Unified Code for Units of Measure explained

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] ANSI X3.50-1986,^[4] 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:

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! style="text-align: center"

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		10^24
zetta	Z		10^21
exa	E		10^18
peta	P		10^15
tera	T		10^12
giga	G		10^9
mega	M		10^6
kilo	k		10^3
hecto	h	100	10^2
deca	da	10	10^1
(none)	(none)	1	10^0
deci	d	0.1	10^−1
centi	c	0.01	10^−2
milli	m	0.001	10^−3
micro	u		10^−6
nano	n		10^−9
pico	p		10^−12
femto	f		10^−15
atto	a		10^−18
zepto	z		10^−21
yocto	y		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		2^40
gibi	Gi		2^30
mebi	Mi		2^20
kibi	Ki		2^10

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^[7]	solid angle	rad^2
millinewton	mN	force, weight	g⋅m⋅s^-2
millipascal	mPa	pressure, stress	g⋅m^-1⋅s^-2
millijoule	mJ	energy, work, heat	g⋅m^2⋅s^-2
milliwatt	mW	power, radiant flux	g⋅m^2⋅s^-3
ampere	A^[8]	electric current	C⋅s^-1
millivolt	mV	voltage, electrical potential difference, electromotive force	g⋅m^2⋅s^-2⋅C^-1
kilofarad	kF	electrical capacitance	g^-1⋅m^-2⋅s^3⋅C^2
milliohm	mΩ	electrical resistance, impedance, reactance	g⋅m^2⋅s^-1⋅C^-2
kilosiemens	kS	electrical conductance	g^-1⋅m^-2⋅s^1⋅C^2
milliweber	mWb	magnetic flux	g⋅m^2⋅s^-1⋅C^-1
millitesla	mT	magnetic induction, magnetic flux density	g⋅s^-1⋅C^-1
millihenry	mH	electrical inductance	g⋅m^2⋅C^-2
degree Celsius	°C	Celsius temperature	K
lumen	lm	luminous flux	cd⋅rad^2
lux	lx	illuminance	m^-2⋅cd⋅rad^2
becquerel	Bq	radioactivity (decays per unit time)	s^-1
gray	Gy	absorbed dose (of ionizing radiation)	m^2⋅s^-2
sievert	Sv	equivalent dose (of ionizing radiation)	m^2⋅s^-2
Notes

Kinematic units

Name	Symbol	Quantity	Expression in terms of UCUM base units
	m/s		m⋅s^-1
	m/s^2		m⋅s^-2
metre per second cubed	m/s^3		m⋅s^-3
metre per second to the fourth	m/s^4		m⋅s^-4
	rad/s		rad⋅s^-1
	rad/s^2		rad⋅s^-2
hertz per second	Hz/s		s^-2
	m^3/s		m^3⋅s^-1

Mechanical units

Name	Symbol	Quantity	Expression in terms of UCUM base units
	m^2		m^2
	m^3		m^3
millinewton second	mN⋅s		m⋅g⋅s^-1
millijoule second per radian	mN⋅m⋅s/rad		m^2⋅g⋅rad⋅s^-1
millijoule per radian	mN⋅m/rad = mJ/rad		m^2⋅g⋅rad⋅s^-2
millinewton per second	mN/s		m⋅g⋅s^-3
	m^-1		m^-1
gram per square metre	g/m^2		m^-2⋅g
gram per cubic metre	g/m^3	density, mass density	m^-3⋅g
cubic metre per gram	m^3/g		m^3⋅g^-1
millijoule second	mJ⋅s		m^2⋅g⋅s^-1
millijoule per gram	mJ/g		m^2⋅s^-2
millijoule per cubic metre	mJ/m^3		m^-1⋅g⋅s^-2
millinewton per metre	mN/m = mJ/m^2		g⋅s^-2
milliwatt per square metre	mW/m^2		g⋅s^-3
square metre per second	m^2/s	kinematic viscosity, thermal diffusivity, diffusion coefficient	m^2⋅s^-1
millipascal second	mPa⋅s = mN⋅s/m^2		m^-1⋅g⋅s^-1
gram per metre	g/m		m^-1⋅g
gram per second	g/s		g⋅s^-1
milliwatt per steradian square metre	mW/(sr⋅m^2)		g⋅rad^-2⋅s^-3
milliwatt per steradian cubic metre	mW/(sr⋅m^3)		m^-1⋅g⋅rad^-2⋅s^-3
milliwatt per metre	mW/m		m⋅g⋅s^-3
gray per second	Gy/s	absorbed dose rate	m^2⋅s^-3
metre per cubic metre	m/m^3		m^-2
milliwatt per cubic metre	mW/m^3		m^-1⋅g⋅s^-3
millijoule per square metre second	mJ/(m^2⋅s)		g⋅s^-3
reciprocal millipascal	mPa^-1		m⋅g^-1⋅s^2
millijoule per square metre	mJ/m^2		g⋅s^-2
gram square metre per steradian	g⋅m^2/sr		m^2⋅g⋅rad^-2
millijoule second per radian per gram	mN⋅m⋅s/rad/g		m^2⋅s^-1⋅rad^-1
milliwatt per steradian	mW/sr		m^2⋅g⋅rad^-2⋅s^-3
milliwatt per steradian metre	mW/(sr⋅m)		m⋅g⋅rad^-2⋅s^-3

Electromagnetic units

Name	Symbol	Quantity	Expression in terms of UCUM base units
coulomb per square metre	C/m^2		m^-2⋅C
coulomb per cubic metre	C/m^3		m^-3⋅C
ampere per square metre	A/m^2		m^-2⋅s^-1⋅C
kilosiemens per metre	kS/m	electrical conductivity	m^-3⋅g^-1⋅s^1⋅C^2
kilofarad per metre	kF/m		m^-3⋅g^-1⋅s^2⋅C^2
millihenry per metre	mH/m		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		m^3⋅g⋅s^-1⋅C^-2
coulomb per metre	C/m		m^-1⋅C
millijoule per millitesla	mJ/mT		m^2⋅s^-1⋅C
square metre per millivolt second	m^2/(mV⋅s)		g^-1⋅s⋅C
reciprocal millihenry	mH^-1		m^-2⋅g^-1⋅C^2
milliweber per metre	mWb/m		m⋅g⋅s^-1⋅C^-1
milliweber metre	mWb⋅m		m^3⋅g⋅s^-1⋅C^-1
millitesla metre	mT⋅m		m⋅g⋅s^-1⋅C^-1
ampere radian	A⋅rad		C⋅rad⋅s^-1
metre per millihenry	m/mH		m^-1⋅g^-1⋅C^2

Photometric units

Name	Symbol	Quantity	Expression in terms of UCUM base units
	lm⋅s		s⋅cd⋅rad^2
	lx⋅s		m^-2⋅s⋅cd⋅rad^2
	cd/m^2		m^-2⋅cd
lumen per milliwatt	lm/mW		m^-2⋅g^-1⋅s^3⋅cd⋅rad^2

Thermodynamic units

Name	Symbol	Quantity	Expression in terms of UCUM base units
millijoule per kelvin	mJ/K		m^2⋅g⋅s^-2⋅K^-1
millijoule per gram kelvin	mJ/(K⋅g)	specific heat capacity, specific entropy	m^2⋅s^-2⋅K^-1
milliwatt per metre kelvin	mW/(m⋅K)		m⋅g⋅s^-3⋅K^-1
kelvin per milliwatt	K/mW		m^-2⋅g^-1⋅s^3⋅K
reciprocal kelvin	K^-1		K^-1
kelvin per metre	K/m		m^-1⋅K

See also

• Outline of metrology and measurement
• GNU Units
• International vocabulary of metrology

Further reading

• Schadow. Gunther. McDonald. Clement J.. Jeffrey G.. Suico. Föhring. Ulrich . Tolxdorff. Thomas. 1999-03-01. Units of Measure in Clinical Information Systems. Journal of the American Medical Informatics Association. 6. 2. 151 - 162. 10.1136/jamia.1999.0060151. 10094068. 61354. free.

External links

• • 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)

Notes and References

1. Web site: UCUM . The UCUM Organization . May 1, 2019.
2. Web site: Unified Code for Units of Measure (UCUM) . . 2024-07-07.
3. ISO 2955:1983 Information processing — Representation of SI and other units in systems with limited character sets https://www.iso.org/standard/8005.html
4. https://global.ihs.com/doc_detail.cfm?document_name=ANSI%20X3%2E5&item_s_key=00009726 FLOWCHART SYMBOLS AND THEIR USAGE IN INFORMATION PROCESSING
5. Web site: The Unified Code for Units of Measure, version 2.1 . Gunther . Schadow . Clement J. . McDonald . November 21, 2017 . Regenstrief Institute and the UCUM Organization . 2019-05-13.
6. Web site: The Unified Code for Units of Measure (XML specification), version 2.1 . Gunther . Schadow . Clement J. . McDonald . November 21, 2017 . Regenstrief Institute and the UCUM Organization . 2019-12-20.
7. In the SI, both the radian and steradian are dimensionless derived units.
8. In the SI, the coulomb is derived from the ampere. 1 C = 1 A × 1 s.