length
Printer's pica PCA_PR 12.0 * PNT_PR Meter Length
Pied PIED 32.48 * CM Meter Length
Pounce POUNCE PIED / 12.0 Meter Length
Ligne LIGNE POUNCE / 12.0 Meter Length
Didot DIDOT LIGNE / 6.0 Meter Length
Cicero CICERO 12.0 * DIDOT Meter Length
Charrière CH 1.0 / 3.0 * MILLI * M Meter Length
Ångström AO 0.1 * NANO * M Meter Length
Smoot SMOOT 67.0 * IN_I Meter Length
Minute MIN 60.0 * S Second Time
Hour HR 60.0 * MIN Second Time
Day D 24.0 * HR Second Time
Tropical year ANN_T 365.24219 * D Second Time
Mean Julian year ANN_J 365.25 * D Second Time
Mean Gregorian year ANN_G 365.2425 * D Second Time
year ANN ANN_J Second Time
week WK 7.0 * D Second Time
Synodal month MO_S 29.53059 * D Second Time
Mean Julian month MO_J ANN_J / 12.0 Second Time
Mean Gregorian month MO_G ANN_G / 12.0 Second Time
Month MO MO_J Second Time
Svedberg unit S_ 1.0e-13 * S Second Time
Kilogram KG KILO * G Gram Mass
Tonne TNE 1.0e3 * KG Gram Mass
Unified atomic mass unit AMU 1.6605402e-24 * G Gram Mass
Electron mass M_E 9.10938356e-31 * KG Gram Mass
Proton mass M_P 1.6726231e-24 * G Gram Mass
Grain GR 64.79891 * MILLI * G Gram Mass
Avoirdupois pound LB_AV 7000.0 * GR Gram Mass
Avoirdupois ounce OZ_AV LB_AV / 16.0 Gram Mass
Avoirdupois dram DR_AV OZ_AV / 16.0 Gram Mass
Avoirdupois short hundredweight SCWT_AV 100.0 * LB_AV Gram Mass
Avoirdupois long hundredweight LCWT_AV 112.0 * LB_AV Gram Mass
Avoirdupois short ton STON_AV 20.0 * SCWT_AV Gram Mass
Avoirdupois long ton LTON_AV 20.0 * LCWT_AV Gram Mass
Avoirdupois stone STONE_AV 14.0 * LB_AV Gram Mass
Troy pennyweight PWT_TR 24.0 * GR Gram Mass
Troy ounce OZ_TR 20.0 * PWT_TR Gram Mass
Troy pound LB_TR 12.0 * OZ_TR Gram Mass
Apothecary scruple SC_AP 20.0 * GR Gram Mass
Apothecary dram DR_AP 3.0 * SC_AP Gram Mass
Apothecary ounce OZ_AP 8.0 * DR_AP Gram Mass
Apothecary pound LB_AP 12.0 * OZ_AP Gram Mass
Apothecary ounce OZ_M 28.0 * G Gram Mass
Metric carat CAR_M 0.2 * G Gram Mass
Gon, grade GON 0.9 * DEG Radian
Degree DEG 2.0 * consts::PI / 360.0 * RAD Radian
Circle CIRC 2.0 * consts::PI * RAD Radian
Degree Rankine DEGR 5.0 / 9.0 * K Kelvin Temperature
Elementary charge E 1.6021766208e-19 * C Coulomb Charge
Sphere SPH 4.0 * consts::PI * SR Steradian
Katal KAT MOL / S Hertz Frequency
Unit U MICRO * MOL / MIN Hertz Frequency
Newton N KILO * MILLIN MilliNewton Force
Gram force GF G * G_ MilliNewton Force
Pound force LBF_AV LB_AV * G_ MilliNewton Force
Dyne DYN G * CM / S2 MilliNewton Force
Pascal PA KILO * MILLIPA MilliPascal Pressure
Bar BAR 1.0e5 * PA MilliPascal Pressure
Standard atmosphere ATM 101325.0 * PA MilliPascal Pressure
Meter of water column MH20 9.80665 * KILO * PA MilliPascal Pressure
Meter of mercury column MHG 133.3220 * KILO * PA MilliPascal Pressure
Technical atmosphere ATT KILO * GF / CM / CM MilliPascal Pressure
Pound per square inch PSI LBF_AV / IN_I / IN_I MilliPascal Pressure
Joule J KILO * MILLIJ MilliJoule Energy
Electronvolt EV E * V MilliJoule Energy
Erg ERG DYN * CM MilliJoule Energy
Calorie at 15 °C CAL_15 4.18580 * J MilliJoule Energy
Calorie at 20 °C CAL_20 4.18190 * J MilliJoule Energy
Mean calorie CAL_M 4.19002 * J MilliJoule Energy
International table calorie CAL_IT 4.1868 * J MilliJoule Energy
Thermochemical calorie CAL_TH 4.184 * J MilliJoule Energy
Calorie CAL CAL_TH MilliJoule Energy
Nutrition label calorie CAL_ KILO * CAL MilliJoule Energy
British thermal unit at 39 °F BTU_39 1.05967 * KILO * J MilliJoule Energy
British thermal unit at 59 °F BTU_59 1.05480 * KILO * J MilliJoule Energy
British thermal unit at 60 °F BTU_60 1.05468 * KILO * J MilliJoule Energy
Mean British thermal unit BTU_M 1.05587 * KILO * J MilliJoule Energy
International table British thermal unit BTU_IT 1.05505585262 * KILO * J MilliJoule Energy
Thermochemical British thermal unit BTU_TH 1.054350 * KILO * J MilliJoule Energy
British thermal unit BTU BTU_TH MilliJoule Energy
Watt W KILO * MILLIW MilliWatt Power
Horsepower HP 550.0 * FT_I * LBF_AV / S MilliWatt Power
Biot BI 10.0 * A Ampere Current
Gilbert GB OE * CM Ampere Current
Volt V KILO * MILLIV MilliVolt ElectricPotential
Farad F MILLI * KILOF KiloFarad Capacitance
Ohm OHM KILO * MILLIOHM MilliOhm Resistance
Siemens SIE MILLI * KILOSIE KiloSiemens Conductance
Mho MHO MILLI * SIE KiloSiemens Conductance
Weber WB KILO * MILLIWB MilliWeber MagneticFlux
Maxwell MX 1.0e-8 * WB MilliWeber MagneticFlux
Tesla T KILO * MILLIT MilliTesla
Gauss GS 1.0e-4 * T MilliTesla
Henry H KILO * MILLIH MilliHenry Inductance
Phot PHT 1.0e-4 * LX Lux
Curie CI 3.7e10 * BQ Becquerel
Are AR 100.0 * M2 Meter2 Area
International square inch SIN_I IN_I * IN_I Meter2 Area
International square foot SFT_I FT_I * FT_I Meter2 Area
International square yard SYD_I YD_I * YD_I Meter2 Area
International circular mil CML_I consts::PI / 4.0 * MIL_I * MIL_I Meter2 Area
US acre ACR_US 160.0 * RD_US * RD_US Meter2 Area
US square rod SRD_US RD_US * RD_US Meter2 Area
US square mile SMI_US MI_US * MI_US Meter2 Area
Section SCT MI_US * MI_US Meter2 Area
Township TWP 36.0 * SCT Meter2 Area
British acre ACR_BR 4840.0 * YD_BR * YD_BR Meter2 Area
Barn BRN 100.0 * FEMTO * M * FEMTO * M Meter2 Area
Liter L 0.1 * 0.1 * 0.1 * M3 Meter3 Volume
International cubic inch CIN_I IN_I * IN_I * IN_I Meter3 Volume
International cubic foot CFT_I FT_I * FT_I * FT_I Meter3 Volume
International cubic yard CYD_I YD_I * YD_I * YD_I Meter3 Volume
International board foot BF_I 144.0 * CIN_I Meter3 Volume
International cord CR_I 128.0 * CFT_I Meter3 Volume
Queen Anne's wine gallon GAL_US 231.0 * IN_I * IN_I * IN_I Meter3 Volume
US barrel BBL_US 42.0 * GAL_US Meter3 Volume
US quart QT_US GAL_US / 4.0 Meter3 Volume
US pint PT_US QT_US / 2.0 Meter3 Volume
US gill GIL_US PT_US / 4.0 Meter3 Volume
US fluid Ounce FOZ_US GIL_US / 4.0 Meter3 Volume
US fluid Dram FDR_US FOZ_US / 8.0 Meter3 Volume
US minim MIN_US FDR_US / 60.0 Meter3 Volume
US cord CRD_US CR_I Meter3 Volume
US bushel BU_US 2150.42 * IN_I * IN_I * IN_I Meter3 Volume
Historical winchester gallon GAL_WI BU_US / 8.0 Meter3 Volume
US peck PK_US BU_US / 4.0 Meter3 Volume
US dry quart DQT_US PK_US / 8.0 Meter3 Volume
US dry pint DPT_US DQT_US / 2.0 Meter3 Volume
US tablespoon TBS_US FOZ_US / 2.0 Meter3 Volume
US teaspoon TSP_US TBS_US / 3.0 Meter3 Volume
US cup CUP_US 16.0 * TBS_US Meter3 Volume
Metric fluid ounce FOZ_M 30.0 * MILLI * L Meter3 Volume
Metric cup CUP_M 240.0 * MILLI * L Meter3 Volume
Metric teaspoon TSP_M 5.0 * MILLI * L Meter3 Volume
Metric tablespoon TBS_M 15.0 * MILLI * L Meter3 Volume
British gallon GAL_BR 4.54609 * L Meter3 Volume
British peck PK_BR 2.0 * GAL_BR Meter3 Volume
British bushel BU_BR 4.0 * PK_BR Meter3 Volume
British quart QT_BR GAL_BR / 4.0 Meter3 Volume
British pint PT_BR QT_BR / 2.0 Meter3 Volume
British gill GIL_BR PT_BR / 4.0 Meter3 Volume
British fluid ounce FOZ_BR GIL_BR / 5.0 Meter3 Volume
British fluid dram FDR_BR FOZ_BR / 8.0 Meter3 Volume
British minim MIN_BR FDR_BR / 60.0 Meter3 Volume
Drop DRP MILLI * L / 20.0 Meter3 Volume
Stere STR 1.0 * M3 Meter3 Volume
Kayser KY 1.0 / CM PerMeter ReciprocalLength
Diopter DIOP 1.0 / M PerMeter ReciprocalLength
Mesh MESH_I 1.0 / IN_I PerMeter ReciprocalLength
Speed of light in a vacuum C_ 299792458.0 * MPS MeterPerSecond Velocity
International knot KN_I NMI_I / HR MeterPerSecond Velocity
British knot KN_BR NMI_BR / HR MeterPerSecond Velocity
Standard acceleration of free fall G_ 9.80665 * M / S2 MeterPerSecond2 Acceleration
Gal GL CM / S2 MeterPerSecond2 Acceleration
Stokes ST CM * CM / S Meter2PerSecond
Radiation absorbed dose RAD_ 100.0 * ERG / G Meter2PerSecond2
Radiation equivalent man REM_ RAD_ Meter2PerSecond2
Oersted OE 250.0 / consts::PI * A / M AmperePerMeter
Stilb SB CD / CM / CM CandelaPerMeter2
Lambert LMB SB / consts::PI CandelaPerMeter2
Roentgen ROE 2.58e-4 * C / KG CoulombPerGram
Tex TEX 1.0 * G / (KILO * M) GramPerMeter
Denier DEN TEX / 9.0 GramPerMeter
Peripheral vascular resistance unit PRU MHG * S / L GramPerMeter4Second
Planck constant H_ 6.6260755e-34 * J * S MilliJouleSecond
Boltzmann constant K_ 1.380658e-23 * J / K MilliJoulePerKelvin
Permittivity of vacuum EPS_0 8.854187817e-12 * F / M KiloFaradPerMeter
Permeability of vacuum MU_0 4.0e-7 * consts::PI * N / A / A MilliNewtonPerAmpere2
Newtonian constant of gravitation GC 6.67259e-11 * M3 / KG / S2 Meter3PerGramSecond2
Poise P DYN * S / CM / CM MilliPascalSecond
Metabolic equivalent MET 3.5 * MILLI * L / MIN / KG Meter3PerSecondGram


pub use self::f64consts::*;



Constants defined for $System of value type $t


Constants defined for $System of value type $t



The $System unit system

Type Definitions