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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 are either dimensionless, or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

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 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"; but the symbol for metre is "m".[1]

Derived units with special names[edit]

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/s s−1
radian rad angle m/m 1
steradian sr solid angle m2/m2 1
newton N force, weight kg⋅m/s2 kg⋅m⋅s−2
pascal Pa pressure, stress N/m2 kg⋅m−1⋅s−2
joule J energy, work, heat N⋅m
watt W power, radiant flux J/s
coulomb C electric charge or quantity of electricity s⋅A
volt V voltage, electrical potential difference, electromotive force W/A
farad F electrical capacitance C/V
ohm Ω electrical resistance, impedance, reactance 1/S
siemens S electrical conductance 1/Ω
weber Wb magnetic flux J/A
tesla T magnetic field strength, magnetic flux density V⋅s/m2
henry H electrical inductance V⋅s/A
degree Celsius °C temperature relative to 273.15 K K K
lumen lm luminous flux cd⋅sr cd
lux lx illuminance lm/m2 m−2⋅cd
becquerel Bq radioactivity (decays per unit time) 1/s s−1
gray Gy absorbed dose (of ionizing radiation) J/kg m2⋅s−2
sievert Sv equivalent dose (of ionizing radiation) J/kg m2⋅s−2
katal kat catalytic activity mol/s s−1⋅mol

Examples of derived quantities and units[edit]

Some SI derived units
Name Symbol Quantity Expression in terms
of SI base units
square metre m2 area m2
cubic metre m3 volume m3
metre per second m/s speed, velocity m⋅s−1
cubic metre per second m3/s volumetric flow m3⋅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 s−1
radian per second squared rad/s2 angular acceleration s−2
newton second N⋅s momentum, impulse m⋅kg⋅s−1
newton metre second N⋅m⋅s angular momentum m2⋅kg⋅s−1
newton metre N⋅m = J/rad torque, moment of force m2⋅kg⋅s−2
newton per second N/s yank m⋅kg⋅s−3
reciprocal metre m−1 wavenumber, optical power, curvature, spatial frequency m−1
kilogram per square metre kg/m2 area density m−2⋅kg
kilogram per cubic metre kg/m3 density, mass density m−3⋅kg
cubic metre per kilogram m3/kg specific volume m3⋅kg−1
mole per cubic metre mol/m3 molarity, amount of substance concentration m−3⋅mol
cubic metre per mole m3/mol molar volume m3⋅mol−1
joule second J⋅s action m2⋅kg⋅s−1
joule per kelvin J/K heat capacity, entropy m2⋅kg⋅s−2⋅K−1
joule per kelvin mole J/(K⋅mol) molar heat capacity, molar entropy m2⋅kg⋅s−2⋅K−1⋅mol−1
joule per kilogram kelvin J/(K⋅kg) specific heat capacity, specific entropy m2⋅s−2⋅K−1
joule per mole J/mol molar energy m2⋅kg⋅s−2⋅mol−1
joule per kilogram J/kg specific energy m2⋅s−2
joule per cubic metre J/m3 energy density m−1⋅kg⋅s−2
newton per metre N/m = J/m2 surface tension, stiffness kg⋅s−2
watt per square metre W/m2 heat flux density, irradiance kg⋅s−3
watt per metre kelvin W/(m⋅K) thermal conductivity m⋅kg⋅s−3⋅K−1
square metre per second m2/s kinematic viscosity, thermal diffusivity, diffusion coefficient m2⋅s−1
pascal second Pa⋅s = N⋅s/m2 dynamic viscosity m−1⋅kg⋅s−1
coulomb per square metre C/m2 electric displacement field, polarization density m−2⋅s⋅A
coulomb per cubic metre C/m3 electric charge density m−3⋅s⋅A
ampere per square metre A/m2 electric current density m−2⋅A
siemens per metre S/m electrical conductivity m−3⋅kg−1⋅s3⋅A2
siemens square metre per mole S⋅m2/mol molar conductivity kg−1⋅s3⋅A2⋅mol−1
farad per metre F/m permittivity m−3⋅kg−1⋅s4⋅A2
henry per metre H/m magnetic permeability m⋅kg⋅s−2⋅A−2
volt per metre V/m electric field strength m⋅kg⋅s−3⋅A−1
ampere per metre A/m magnetization, magnetic field strength m−1⋅A
candela per square metre cd/m2 luminance m−2⋅cd
lumen second lm⋅s luminous energy s⋅cd⋅sr
lux second lx⋅s luminous exposure m−2⋅s⋅cd⋅sr
coulomb per kilogram C/kg exposure (X and gamma rays) kg−1⋅s⋅A
gray per second Gy/s absorbed dose rate m2⋅s−3
ohm metre Ω⋅m resistivity m3⋅kg⋅s−3⋅A−2
kilogram per metre kg/m linear mass density m−1⋅kg
coulomb per metre C/m linear charge density m−1⋅s⋅A
mole per kilogram mol/kg molality kg−1⋅mol
kilogram per mole kg/mol molar mass kg⋅mol−1
metre per cubic metre m/m3 fuel efficiency m−2
kilogram per second kg/s mass flow rate kg⋅s−1
joule per tesla J/T magnetic dipole moment m2⋅A
watt per cubic metre W/m3 spectral irradiance, power density m−1⋅kg⋅s−3
kelvin per watt K/W thermal resistance m−2⋅kg−1⋅s3⋅K
reciprocal kelvin K−1 thermal expansion coefficient K−1
kelvin per metre K/m temperature gradient m−1⋅K
square metre per volt second m2/(V⋅s) electron mobility kg−1⋅s2⋅A
joule per square metre second J/(m2⋅s) energy flux density kg⋅s−3
reciprocal pascal Pa−1 compressibility m⋅kg−1⋅s2
reciprocal henry H−1 magnetic reluctance m−2⋅kg−1⋅s2⋅A2
weber per metre Wb/m magnetic vector potential m⋅kg⋅s−2⋅A−1
weber metre Wb⋅m magnetic moment m3⋅kg⋅s−2⋅A−1
tesla metre T⋅m magnetic rigidity m⋅kg⋅s−2⋅A−1
joule per square metre J/m2 radiant exposure kg⋅s−2
cubic metre per mole second m3/(mol⋅s) catalytic efficiency m3⋅s−1⋅mol−1
kilogram square metre kg⋅m2 moment of inertia m2⋅kg
newton metre second per kilogram N⋅m⋅s/kg specific angular momentum m2⋅s−1
hertz per second Hz/s frequency drift s−2
lumen per watt lm/W luminous efficacy m−2⋅kg−1⋅s3⋅cd⋅sr
ampere radian A⋅rad magnetomotive force A
metre per henry m/H magnetic susceptibility m−1⋅kg−1⋅s2⋅A2
watt per steradian W/sr radiant intensity m2⋅kg⋅s−3
watt per steradian metre W/(sr⋅m) spectral intensity m⋅kg⋅s−3
watt per steradian square metre W/(sr⋅m2) radiance kg⋅s−3
watt per steradian cubic metre W/(sr⋅m3) spectral radiance m−1⋅kg⋅s−3
watt per metre W/m spectral power m⋅kg⋅s−3

Other units used with SI[edit]

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[edit]

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[edit]



  • 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. 


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