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International System of Units (SI)
 

 
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SI base units

 
The International System of Units, the SI, is the internationally agreed basis for expressing measurements at all levels of precision and in all areas of science, technology, and human endeavour.
 
There are two classes of units in the SI, base units and derived units. The seven base units of the SI provide the reference used to define all the measurement units of the International System.
 

SI base units

Base quantitySI base unit
NameSymbol
lengthmetrem
masskilogramkg
time, durationseconds
electric currentampereA
thermodynamic temperaturekelvinK
amount of substancemolemol
luminous intensitycandelacd
 
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SI derived units

 
Derived units are expressed algebraically in terms of base units or other derived units. The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. For example, the derived unit for the derived quantity molar mass — mass divided by amount of substance — is the kilogram per mole, symbol kg/mol.
 

SI derived units
Examples of coherent derived units in the SI expressed in terms of base units

Derived quantitySI coherent derived unit
NameSymbol
areasquare metrem2
volumecubic metrem3
speed, velocitymetre per secondm/s
accelerationmetre per second squaredm/s2
wavenumberreciprocal metrem1
density, mass densitykilogram per cubic metrekg/m3
surface densitykilogram per square metrekg/m2
specific volumecubic metre per kilogramm3/kg
current densityampere per square metreA/m2
magnetic field strengthampere per metreA/m
amount concentration(a), concentrationmole per cubic metremol/m3
mass concentrationkilogram per cubic metrekg/m3
luminancecandela per square metrecd/m2
refractive index(b)one1
relative permeability(b)one1
(a) In the field of clinical chemistry this quantity is also called substance concentration.
(a) These are dimensionless quantities, or quantities of dimension one, and the symbol "1" for the unit (the number "one") is generally omitted in specifying the values of dimensionless quantities.
 
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SI Derived units with special names

 
Some derived units are given a special name, this being simply a compact form for the expression of combinations of base units that are used frequently. There are 22 special names for units approved for use in the SI.
 

Derived units with special names in the SI

Derived quantitySI coherent derived unit (a)
NameSymbolExpressed in terms of SI base units
1plane angleradian (b)radm/m = 1
2solid anglesteradian (b)sr (c)m2/m2=1
3frequencyhertz (a)Hzs-1
4forcenewtonNm kg s-2
5pressure, stress pascal Pa N/m2 = m-1 kg s-2
6energy, work, amount of heat joule J N m = m2 kg s-2
7power, radiant flux watt W J/s = m2 kg s-3
8electric charge, amount of electricity coulomb C s A
9electric potential difference, electromotive force volt V W/A = m2 kg s-3 A-1
10capacitance farad F C/V = m-2 kg-1 s4 A2
11electric resistance ohm ΩV/A = m2 kg s-3 A-2
12electric conductance siemens S A/V = m-2 kg-1 s3 A2
13magnetic flux weber Wb V s = m2 kg s-2 A-1
14magnetic flux density tesla T Wb/m2 = kg s-2 A-1
15inductance henry H Wb/A = m2 kg s-2 A-2
16Celsius temperature degree Celsius (e)°C K
17luminous flux lumen lm cd sr (c) = cd
18illuminance lux lx lm/m2 = m-2 cd
19activity referred to a radionuclide (f) becquerel (d)Bqs1
20absorbed dose, specific energy (imparted), kerma gray Gy J/kg = m2 s-2
21dose equivalent, ambient dose equivalent, directional dose equivalent, personal dose equivalent sievert (g) Sv J/kg = m2 s-2
22catalytic activity katal kat s-1 mol
(a) The SI prefixes may be used with any of the special names and symbols, but when this is done the resulting unit will no longer be coherent.
(b) The radian and steradian are special names for the number one that may be used to convey information about the quantity concerned. In practice the symbols rad and sr are used where appropriate, but the symbol for the derived unit one is generally omitted in specifying the values of dimensionless quantities.
(c) In photometry the name steradian and the symbol sr are usually retained in expressions for units.
(d) The hertz is used only for periodic phenomena, and the becquerel is used only for stochastic processes in activity referred to a radionuclide.
(e) The degree Celsius is the special name for the kelvin used to express Celsius temperatures. The degree Celsius and the kelvin are equal in size, so that the numerical value of a temperature difference or temperature interval is the same when expressed in either degrees Celsius or in kelvins.
(f) Activity referred to a radionuclide is sometimes incorrectly called radioactivity.
(g) The name gray should be used instead of joules per kilogram for the unit of absorbed dose D of ionizing radiation, and the name sievert instead of joules per kilogram for the unit of dose equivalent H, which is the product of the absorbed dose D and the dimensionless quality factor Q.
 
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Decimal multiples and sub-multiples of SI units

 
A set of multiple and sub-multiple prefixes have been adopted for use with the SI units. They may be used with any of the base units and with any of the derived units with special names. When the prefixes are used, the prefix name and the unit name are combined to form a single word, and similarly the prefix symbol and the unit symbol are written without any space to form a single symbol, which may itself be raised to any power.
 

SI prefixes
Decimal multiples and submultiples

MultiplesSubmultiples
FactorNameSymbolFactorNameSymbol
101decada 10-1deci d
102hecto h 10-2centi c
103 = (103)1kilo k 10-3 = (103)-1milli m
106 = (103)2megaM10-6 = (103)-2microμ
109 = (103)3gigaG 10-9 = (103)-3nanon
1012 = (103)4teraT10-12 = (103)-4pico p
1015 = (103)5peta P 10-15 = (103)-5femto f
1018 = (103)6exaE10-18 = (103)-6attoa
1021 = (103)7zetta Z 10-21 = (103)-7zeptoz
1024 = (103)8yottaY10-24 = (103)-8yoctoy
 
For example, we may write: kilometre, km; microvolt, μV; 50 V/cm = 50 V (102m)1 = 5000 V/m.
 
The kilogram, kg, is an exception, because although it is a base unit the name already includes the prefix kilo, for historical reasons. Multiples and sub-multiples of the kilogram are written by combining prefi xes with the gram: thus we write milligram, mg, not microkilogram, μkg.
 
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