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]

Contents

The code set includes all units defined in ISO 1000, ISO 2955-1983, [2] [lower-alpha 1] ANSI X3.50-1986, [3] [lower-alpha 2] 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. There is also an OSGi-based implementation at Eclipse Foundation.

Base units

Units are represented in UCUM with reference to a set of seven base units. [4] 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
NameSymbolMeasure Dimension
symbol [5]
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

Metric prefixes in everyday use
PrefixSymbolFactorPower
teraT10000000000001012
gigaG1000000000109
megaM1000000106
kilok1000103
hectoh100102
decada10101
(none)(none)1100
decid0.110−1
centic0.0110−2
millim0.00110−3
microμ0.00000110−6
nanon0.00000000110−9
picop0.00000000000110−12

Each unit represented in UCUM is identified as either "metric" or "non-metric". [4] 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. [4]

Binary prefixes are also supported.

Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units. [4] 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

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
Equivalents
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 mΩ 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
Notes
  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
NameSymbolQuantityExpression 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 cubedm/s3 jerk, jolt m⋅s−3
metre per second to the fourthm/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 secondHz/s frequency drift s−2
cubic metre per second m3/s volumetric flow m3⋅s−1
Mechanical units
NameSymbolQuantityExpression in terms
of UCUM base units
square metre m2 area m2
cubic metre m3 volume m3
millinewton secondmN⋅s momentum, impulse m⋅g⋅s−1
millijoule second per radianmN⋅m⋅s/rad angular momentum m2⋅g⋅rad⋅s−1
millijoule per radianmN⋅m/rad = mJ/rad torque m2⋅g⋅rad⋅s−2
millinewton per secondmN/s yank m⋅g⋅s−3
reciprocal metre m−1 wavenumber, optical power, curvature, spatial frequency m−1
gram per square metreg/m2 area density m−2⋅g
gram per cubic metreg/m3 density, mass densitym−3⋅g
cubic metre per gramm3/g specific volume m3⋅g−1
millijoule secondmJ⋅s action m2⋅g⋅s−1
millijoule per grammJ/g specific energy m2⋅s−2
millijoule per cubic metremJ/m3 energy density m−1⋅g⋅s−2
millinewton per metremN/m = mJ/m2 surface tension, stiffness g⋅s−2
milliwatt per square metremW/m2heat flux density, irradiance g⋅s−3
square metre per secondm2/s kinematic viscosity, thermal diffusivity, diffusion coefficientm2⋅s−1
millipascal secondmPa⋅s = mN⋅s/m2dynamic viscosity m−1⋅g⋅s−1
gram per metreg/m linear mass density m−1⋅g
gram per secondg/s mass flow rate g⋅s−1
milliwatt per steradian square metremW/(sr⋅m2) radiance g⋅rad−2⋅s−3
milliwatt per steradian cubic metremW/(sr⋅m3) radiance m−1⋅g⋅rad−2⋅s−3
milliwatt per metremW/m spectral power m⋅g⋅s−3
gray per secondGy/s absorbed dose ratem2⋅s−3
metre per cubic metrem/m3 fuel efficiency m−2
milliwatt per cubic metremW/m3 spectral irradiance, power density m−1⋅g⋅s−3
millijoule per square metre secondmJ/(m2⋅s) energy flux density g⋅s−3
reciprocal millipascalmPa−1 compressibility m⋅g−1⋅s2
millijoule per square metremJ/m2 radiant exposure g⋅s−2
gram square metre per steradiang⋅m2/sr moment of inertia m2⋅g⋅rad−2
millijoule second per radian per grammN⋅m⋅s/rad/g specific angular momentum m2⋅s−1⋅rad−1
milliwatt per steradianmW/sr radiant intensity m2⋅g⋅rad−2⋅s−3
milliwatt per steradian metremW/(sr⋅m) spectral intensity m⋅g⋅rad−2⋅s−3
Electromagnetic units
NameSymbolQuantityExpression in terms
of UCUM base units
coulomb per square metreC/m2 electric displacement field, polarization density m−2⋅C
coulomb per cubic metreC/m3electric charge density m−3⋅C
ampere per square metreA/m2electric current density m−2⋅s−1⋅C
kilosiemens per metrekS/m electrical conductivity m−3⋅g−1⋅s1⋅C2
kilofarad per metrekF/m permittivity m−3⋅g−1⋅s2⋅C2
millihenry per metremH/m magnetic permeability m⋅g⋅C−2
millivolt per metremV/m electric field strengthm⋅g⋅s−2⋅C−1
ampere per metreA/m magnetization, magnetic field strengthm−1⋅s−1⋅C
coulomb per gramC/g exposure (X and gamma rays)g−1⋅C
milliohm metremΩ⋅m resistivity m3⋅g⋅s−1⋅C−2
coulomb per metreC/m linear charge density m−1⋅C
millijoule per milliteslamJ/mT magnetic dipole moment m2⋅s−1⋅C
square metre per millivolt secondm2/(mV⋅s) electron mobility g−1⋅s⋅C
reciprocal millihenrymH−1 magnetic reluctance m−2⋅g−1⋅C2
milliweber per metremWb/m magnetic vector potential m⋅g⋅s−1⋅C−1
milliweber metremWb⋅m magnetic moment m3⋅g⋅s−1⋅C−1
millitesla metremT⋅m magnetic rigidity m⋅g⋅s−1⋅C−1
ampere radianA⋅rad magnetomotive force C⋅rad⋅s−1
metre per millihenrym/mH magnetic susceptibility m−1⋅g−1⋅C2
Photometric units
NameSymbolQuantityExpression 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 milliwattlm/mW luminous efficacy m−2⋅g−1⋅s3⋅cd⋅rad2
Thermodynamic units
NameSymbolQuantityExpression in terms
of UCUM base units
millijoule per kelvinmJ/K heat capacity, entropy m2⋅g⋅s−2⋅K−1
millijoule per gram kelvinmJ/(K⋅g) specific heat capacity, specific entropym2⋅s−2⋅K−1
milliwatt per metre kelvinmW/(m⋅K) thermal conductivity m⋅g⋅s−3⋅K−1
kelvin per milliwattK/mW thermal resistance m−2⋅g−1⋅s3⋅K
reciprocal kelvinK−1 thermal expansion coefficient K−1
kelvin per metreK/m temperature gradient m−1⋅K

See also

Notes

  1. ↑ Withdrawn without replacement.
  2. ↑ Superseded by ISO 5807.

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References

  1. ↑ "UCUM". The UCUM Organization. Retrieved May 1, 2019.
  2. ↑ ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets
  3. ↑ FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING
  4. 1 2 3 4 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.
  5. ↑ 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.

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