# SI derived unit: Wikis

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# Encyclopedia

### From Wikipedia, the free encyclopedia

The International System of Units (SI) specifies a set of seven base units from which all other units of measurement are formed. These units are called SI derived units and are also considered part of the standard.

The names of SI units are always written in lowercase. The unit symbols of units named after persons, however, are always spelled with an initial capital letter (e.g., the symbol of hertz is Hz; but meter becomes m). The exception is the Celsius, which refers to divisions on the Celsius temperature scale.

## Derived units with special names

Base units can be combined to derive units of measurement for other quantities. 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
Name Symbol Quantity Expression in terms of other units Expression in terms of SI base units
hertz Hz frequency 1/s s-1
radian rad angle m∙m-1 dimensionless
steradian sr solid angle m2∙m-2 dimensionless
newton N force, weight kg∙m/s2 kg∙m∙s−2
pascal Pa pressure, stress N/m2 m−1∙kg∙s−2
joule J energy, work, heat N∙m = C·V = W·s m2∙kg∙s−2
watt W power, radiant flux J/s = V·A 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 strength, magnetic flux density 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 temperature K − 273.15 K − 273.15
lumen lm luminous flux lx·m2 cd·sr
lux lx illuminance lm/m2 m−2∙cd∙sr
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 common units, such as the litre, are not SI units, but are accepted for use with SI (cf. non-SI units accepted for use with SI).

## Other quantities and units

Compound units derived from SI units
Name Symbol Quantity Expression in terms
of SI base units
square meter m2 area m2
cubic meter m3 volume m3
meter per second m/s speed, velocity m·s−1
cubic meter per second m3/s volumetric flow m3·s−1
meter per second squared m/s2 acceleration m·s−2
meter per second cubed m/s3 jerk, jolt m·s−3
meter per quartic second m/s4 snap, jounce m·s−4
radian per second rad/s angular velocity s−1
newton second N·s momentum, impulse m·kg·s−1
newton meter second N·m·s angular momentum m2·kg·s−1
newton meter N·m = J/rad torque, moment of force m2·kg·s−2
newton per second N/s yank m·kg·s−3
reciprocal meter m−1 wavenumber m−1
kilogram per square meter kg/m2 surface density m−2·kg
kilogram per cubic meter kg/m3 density, mass density m−3·kg
cubic meter per kilogram m3/kg specific volume m3·kg−1
mole per cubic meter mol/m3 amount (-of-substance) concentration m−3·mol
cubic meter per mole m3/mol molar volume m3·mol−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 meter J/m3 energy density m−1·kg·s−2
newton per meter N/m = J/m2 surface tension kg·s−2
watt per square meter W/m2 heat flux density, irradiance kg·s−3
watt per meter kelvin W/(m·K) thermal conductivity m·kg·s−3·K−1
square meter per second m2/s kinematic viscosity, diffusion coefficient m2·s−1
pascal second Pa·s = N·s/m2 dynamic viscosity m−1·kg·s−1
coulomb per square meter C/m2 electric displacement field m−2·s·A
coulomb per cubic meter C/m3 electric charge density m−3·s·A
ampere per square meter A/m2 electric current density A·m−2
siemens per meter S/m conductivity m−3·kg−1·s3·A2
siemens square meter per mole S·m2/mol molar conductivity kg-1·s3·mol−1·A2
farad per meter F/m permittivity m−3·kg−1·s4·A2
henry per meter H/m permeability m·kg·s−2·A−2
volt per meter V/m electric field strength m·kg·s−3·A−1
ampere per meter A/m magnetic field strength A·m−1
candela per square meter 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
ohm meter Ω·m resistivity m3·kg·s−3·A−2
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## References

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