International System of Units

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The International System of Units, abbreviated SI from its French language name, Système international d'unités, is a comprehensive set of units of measurement. The SI is based on the original metric system developed in France in the 1790s. In October 1960 the 11th international "General Conference on Weights and Measures" met in Paris and renamed the Metric System (MKSA) of units (based on the six base units: meter, kilogram, second, ampere, kelvin and candela—in 1971 mole was added as seventh base unit) to the "International System of Units." The 11th Conference also established the abbreviation "SI" as the official abbreviation, to be used in all languages. Adoption of the abbreviation SI, especially outside scientific circles, is slow. The terms "metric system" or "MKSA units" are still frequently being used.


Base units

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent:

SI base units
Name Symbol Quantity Definition
metre m length The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
kilogram kg mass The kilogram is equal to the mass of the international prototype of the kilogram.
second s time The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
ampere A electrical current The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.
kelvin K temperature The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
mole mol amount of substance The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12
candela cd luminous intensity The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.


To allow for ease of discussion of quantities orders of magnitude different from the base units, prefixes may be used to form decimal multiples and submultiples of units. The SI prefixes with their meanings and symbols are:

SI Prefixes
Name yotta zetta exa peta tera giga mega kilo hecto deca
Symbol Y Z E P T G M k h da
Factor 1024 1021 1018 1015 1012 109 106 103 102 101
Name deci centi milli micro nano pico femto atto zepto yocto
Symbol d c m µ n p f a z y
Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24

It is important to note that the kilogram is the only SI unit with a prefix as part of its name and symbol. Because multiple prefixes may not be used, in the case of the kilogram the prefix names are used with the unit name "gram" and the prefix symbols are used with the unit symbol "g." With this exception, any SI prefix may be used with any SI unit, including the degree Celsius and its symbol °C.[1]

Derived units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units.

Dimensionless derived units

There are two dimensionless derived units, for plane angle and solid angle:

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.

Named derived units

Twenty other derived units have specific names; most are named after pioneering researchers in the fields in which they are used. These are:

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
joule J Energy, Work, Heat N∙m m2∙kg∙s−2
watt W Power, Radiant flux J/s m2∙kg∙s−3
pascal Pa Pressure, Stress N/m2 m−1∙kg∙s−2
lumen lm Luminous flux cd∙sr cd
lux lx Illuminance lm/m2 m−2∙cd
coulomb C Electric charge or flux s∙A s∙A
volt V Electrical potential difference, Electromotive force W/A = J/C m2∙kg∙s−3∙A−1
ohm Ω Electric resistance, Impedance, Reactance V/A m2∙kg∙s−3∙A−2
farad F Electric capacitance C/V m−2∙kg−1∙s4∙A2
weber Wb Magnetic flux J/A m2∙kg∙s−2∙A−1
tesla T Magnetic flux density, magnetic induction V∙s/m2 = Wb/m2 kg∙s−2∙A−1
henry H Inductance V∙s/A = Wb/A m2∙kg∙s−2∙A−2
siemens S Electric conductance 1/Ω m−2∙kg−1∙s3∙A2
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
degree Celsius °C Thermodynamic temperature T°C = TK − 273.15

Other derived units

Some derived units are named after the basic units from which they are derived, sometimes including the dimension. Other derived units have names which are a mix of base unit names and derived unit names. Some are listed below:

Compound units derived from basic 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−1 speed, velocity m·s−1
metre per second squared m·s−2 acceleration m·s−2
metre per second cubed m·s−3 jerk m·s−3
radian per second rad·s−1 angular velocity s−1
reciprocal metre m−1 wavenumber m−1
kilogram per cubic metre kg·m−3 Density, mass density kg·m−3
cubic metre per kilogram kg−1·m3 specific volume kg−1·m3
mole per cubic metre m−3·mol amount (-of-substance) concentration m−3·mol
cubic metre per mole m3·mol−1 molar volume m3·mol−1
square metre per second m2·s−1 kinematic viscosity, diffusion coefficient m2·s−1
ampere per square metre A·m−2 electric current density A·m−2
ampere per metre A·m−1 magnetic field strength A·m−1
candela per square metre cd·m−2 luminance cd·m−2

Compound units derived from SI units
Name Symbol Quantity Expression in terms
of SI base units
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
joule per kelvin J·K−1 heat capacity, entropy kg·m2·s−2·K−1
joule per kelvin mole J·K−1·mol−1 molar heat capacity, molar entropy kg·m2·s−2·K−1·mol−1
joule per kilogram kelvin J·K−1·kg−1 specific heat capacity, specific entropy m2·s−2·K−1
joule per mole J·mol−1 molar energy kg·m2·s−2·mol−1
joule per kilogram J·kg−1 specific energy m2·s−2
joule per cubic metre J·m−3 energy density kg·m−1·s−2
newton per metre N·m−1 = J·m−2 surface tension kg·s−2
watt per square metre W·m−2 heat flux density, irradiance kg·s−3
watt per metre kelvin W·m−1·K−1 thermal conductivity kg·m·s−3·K−1
pascal second Pa·s = N·s·m−2 dynamic viscosity kg·m−1·s−1
coulomb per cubic metre C·m−3 electric charge density m−3·s·A
siemens per metre S·m−1 conductivity kg−1·m−3·s3·A2
siemens square metre per mole S·m2·mol−1 molar conductivity kg-1·s3·mol−1·A2
farad per metre F·m−1 permittivity kg−1·m−3·s4·A2
henry per metre H·m−1 permeability kg·m·s−2·A−2
volt per metre V·m−1 electric field strength kg·m·s−3·A−1
coulomb per kilogram C·kg−1 exposure (X and gamma rays) kg−1·s·A
gray per second Gy·s−1 absorbed dose rate m2·s−3

Non-SI units accepted for use

The 2006 edition of the International System of Units, published by the International Bureau of Weights and Measures (BIPM) includes non-SI units that are accepted for use with the International System because they are widely used in everyday life.[2] Their use is expected to continue indefinitely, and each has an exact definition in terms of an SI unit. The values in the table below were extracted from Tables 6 and 8 of the 2006 Edition:

Non-SI units accepted for use with the International System of Units
Quantity Name Symbol Value in Si units
time minute min 1 min = 60 s
hour h 1 h = 60 min = 3600 s
day d 1 d = 24 h = 86400 s
area hectare ha 1 ha = 1 hm2 = 104m2
volume litre L or l 1 L = 1 dm3 = 103 cm3 = 10−3 m3
mass tonne t 1 t = 103 kg
plane angle degree ° 1 ° = (π/180) rad
minute ' 1 ' = (1/60)° = (π/10800) rad
second " 1 " = (1/60)' = (π/648000) rad
pressure bar bar 1 bar = 0.1 MPa = 100 kPa = 105 Pa
millimetre of mercury mmHg 1 mmHg ≈ 133.322 Pa
speed knot kn 1 kn = (1852/3600) m/s

SI writing style

Spelling variations


  1. 1.0 1.1 Taylor, Barry N. (December 2003). The NIST Reference on Constants, Units, and Uncertainty. National Institute of Standards and Technology. Retrieved on 1 March 2007.
  2. 2.0 2.1 Bureau International des Poids et Mesures (2006). The International System of Units (SI). 8th ed.. Retrieved on 14 July 2006.
  3. 3.0 3.1 Taylor, B.N. (1995). NIST Special Publication 811: Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. Retrieved on 9 June 2006.
  4. Taylor, B.N. (1995). NIST Special Publication 811: Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology. Retrieved on 1 March 2007.
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