# 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. UCUM is used by different organizations like IEEE, and standards like DICOM, LOINC, HL7, and ISO 11240:2012.
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. 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. 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 |
| 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 | 10$^{24}$ |
| zetta | Z | 1000000000000000000000 | 10$^{21}$ |
| exa | E | 1000000000000000000 | 10$^{18}$ |
| peta | P | 1000000000000000 | 10$^{15}$ |
| tera | T | 1000000000000 | 10$^{12}$ |
| giga | G | 1000000000 | 10$^9$ |
| mega | M | 1000000 | 10$^6$ |
| kilo | k | 1000 | 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 | 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". 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.
Binary prefixes are also supported.
UCUM Binary prefixes :
| Prefix | UCUM Symbol | Factor | Power |
| tebi | Ti | 1099511627776 | 2$^{40}$ |
| gibi | Gi | 1073741824 | 2$^{30}$ |
| mebi | Mi | 1048576 | 2$^{20}$ |
| kibi | Ki | 1024 | 2$^{10}$ |

## Arbitrary units

UCUM recognizes units that are defined by a particular measurement procedure, and which cannot be related to the base units. 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 | 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 | 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 ↑ 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/s$^2$ | acceleration | m⋅s$^{−2}$ |
| metre per second cubed | m/s$^3$ | jerk, jolt | m⋅s$^{−3}$ |
| metre per second to the fourth | m/s$^4$ | snap, jounce | m⋅s$^{−4}$ |
| radian per second | rad/s | angular velocity | rad⋅s$^{−1}$ |
| radian per second squared | rad/s$^2$ | angular acceleration | rad⋅s$^{−2}$ |
| hertz per second | Hz/s | frequency drift | s$^{−2}$ |
| cubic metre per second | m$^3$/s | volumetric flow | m$^3$⋅s$^{−1}$ |
Mechanical units :
| Name | Symbol | Quantity | Expression in terms of UCUM base units |
| square metre | m$^2$ | area | m$^2$ |
| cubic metre | m$^3$ | volume | m$^3$ |
| millinewton second | mN⋅s | momentum, impulse | m⋅g⋅s$^{−1}$ |
| millijoule second per radian | mN⋅m⋅s/rad | angular momentum | m$^2$⋅g⋅rad⋅s$^{−1}$ |
| millijoule per radian | mN⋅m/rad = mJ/rad | torque | m$^2$⋅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/m$^2$ | area density | m$^{−2}$⋅g |
| gram per cubic metre | g/m$^3$ | density, mass density | m$^{−3}$⋅g |
| cubic metre per gram | m$^3$/g | specific volume | m$^3$⋅g$^{−1}$ |
| millijoule second | mJ⋅s | action | m$^2$⋅g⋅s$^{−1}$ |
| millijoule per gram | mJ/g | specific energy | m$^2$⋅s$^{−2}$ |
| millijoule per cubic metre | mJ/m$^3$ | energy density | m$^{−1}$⋅g⋅s$^{−2}$ |
| millinewton per metre | mN/m = mJ/m$^2$ | surface tension, stiffness | g⋅s$^{−2}$ |
| milliwatt per square metre | mW/m$^2$ | heat flux density, irradiance | 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$^2$ | 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⋅m$^2$) | radiance | g⋅rad$^{−2}$⋅s$^{−3}$ |
| milliwatt per steradian cubic metre | mW/(sr⋅m$^3$) | 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 | m$^2$⋅s$^{−3}$ |
| metre per cubic metre | m/m$^3$ | fuel efficiency | m$^{−2}$ |
| milliwatt per cubic metre | mW/m$^3$ | spectral irradiance, power density | m$^{−1}$⋅g⋅s$^{−3}$ |
| millijoule per square metre second | mJ/(m$^2$⋅s) | energy flux density | g⋅s$^{−3}$ |
| reciprocal millipascal | mPa$^{−1}$ | compressibility | m⋅g$^{−1}$⋅s$^2$ |
| millijoule per square metre | mJ/m$^2$ | radiant exposure | g⋅s$^{−2}$ |
| gram square metre per steradian | g⋅m$^2$/sr | moment of inertia | m$^2$⋅g⋅rad$^{−2}$ |
| millijoule second per radian per gram | mN⋅m⋅s/rad/g | specific angular momentum | m$^2$⋅s$^{−1}$⋅rad$^{−1}$ |
| milliwatt per steradian | mW/sr | radiant intensity | m$^2$⋅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/m$^2$ | electric displacement field, polarization density | m$^{−2}$⋅C |
| coulomb per cubic metre | C/m$^3$ | electric charge density | m$^{−3}$⋅C |
| ampere per square metre | A/m$^2$ | electric current density | 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 | permittivity | m$^{−3}$⋅g$^{−1}$⋅s$^2$⋅C$^2$ |
| 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 | m$^3$⋅g⋅s$^{−1}$⋅C$^{−2}$ |
| coulomb per metre | C/m | linear charge density | m$^{−1}$⋅C |
| millijoule per millitesla | mJ/mT | magnetic dipole moment | m$^2$⋅s$^{−1}$⋅C |
| square metre per millivolt second | m$^2$/(mV⋅s) | electron mobility | g$^{−1}$⋅s⋅C |
| reciprocal millihenry | mH$^{−1}$ | magnetic reluctance | m$^{−2}$⋅g$^{−1}$⋅C$^2$ |
| milliweber per metre | mWb/m | magnetic vector potential | m⋅g⋅s$^{−1}$⋅C$^{−1}$ |
| milliweber metre | mWb⋅m | magnetic moment | m$^3$⋅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$^{−1}$⋅C$^2$ |
Photometric units :
| Name | Symbol | Quantity | Expression in terms of UCUM base units |
| lumen second | lm⋅s | luminous energy | s⋅cd⋅rad$^2$ |
| lux second | lx⋅s | luminous exposure | m$^{−2}$⋅s⋅cd⋅rad$^2$ |
| candela per square metre | cd/m$^2$ | luminance | m$^{−2}$⋅cd |
| lumen per milliwatt | lm/mW | luminous efficacy | 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 | heat capacity, entropy | 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) | thermal conductivity | m⋅g⋅s$^{−3}$⋅K$^{−1}$ |
| kelvin per milliwatt | K/mW | thermal resistance | m$^{−2}$⋅g$^{−1}$⋅s$^3$⋅K |
| reciprocal kelvin | K$^{−1}$ | thermal expansion coefficient | K$^{−1}$ |
| kelvin per metre | K/m | temperature gradient | m$^{−1}$⋅K |