Unified Code for Units of Measure

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The Unified Code for Units of Measure (UCUM) is a system of codes for unambiguously representing measurement units. Its primary purpose is machine-to-machine communication rather than communication between humans.[1]

The code set includes all units defined in ISO 1000, ISO 2955-1983, ANSI X3.50-1986, HL7 and ENV 12435, and explicitly and verifiably addresses the naming conflicts and ambiguities in those standards to resolve them. It provides for representations of units in 7 bit ASCII for machine-to-machine communication, with unambiguous mapping between case-sensitive and case-insensitive representations.

A reference open-source implementation is available as a Java applet. Also an OSGi based implementation at Eclipse Foundation.

Base units[edit]

Units are represented in UCUM with reference to a set of seven base units.[2] The UCUM base units are the metre for measurement of length, the second for time, the gram for mass, the coulomb for charge, the kelvin for temperature, the candela for luminous intensity, and the radian for plane angle. The UCUM base units form a set of mutually independent dimensions as required by dimensional analysis.

Some of the UCUM base units are different from the SI base units. UCUM is compatible with, but not isomorphic with SI. There are four differences between the two sets of base units:

  1. The gram is the base unit of mass instead of the kilogram, since in UCUM base units do not have prefixes.
  2. Electric charge is the base quantity for electromagnetic phenomena instead of electric current, since the elementary charge of electrons is more fundamental physically.
  3. The mole is dimensionless in UCUM, since it can be defined in terms of the Avogadro number,
  4. The radian is a distinct base unit for plane angle, to distinguish angular velocity from rotational frequency and to distinguish the radian from the steradian for solid angles.
UCUM base units
Name Symbol Measure Dimension
metre m length L
second s time T
gram g mass M
coulomb C charge Q
kelvin K thermodynamic temperature C
candela cd luminous intensity F
radian rad plane angle A

Metric and non-metric units[edit]

Prefix Symbol Factor Power
tera T 1000000000000 1012
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
hecto h 100 102
deca da 10 101
(none) (none) 1 100
deci d 0.1 10−1
centi c 0.01 10−2
milli m 0.001 10−3
micro μ 0.000001 10−6
nano n 0.000000001 10−9
pico p 0.000000000001 10−12

Each unit represented in UCUM is identified as either "metric" or "non-metric".[2] Metric units can accept metric prefixes as in SI. Non-metric units are not permitted to be used with prefixes. All of the base units are metric.

UCUM refers to units that are defined on non-ratio scales as "special units". Common examples include the bel and degree Celsius. While these are not considered metric units by UCUM, UCUM nevertheless allows metric prefixes to be used with them where this is common practice.[2]

Binary prefixes are also supported.

Arbitrary units[edit]

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units.[2] These units are identified as "arbitrary units". Arbitrary units are not commensurable with any other unit; measurements in arbitrary units cannot be compared with or converted into measurements in any other units. Many of the recognized arbitrary units are used in biochemistry and medicine.

Derived units[edit]

Any metric unit in any common system of units can be expressed in terms of the UCUM base units

Units derived from UCUM base units
Name Symbol Quantity UCUM base unit
hertz Hz frequency s−1
steradian sr[n 1] solid angle rad2
millinewton mN force, weight g⋅m⋅s−2
millipascal mPa pressure, stress g⋅m−1⋅s−2
millijoule mJ energy, work, heat g⋅m2⋅s−2
milliwatt mW power, radiant flux g⋅m2⋅s−3
ampere A[n 2] electric current C⋅s−1
millivolt mV voltage, electrical potential difference, electromotive force g⋅m2⋅s−2⋅C−1
kilofarad kF electrical capacitance g−1⋅m−2⋅s3⋅C2
milliohm electrical resistance, impedance, reactance g⋅m2⋅s−1⋅C−2
kilosiemens kS electrical conductance g−1⋅m−2⋅s1⋅C2
milliweber mWb magnetic flux g⋅m2⋅s−1⋅C−1
millitesla mT magnetic induction, magnetic flux density g⋅s−1⋅C−1
millihenry mH electrical inductance g⋅m2⋅C−2
degree Celsius °C Celsius temperature K
lumen lm luminous flux cd⋅rad2
lux lx illuminance m−2⋅cd⋅rad2
becquerel Bq radioactivity (decays per unit time) s−1
gray Gy absorbed dose (of ionizing radiation) m2⋅s−2
sievert Sv equivalent dose (of ionizing radiation) m2⋅s−2
  1. ^ In the SI, both the radian and steradian are dimensionless derived units.
  2. ^ In the SI, the coulomb is derived from the ampere. 1 C = 1 A × 1 s.
Kinematic units
Name Symbol Quantity Expression in terms
of UCUM base units
metre per second m/s speed, velocity m⋅s−1
metre per second squared m/s2 acceleration m⋅s−2
metre per second cubed m/s3 jerk, jolt m⋅s−3
metre per second to the fourth m/s4 snap, jounce m⋅s−4
radian per second rad/s angular velocity rad⋅s−1
radian per second squared rad/s2 angular acceleration rad⋅s−2
hertz per second Hz/s frequency drift s−2
cubic metre per second m3/s volumetric flow m3⋅s−1
Mechanical units
Name Symbol Quantity Expression in terms
of UCUM base units
square metre m2 area m2
cubic metre m3 volume m3
millinewton second mN⋅s momentum, impulse m⋅g⋅s−1
millijoule second per radian mN⋅m⋅s/rad angular momentum m2⋅g⋅rad⋅s−1
millijoule per radian nN⋅m/rad = mJ/rad torque m2⋅g⋅rad⋅s−2
millinewton per second mN/s yank m⋅g⋅s−3
reciprocal metre m−1 wavenumber, optical power, curvature, spatial frequency m−1
gram per square metre g/m2 area density m−2⋅g
gram per cubic metre g/m3 density, mass density m−3⋅g
cubic metre per gram m3/g specific volume m3⋅g−1
millijoule second mJ⋅s action m2⋅g⋅s−1
millijoule per gram mJ/g specific energy m2⋅s−2
millijoule per cubic metre mJ/m3 energy density m−1⋅g⋅s−2
millinewton per metre mN/m = mJ/m2 surface tension, stiffness g⋅s−2
milliwatt per square metre mW/m2 heat flux density, irradiance g⋅s−3
square metre per second m2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2⋅s−1
millipascal second mPa⋅s = mN⋅s/m2 dynamic viscosity m−1⋅g⋅s−1
gram per metre g/m linear mass density m−1⋅g
gram per second g/s mass flow rate g⋅s−1
milliwatt per steradian square metre mW/(sr⋅m2) radiance g⋅rad−2⋅s−3
milliwatt per steradian cubic metre mW/(sr⋅m3) radiance m−1⋅g⋅rad−2⋅s−3
milliwatt per metre mW/m spectral power m⋅g⋅s−3
gray per second Gy/s absorbed dose rate m2⋅s−3
metre per cubic metre m/m3 fuel efficiency m−2
milliwatt per cubic metre mW/m3 spectral irradiance, power density m−1⋅g⋅s−3
millijoule per square metre second mJ/(m2⋅s) energy flux density g⋅s−3
reciprocal millipascal mPa−1 compressibility m⋅g−1⋅s2
millijoule per square metre mJ/m2 radiant exposure g⋅s−2
gram square metre per steradian g⋅m2/sr moment of inertia m2⋅g⋅rad−2
millijoule second per radian per gram mN⋅m⋅s/rad/g specific angular momentum m2⋅s−1⋅rad−1
milliwatt per steradian mW/sr radiant intensity m2⋅g⋅rad−2⋅s−3
milliwatt per steradian metre mW/(sr⋅m) spectral intensity m⋅g⋅rad−2⋅s−3
Electromagnetic units
Name Symbol Quantity Expression in terms
of UCUM base units
coulomb per square metre C/m2 electric displacement field, polarization density m−2⋅C
coulomb per cubic metre C/m3 electric charge density m−3⋅C
ampere per square metre A/m2 electric current density m−2⋅s−1⋅C
kilosiemens per metre kS/m electrical conductivity m−3⋅g−1⋅s1⋅C2
kilofarad per metre kF/m permittivity m−3⋅g−1⋅s2⋅C2
millihenry per metre mH/m magnetic permeability m⋅g⋅C−2
millivolt per metre mV/m electric field strength m⋅g⋅s−2⋅C−1
ampere per metre A/m magnetization, magnetic field strength m−1⋅s−1⋅C
coulomb per gram C/g exposure (X and gamma rays) g−1⋅C
milliohm metre mΩ⋅m resistivity m3⋅g⋅s−1⋅C−2
coulomb per metre C/m linear charge density m−1⋅C
millijoule per millitesla mJ/mT magnetic dipole moment m2⋅s−1⋅C
square metre per millivolt second m2/(mV⋅s) electron mobility g−1⋅s⋅C
reciprocal millihenry mH−1 magnetic reluctance m−2⋅g−1⋅C2
milliweber per metre mWb/m magnetic vector potential m⋅g⋅s−1⋅C−1
milliweber metre mWb⋅m magnetic moment m3⋅g⋅s−1⋅C−1
millitesla metre mT⋅m magnetic rigidity m⋅g⋅s−1⋅C−1
ampere radian A⋅rad magnetomotive force C⋅rad⋅s−1
metre per millihenry m/mH magnetic susceptibility m−1⋅g−1⋅C2
Photometric units
Name Symbol Quantity Expression in terms
of UCUM base units
lumen second lm⋅s luminous energy s⋅cd⋅rad2
lux second lx⋅s luminous exposure m−2⋅s⋅cd⋅rad2
candela per square metre cd/m2 luminance m−2⋅cd
lumen per milliwatt lm/mW luminous efficacy m−2⋅g−1⋅s3⋅cd⋅rad2
Thermodynamic units
Name Symbol Quantity Expression in terms
of UCUM base units
millijoule per kelvin mJ/K heat capacity, entropy m2⋅g⋅s−2⋅K−1
millijoule per gram kelvin mJ/(K⋅g) specific heat capacity, specific entropy m2⋅s−2⋅K−1
milliwatt per metre kelvin mW/(m⋅K) thermal conductivity m⋅g⋅s−3⋅K−1
kelvin per milliwatt K/mW thermal resistance m−2⋅g−1⋅s3⋅K
reciprocal kelvin K−1 thermal expansion coefficient K−1
kelvin per metre K/m temperature gradient m−1⋅K

See also[edit]


  1. ^ "UCUM". The UCUM Organization. Retrieved May 1, 2019.
  2. ^ a b c d Schadow, Gunther; McDonald, Clement J. (November 21, 2017). "The Unified Code for Units of Measure, version 2.1". Regenstrief Institute and the UCUM Organization. Retrieved 2019-05-13.
  3. ^ Schadow, Gunther; McDonald, Clement J. (November 21, 2017). "The Unified Code for Units of Measure (XML specification), version 2.1". Regenstrief Institute and the UCUM Organization. Retrieved 2019-12-20.

Further reading[edit]

External links[edit]