SI derived unit

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SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities.


The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg⋅m−3), the SI derived unit of density.

The names of SI derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m". [1]

Special names

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Named units derived from SI base units [2]
Name Symbol Quantity Equivalents SI base unit
hertz Hz frequency 1/ss1
radian rad angle m/m1
steradian sr solid angle m2/m21
newton N force, weight kg⋅m/s2kg⋅m⋅s2
pascal Pa pressure, stress N/m2kg⋅m1⋅s2
joule J energy, work, heat m⋅N, C⋅V, W⋅skg⋅m2⋅s2
watt W power, radiant flux J/s, V⋅Akg⋅m2⋅s3
coulomb C electric charge or quantity of electricity s⋅A, F⋅Vs⋅A
volt V voltage, electrical potential difference, electromotive force W/A, J/Ckg⋅m2⋅s3⋅A1
farad F electrical capacitance C/V, s/Ωkg1⋅m2⋅s4⋅A2
ohm Ω electrical resistance, impedance, reactance 1/S, V/Akg⋅m2⋅s3⋅A2
siemens S electrical conductance 1/Ω, A/Vkg1⋅m2⋅s3⋅A2
weber Wb magnetic flux J/A, T⋅m2,V⋅skg⋅m2⋅s2⋅A1
tesla T magnetic induction, magnetic flux density V⋅s/m2, Wb/m2, N/(A⋅m)kg⋅s2⋅A1
henry H electrical inductance V⋅s/A, Ω⋅s, Wb/Akg⋅m2⋅s2⋅A2
degree Celsius °C temperature relative to 273.15 K KK
lumen lm luminous flux cd⋅srcd
lux lx illuminance lm/m2cd⋅m2
becquerel Bq radioactivity (decays per unit time)1/ss1
gray Gy absorbed dose (of ionizing radiation)J/kgm2⋅s2
sievert Sv equivalent dose (of ionizing radiation)J/kgm2⋅s2
katal kat catalytic activity mol/ss1⋅mol.

Examples of derived quantities and units

Kinematic SI derived units
NameSymbolQuantityExpression in terms
of SI base units
metre per second m/s speed, velocity m⋅s1
metre per second squared m/s2 acceleration m⋅s2
metre per second cubedm/s3 jerk, jolt m⋅s3
metre per second to the fourthm/s4 snap, jounce m⋅s4
radian per second rad/s angular velocity s1
radian per second squared rad/s2 angular acceleration s2
hertz per secondHz/s frequency drift s2
cubic metre per second m3/s volumetric flow m3⋅s1
Mechanical SI derived units
NameSymbolQuantityExpression in terms
of SI base units
square metre m2 area m2
cubic metre m3 volume m3
newton-second N⋅s momentum, impulse m⋅kg⋅s1
newton metre secondN⋅m⋅s angular momentum m2⋅kg⋅s1
newton-metre N⋅m = J/rad torque, moment of force m2⋅kg⋅s2
newton per secondN/s yank m⋅kg⋅s3
reciprocal metre m1 wavenumber, optical power, curvature, spatial frequency m1
kilogram per square metrekg/m2 area density m2⋅kg
kilogram per cubic metre kg/m3 density, mass densitym3⋅kg
cubic metre per kilogramm3/kg specific volume m3⋅kg1
joule-second J⋅s action m2⋅kg⋅s1
joule per kilogramJ/kg specific energy m2⋅s2
joule per cubic metreJ/m3 energy density m1⋅kg⋅s2
newton per metreN/m = J/m2 surface tension, stiffness kg⋅s2
watt per square metreW/m2heat flux density, irradiance kg⋅s3
square metre per secondm2/s kinematic viscosity, thermal diffusivity, diffusion coefficientm2⋅s1
pascal-second Pa⋅s = N⋅s/m2dynamic viscosity m1⋅kg⋅s1
kilogram per metrekg/m linear mass density m1⋅kg
kilogram per secondkg/s mass flow rate kg⋅s1
watt per steradian square metreW/(sr⋅m2) radiance kg⋅s3
watt per steradian cubic metreW/(sr⋅m3) radiance m1⋅kg⋅s3
watt per metreW/m spectral power m⋅kg⋅s3
gray per secondGy/s absorbed dose ratem2⋅s3
metre per cubic metrem/m3 fuel efficiency m2
watt per cubic metreW/m3 spectral irradiance, power density m1⋅kg⋅s3
joule per square metre secondJ/(m2⋅s) energy flux density kg⋅s3
reciprocal pascalPa1 compressibility m⋅kg1⋅s2
joule per square metreJ/m2 radiant exposure kg⋅s2
kilogram square metrekg⋅m2 moment of inertia m2⋅kg
newton metre second per kilogramN⋅m⋅s/kg specific angular momentum m2⋅s1
watt per steradianW/sr radiant intensity m2⋅kg⋅s3
watt per steradian metreW/(sr⋅m) spectral intensity m⋅kg⋅s3
Molar SI derived units
NameSymbolQuantityExpression in terms
of SI base units
mole per cubic metremol/m3 molarity, amount of substance concentrationm3⋅mol
cubic metre per mole m3/mol molar volume m3⋅mol1
joule per kelvin moleJ/(K⋅mol) molar heat capacity, molar entropym2⋅kg⋅s2⋅K1⋅mol1
joule per mole J/molmolar energym2⋅kg⋅s2⋅mol1
siemens square metre per moleS⋅m2/mol molar conductivity kg−1⋅s3⋅A2⋅mol1
mole per kilogrammol/kg molality kg1⋅mol
kilogram per molekg/mol molar mass kg⋅mol1
cubic metre per mole secondm3/(mol⋅s) catalytic efficiency m3⋅s1⋅mol1
Electromagnetic SI derived units
NameSymbolQuantityExpression in terms
of SI base units
coulomb per square metreC/m2 electric displacement field, polarization density m2⋅s⋅A
coulomb per cubic metreC/m3electric charge density m3⋅s⋅A
ampere per square metreA/m2electric current density m2⋅A
siemens per metre S/m electrical conductivity m3⋅kg1⋅s3⋅A2
farad per metreF/m permittivity m3⋅kg1⋅s4⋅A2
henry per metreH/m magnetic permeability m⋅kg⋅s2⋅A2
volt per metreV/m electric field strengthm⋅kg⋅s3⋅A1
ampere per metreA/m magnetization, magnetic field strengthm1⋅A
coulomb per kilogramC/kg exposure (X and gamma rays)kg1⋅s⋅A
ohm metre Ω⋅m resistivity m3⋅kg⋅s3⋅A2
coulomb per metreC/m linear charge density m1⋅s⋅A
joule per teslaJ/T magnetic dipole moment m2⋅A
square metre per volt secondm2/(V⋅s) electron mobility kg1⋅s2⋅A
reciprocal henryH1 magnetic reluctance m2⋅kg1⋅s2⋅A2
weber per metreWb/m magnetic vector potential m⋅kg⋅s2⋅A1
weber metreWb⋅m magnetic moment m3⋅kg⋅s2⋅A1
tesla metreT⋅m magnetic rigidity m⋅kg⋅s2⋅A1
ampere radianA⋅rad magnetomotive force A
metre per henrym/H magnetic susceptibility m1⋅kg1⋅s2⋅A2
Photometric SI derived units
NameSymbolQuantityExpression in terms
of SI base units
lumen second lm⋅s luminous energy s⋅cd
lux second lx⋅s luminous exposure m2⋅s⋅cd
candela per square metre cd/m2 luminance m2⋅cd
lumen per wattlm/W luminous efficacy m2⋅kg1⋅s3⋅cd
Thermodynamic SI derived units
NameSymbolQuantityExpression in terms
of SI base units
joule per kelvinJ/K heat capacity, entropy m2⋅kg⋅s2⋅K1
joule per kilogram kelvinJ/(K⋅kg) specific heat capacity, specific entropym2⋅s2⋅K1
watt per metre kelvinW/(m⋅K) thermal conductivity m⋅kg⋅s3⋅K1
kelvin per wattK/W thermal resistance m2⋅kg1⋅s3⋅K
reciprocal kelvinK1 thermal expansion coefficient K1
kelvin per metreK/m temperature gradient m1⋅K

Other units used with SI

Some other units such as the hour, litre, tonne, bar, and electronvolt 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. [3]

See also

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  1. Suplee, Curt (2 July 2009). "Special Publication 811".
  2. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN   92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
  3. "Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures . Retrieved 23 September 2014.