Unified Code for Units of Measure

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] UCUM is used by different organizations like IEEE, and standards like DICOM, LOINC, HL7, and ISO 11240:2012.^[2]

The code set includes all units defined in ISO 1000, ISO 2955-1983,^[3]^[a] ANSI X3.50-1986,^[4]^[b] 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.^[5] 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:

The gram is the base unit of mass instead of the kilogram, since in UCUM base units do not have prefixes.
Electric charge is the base quantity for electromagnetic phenomena instead of electric current, since the elementary charge of electrons is more fundamental physically.
The mole is dimensionless in UCUM, since it can be defined in terms of the Avogadro number,
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 symbol^[6]
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

UCUM Metric prefixes
Prefix	UCUM Symbol	Factor	Power
yotta	Y	1000000000000000000000000	10²⁴
zetta	Z	1000000000000000000000	10²¹
exa	E	1000000000000000000	10¹⁸
peta	P	1000000000000000	10¹⁵
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	u	0.000001	10⁻⁶
nano	n	0.000000001	10⁻⁹
pico	p	0.000000000001	10⁻¹²
femto	f	0.000000000000001	10⁻¹⁵
atto	a	0.000000000000000001	10⁻¹⁸
zepto	z	0.000000000000000000001	10⁻²¹
yocto	y	0.000000000000000000000001	10⁻²⁴

Each unit represented in UCUM is identified as either "metric" or "non-metric".^[5] 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.^[5]

Binary prefixes are also supported.

UCUM Binary prefixes
Prefix	UCUM Symbol	Factor	Power
tebi	Ti	1099511627776	2⁴⁰
gibi	Gi	1073741824	2³⁰
mebi	Mi	1048576	2²⁰
kibi	Ki	1024	2¹⁰

Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units.^[5] 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 ^ In the SI, both the radian and steradian are dimensionless derived units. ^ 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	mN⋅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

Notes

^ Withdrawn without replacement.
^ Superseded by ISO 5807.

References

^ "UCUM". The UCUM Organization. Retrieved May 1, 2019.
^ "Unified Code for Units of Measure (UCUM)". National Library of Medicine. Retrieved 2024-07-07.
^ ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets [1]
^ FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING
^ ^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.
^ 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.

External links

Media related to Unified Code for Units of Measure at Wikimedia Commons
unitsofmeasure.org - The official UCUM web site. The UCUM Organization
Unified Code for Units of Measure (UCUM) at Lister Hill National Center for Biomedical Communications (LHNCBC), U.S. National Library of Medicine (NLM)
dimensioned::unit_systems::ucum - Rust
- The UCUM-LHC Validator and Converter
- UCUM Web Service (API)
"UOMo", Eclipse Foundation (2010)
"UCUM", Regenstrief Institute (2008)

[9] In the SI, both the radian and steradian are dimensionless derived units.

[10] In the SI, the coulomb is derived from the ampere. 1 C = 1 A × 1 s.

[4] Withdrawn without replacement.

[6] Superseded by ISO 5807.

[UCUM_Home-1] "UCUM". The UCUM Organization. Retrieved May 1, 2019.

[NLM-UCUM-2] "Unified Code for Units of Measure (UCUM)". National Library of Medicine. Retrieved 2024-07-07.

[3] ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets [1]

[5] FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING

[UCUM2.1-7] 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.

[UCUM2.1XML-8] 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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