National Physical Laboratory

The SI units

The International System of Units (SI) is a globally agreed system of measurements that was formalised in 1960. There are seven base units, which make up the SI, and guide the measurement of quantities like physical size, temperature and time.

Kilogram (kg)
Unit of measurement of mass
Metre (m)
Unit of measurement of length
Second (s)
Unit of measurement of time
Ampere (A)
Unit of measurement of electric current
Kelvin (K)
Unit of measurement of thermodynamic temperature
Mole (mol)
Unit of measurement of amount of substance
Candela (cd)
Unit of measurement of luminous intensity

This International System of Units is necessary to ensure that our everyday concepts of measurement, whether a metre or a second, remain comparable and consistent worldwide. Standardising measurements ensures society has confidence in information. For instance, the kilogram is used every day, and defining this quantity means that consumers can trust that the shop is really providing the amount they say they are. Having reliable information on issues such as climate change, pollutions and medical diagnostics is important to society. Reliable measurement allows effective decisions to be made.

See what the expected redefinition in 2018 will mean for the SI units

SI Bots

Using the SI units

Learn more about the SI units and how to apply them

SI derived units

Derived units are units which may be expressed in terms of base units by means of mathematical symbols of multiplication and division.

Certain derived units have been given special names and symbols, and these special names and symbols may themselves be used in combination with the SI and other derived units to express the units of other quantities.

Examples of SI derived units expressed in terms of base units
Derived Quantity SI derived unit
  Name Symbol
area square metre m2
volume cubic metre m3
speed, velocity metre per second m/s
acceleration metre per second squared m/s2
wavenumber 1 per metre m-1
density, mass density kilogram per cubic metre kg/m3
specific volume cubic metre per kilogram m3/kg
current density ampere per square metre A/m2
magnetic field strength ampere per metre A/m
concentration
(of amount of substance)
mole per cubic metre mol/m3
luminance candela per square metre cd/m2
refractive index (the number) one 1(a)
(a) The symbol '1' is generally omitted in combination with a numerical value.

SI prefixes

SI prefixes are used to form decimal multiples and submultiples of SI units.

They should be used to avoid very large or very small numeric values.

The prefix attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit.

Multiplying Factor SI Prefix Scientific Notation
1 000 000 000 000 000 000 000 000 yotta (Y) 1024
1 000 000 000 000 000 000 000 zetta (Z) 1021
1 000 000 000 000 000 000 exa (E) 1018
1 000 000 000 000 000 peta (P) 1015
1 000 000 000 000 tera (T) 1012
1 000 000 000 giga (G) 109
1 000 000 mega (M) 106
1 000 kilo (k) 103
0.001 milli (m) 10-3
0.000 001 micro (µ) 10-6
0.000 000 001 nano (n) 10-9
0.000 000 000 001 pico (p) 10-12
0.000 000 000 000 001 femto (f) 10-15
0.000 000 000 000 000 001 atto (a) 10-18
0.000 000 000 000 000 000 001 zepto (z) 10-21
0.000 000 000 000 000 000 000 001 yocto (y) 10-24

SI conventions

The following is a list of the key recommendations when using SI units:

Writing unit names and symbols

  • Only units of the SI and those units recognised for use with the SI should be used to express the values of quantities.
  • All unit names are written in small letters (newton or kilogram) except Celsius.
  • The unit symbol is in lower case unless the name of the unit is derived from a proper name, in which case the first letter of the symbol is in upper case.
  • Unit symbols are unaltered in the plural.
  • Unit symbols and unit names should not be mixed.
  • Abbreviations such as sec (for either s or second) or mps (for either m/s or meter per second are not allowed.
  • For unit values more than 1 or less than -1 the plural of the unit is used and a singular unit is used for values between 1 and -1.
  • A space is left between the numerical value and unit symbol (25 kg, but not 25-kg or 25kg). If the spelled-out name of a unit is used, the normal rules of English are applied.
  • Unit symbols are in roman type, and quantity symbols are in italic type with superscripts and subscripts in roman or italic type as appropriate.

Numerical Notation

  • A space should be left between groups of 3 digits on either the right or left hand side of the decimal place (15 739.012 53). In four digit numbers the space may be omitted. Commas should not be used.
  • The decimal marker shall be either the point on the line or the comma on the line. The decimal marker chosen should be that which is customary in the context concerned.
  • Mathematical operations should only be applied to unit symbols (kg/m2) and not unit names (kilogram/cubic metre).
  • Values of quantities should be expressed as 2.0 µs or 2.0 x 10-6 and not in terms such as parts per million.
  • It should be clear to which unit symbol a numerical value belongs and which mathematical operation applies to the value of a quantity (35 cm x 48 cm, not 35 x 48 cm; or 100 g ± 2 g, not 100 ± 2g).
  • The value must apply to the whole symbol and not any particular unit within the symbol.

Non-SI units

There are certain units, which are accepted for use with the SI. It includes units which are in continuous everyday use, in particular the traditional units of time and of angle, together with a few other units which have assumed increasing technical importance.

There are also units which are currently accepted for use with the SI to satisfy the needs of commercial, legal and specialist scientific interests or are important for the interpretation of older texts.

Non-SI units accepted for use with the International System
Name Symbol Value in SI Units
minute min 1 min = 60 s
hour (1) h 1 h = 60 min = 3600 s
day d 1 d = 24 h = 86 400 s
degree of arc (2) ° 1° = (π/180) rad
minute of arc ' 1' = (1/60)° = (π/10 800) rad
second of arc " 1" = (1/60)' = (π/648 000) rad
litre (3) l, L 1 l = 1 dm3 = 10-3 m3
tonne (4, 5) t 1 t = 103 kg
neper (6, 8) Np 1 Np = 1
bel (7, 8) B 1 B = (1/2) ln 10 (Np)(9)


Notes:

  1. The symbol of this unit is included in Resolution 7 of the 9th CGPM (1948; CR, 70).
  2. ISO 31 recommends that the degree be subdivided decimally rather than using the minute and second.
  3. This unit and the symbol l were adopted by CIPM in 1879 (PV, 1879, 41). The alternative symbol, L, was adopted by the 16th CGPM (1979, Resolution 6; CR, 101 and Metrologia, 1980, 16, 56-57) in order to avoid the risk of confusion between the letter l and the number 1. The present definition of the litre is given in Resolution 6 of the 12th CGPM (1964; CR, 93).
  4. This unit and its symbol were adopted by the CIPM in 1879 (PV, 1879, 41).
  5. In some English-speaking countries this is called 'metric ton'.
  6. The neper is used to express values of such logarithmic quantities as field level, power level, sound pressure level, and logarithmic decrement. Natural logarithms are used to obtain the numerical values of quantities expressed in nepers. The neper is coherent with the SI, but not yet adopted by the CGPM as an SI unit. For further information see International Standard ISO 31.
  7. The bel is used to express values of such logarithmic quantities as field level, power level, sound pressure level, and attenuation. Logarithms to base ten are used to obtain the numerical values of quantities expressed in bels. The submultiple decibel, dB, is commonly used. For further information see International Standard ISO 31.
  8. In using these units it is particularly important that the quantity be specified. The unit must not be used to imply the quantity.
  9. Np is enclosed in parentheses because, although the neper is coherent with the SI, it has not yet been adopted by the CGPM.
 

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