# SI derived unit

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The International System of Units (SI) specifies a set of seven base units from which all other SI units of measurement are derived. Each of these other units (SI derived units) is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units.

For example, the SI derived unit of area is the square metre (m2), and the SI derived unit of density is the kilogram per cubic metre (kg/m3 or kg m−3). The degree Celsius (see the table below) has a somewhat unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase. The symbols for units named after persons, however, are always written with an uppercase initial letter (e.g. the symbol for the hertz is "Hz"; but the symbol for the metre is "m").[1]

## Derived units with special names

In addition to the two dimensionless derived units radian (rad) and steradian (sr), 20 other derived units have special names.

Named units derived from SI base units
NameSymbolQuantityEquivalentsSI base unit
Equivalents
hertzHzfrequency1/ss−1
radianradanglem/mdimensionless
steradiansrsolid anglem2/m2dimensionless
newtonNforce, weightkg⋅m/s2kg⋅m⋅s−2
pascalPapressure, stressN/m2kg⋅m−1⋅s−2
jouleJenergy, work, heatN⋅m
C⋅V
W⋅s
kg⋅m2⋅s−2
wattWpower, radiant fluxJ/s
V⋅A
kg⋅m2⋅s−3
coulombCelectric charge or quantity of electricitys⋅As⋅A
voltVvoltage, electrical potential difference, electromotive forceW/A
J/C
kg⋅m2⋅s−3⋅A−1
faradFelectrical capacitanceC/V
s/Ω
kg−1⋅m−2⋅s4⋅A2
ohmΩelectrical resistance, impedance, reactanceV/Akg⋅m2⋅s−3⋅A−2
siemensSelectrical conductance1/Ω
A/V
kg−1⋅m−2⋅s3⋅A2
weberWbmagnetic fluxJ/A
T⋅m2
kg⋅m2⋅s−2⋅A−1
teslaTmagnetic field strength, magnetic flux densityV⋅s/m2
Wb/m2
N/(A⋅m)
kg⋅s−2⋅A−1
henryHinductanceV⋅s/A
Ω⋅s
Wb/A
kg⋅m2⋅s−2⋅A−2
degree Celsius°Ctemperature relative to 273.15 KK − 273.15K − 273.15
lumenlmluminous fluxcd⋅srcd
luxlxilluminancelm/m2m−2⋅cd
becquerelBqradioactivity (decays per unit time)1/ss−1
grayGyabsorbed dose (of ionizing radiation)J/kgm2⋅s−2
sievertSvequivalent dose (of ionizing radiation)J/kgm2⋅s−2
katalkatcatalytic activitymol/ss−1⋅mol

## Examples of derived quantities and units

Some SI derived units
NameSymbolQuantityExpression in terms
of SI base units
square metrem2aream2
cubic metrem3volumem3
metre per secondm/sspeed, velocitym⋅s−1
cubic metre per secondm3/svolumetric flowm3⋅s−1
metre per second squaredm/s2accelerationm⋅s−2
metre per second cubedm/s3jerk, joltm⋅s−3
metre per quartic secondm/s4snap, jouncem⋅s−4
radian per secondrad/sangular velocitys−1
newton secondN⋅smomentum, impulsem⋅kg⋅s−1
newton metre secondN⋅m⋅sangular momentumm2⋅kg⋅s−1
newton metreN⋅m = J/radtorque, moment of forcem2⋅kg⋅s−2
newton per secondN/syankm⋅kg⋅s−3
reciprocal metrem−1wavenumberm−1
kilogram per square metrekg/m2area densitym−2⋅kg
kilogram per cubic metrekg/m3density, mass densitym−3⋅kg
cubic metre per kilogramm3/kgspecific volumem3⋅kg−1
mole per cubic metremol/m3amount of substance concentrationm−3⋅mol
cubic metre per molem3/molmolar volumem3⋅mol−1
joule secondJ⋅sactionm2⋅kg⋅s−1
joule per kelvinJ/Kheat capacity, entropym2⋅kg⋅s−2⋅K−1
joule per kelvin moleJ/(K⋅mol)molar heat capacity, molar entropym2⋅kg⋅s−2⋅K−1⋅mol−1
joule per kilogram kelvinJ/(K⋅kg)specific heat capacity, specific entropym2⋅s−2⋅K−1
joule per moleJ/molmolar energym2⋅kg⋅s−2⋅mol−1
joule per kilogramJ/kgspecific energym2⋅s−2
joule per cubic metreJ/m3energy densitym−1⋅kg⋅s−2
newton per metreN/m = J/m2surface tension, stiffnesskg⋅s−2
watt per square metreW/m2heat flux density, irradiancekg⋅s−3
watt per metre kelvinW/(m⋅K)thermal conductivitym⋅kg⋅s−3⋅K−1
square metre per secondm2/skinematic viscosity, diffusion coefficientm2⋅s−1
pascal secondPa⋅s = N⋅s/m2dynamic viscositym−1⋅kg⋅s−1
coulomb per square metreC/m2electric displacement field, polarization vectorm−2⋅s⋅A
coulomb per cubic metreC/m3electric charge densitym−3⋅s⋅A
ampere per square metreA/m2electric current densityA⋅m−2
siemens per metreS/mconductivitym−3⋅kg−1⋅s3⋅A2
siemens square metre per moleS⋅m2/molmolar conductivitykg-1⋅s3⋅mol−1⋅A2
farad per metreF/mpermittivitym−3⋅kg−1⋅s4⋅A2
henry per metreH/mpermeabilitym⋅kg⋅s−2⋅A−2
volt per metreV/melectric field strengthm⋅kg⋅s−3⋅A−1
ampere per metreA/mmagnetic field strengthA⋅m−1
candela per square metrecd/m2luminancecd⋅m−2
lumen secondlm⋅sluminous energycd⋅sr⋅s
lux secondlx⋅sluminous exposurecd⋅sr⋅s⋅m−2
coulomb per kilogramC/kgexposure (X and gamma rays)kg−1⋅s⋅A
gray per secondGy/sabsorbed dose ratem2⋅s−3
ohm metreΩ⋅mresistivitym3⋅kg⋅s−3⋅A−2

## Other units used with SI

Some other units such as the hour, litre, tonne, and electron volt are not SI units, but are widely used in conjunction with SI units.

## Supplementary units

Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned and the units were grouped as derived units.[2]

## Bibliography

• I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Blackwell Science Inc. p. 72.