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# SI derived unit

SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.

## Dimensionless derived units

The following SI units are actually dimensionless ratios, formed by dividing two identical SI units. They are therefore considered by the BIPM to be derived. Formally, their SI unit is simply the number 1, but they are given these special names, for use whenever the lack of a unit might be confusing.

Dimensionless SI units
Name Symbol Quantity Definition
radian rad angle The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are radians in a circle.
steradian sr solid angle The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are steradians on a sphere.

## Derived units with special names

Base units can be put together to derive units of measurement for other quantities. In addition to the two dimensionless derived units rad and sr there are 20 derived units having special names:

Named units derived from SI base units

Name Symbol Quantity Expression in terms of other units Expression in terms of SI base units
hertz Hz frequency 1/s s−1
newton N force, weight m∙kg/s2 m∙kg∙s−2
pascal Pa pressure, stress N/m2 m−1∙kg∙s−2
joule J energy, work, heat N∙m m2∙kg∙s−2
watt W power, radiant flux J/s m2∙kg∙s−3
coulomb C electric charge or electric flux s∙A s∙A
volt V voltage, electrical potential difference, electromotive force W/A = J/C m2∙kg∙s−3∙A−1
farad F electric capacitance C/V m−2∙kg−1∙s4∙A2
ohm Ω electric resistance, impedance, reactance V/A m2∙kg∙s−3∙A−2
siemens S electrical conductance 1/Ω m−2∙kg−1∙s3∙A2
weber Wb magnetic flux J/A m2∙kg∙s−2∙A−1
tesla T magnetic field V∙s/m2 = Wb/m2 = N/A∙m kg∙s−2∙A−1
henry H inductance V∙s/A = Wb/A m2∙kg∙s−2∙A−2
Celsius °C Celsius Temperature t°C = tK − 273.15 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

## Other quantities and units

Compound units derived from SI 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
metre per second squared m/s2 acceleration m·s−2
metre per second cubed m/s3 jerk m·s−3
radian per second rad/s angular velocity s−1
newton second N·s momentum, impulse kg·m·s−1
newton metre second N·m·s angular momentum kg·m2·s−1
newton metre N·m torque, moment of force kg·m2·s−2
reciprocal metre m−1 wavenumber m−1
kilogram per cubic metre kg/m3 density, mass density kg·m−3
cubic metre per kilogram m3/kg specific volume kg−1·m3
mole per cubic metre mol/m3 amount (-of-substance) concentration m−3·mol
cubic metre per mole m3/mol molar volume m3·mol−1
joule per kelvin J/K heat capacity, entropy kg·m2·s−2·K−1
joule per kelvin mole J/(K·mol) molar heat capacity, molar entropy kg·m2·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 kg·m2·s−2·mol−1
joule per kilogram J/kg specific energy m2·s−2
joule per cubic metre J/m3 energy density kg·m−1·s−2
newton per metre N/m = J/m2 surface tension 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 kg·m·s−3·K−1
square metre per second m2/s kinematic viscosity, diffusion coefficient m2·s−1
pascal second Pa·s = N·s/m2 dynamic viscosity kg·m−1·s−1
coulomb per cubic metre C/m3 electric charge density m−3·s·A
ampere per square metre A/m2 electric current density A·m−2
siemens per metre S/m conductivity kg−1·m−3·s3·A2
siemens square metre per mole S·m2/mol molar conductivity kg-1·s3·mol−1·A2
farad per metre F/m permittivity kg−1·m−3·s4·A2
henry per metre H/m permeability kg·m·s−2·A−2
volt per metre V/m electric field strength kg·m·s−3·A−1
ampere per metre A/m magnetic field strength A·m−1
candela per square metre cd/m2 luminance cd·m−2
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
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