International system of units
These units are either part of the International System of Units (SI) or accepted for use with the SI. For old units and popular units not recommended for scientific use, see Deprecated units.
Contents
Prefixes
Avoid using compound prefixes, such as micromicro for pico and kilomega for giga. The abbreviation of a prefix is considered to be combined with the abbreviation/symbol to which it is directly attached, forming with it a new unit symbol, which can be raised to a positive or negative power and which can be combined with other unit abbreviations/symbols to form abbreviations/symbols for compound units. For example:
- 1 cm3 = (10-2 m)3 = 10-6 m3
- 1 µs-1 = (10-6 s)-1 = 106 s-1
- 1 mm2/s = (10-3 m)2/s = 10-6 m2/s
Prefix | Abbreviation | Decimal | Multiple |
---|---|---|---|
yotta | Y | 1 000 000 000 000 000 000 000 000 | 1024 |
zetta | Z | 1 000 000 000 000 000 000 000 | 1021 |
exa | E | 1 000 000 000 000 000 000 | 1018 |
peta | P | 1 000 000 000 000 000 | 1015 |
tera | T | 1 000 000 000 000 | 1012 |
giga | G | 1 000 000 000 | 109 |
mega | M | 1 000 000 | 106 |
kilo | k | 1000 | 103 |
hecto | h | 100 | 102 |
deka | da | 10 | 101 |
deci | d | 0.1 | 10-1 |
centi | c | 0.01 | 10-2 |
mili | m | 0.001 | 10-3 |
micro | µ | 0.000 001 | 10-6 |
nano | n | 0.000 000 001 | 10-9 |
pico | p | 0.000 000 000 001 | 10-12 |
femto | f | 0.000 000 000 000 001 | 10-15 |
atto | a | 0.000 000 000 000 000 001 | 10-18 |
zepto | z | 0.000 000 000 000 000 000 001 | 10-21 |
yocto | y | 0.000 000 000 000 000 000 000 001 | 10-24 |
Length
Metre
Metre (m) is an SI base unit.
The metre is the length of the path travelled by light in vacuum during a time interval of 1 / 299 792 458 of a second. Note that the effect of this definition is to fix the speed of light at exactly 299 792 458 m·s-1. (see Constants)
Astronomical unit
Astronomical unit (ua) is accepted for use with the IS and the value is obtained experimentally.
1 ua = 1.495 978 70(30) x 1011m
Nautical mile
Nautical mile should be defined in relation to the SI in every document in which it is used. Its use is not encouraged. There is no standard unit but NM, nm or nmi is commonly used.
1 nautical mile = 1852 m (exactly)
Ångström (Angstrom)
Ångström (Å) should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 Å = 0.1 nanometer (exactly)
Area
Square metre
Square metre (m2) is a derived SI unit.
Hectare
Hectare (ha) is a non-SI unit currently accepted for use with the International System. It should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 ha = 1 hm2 = 104 m2
Are
Are (a) is a non-SI unit currently accepted for use with the International System. It should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 a = 1 dam2 = 102 m2
Barn
Barn (b) is a non-SI unit currently accepted for use with the International System. It should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 b = 100 fm2 = 10–28 m2
Volume
Cubic metre
Cubic metre m3 is a derived SI unit.
Litre
Litre (l, L) is a non-SI unit accepted for use with the International System.
1 L = 1 dm3 = 10-3 m3
Time interval
Second
Second (s) is an SI base unit.
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. This definition refers to a cesium atom at rest at a temperature of 0 K.
Minute
Minute (min) is accepted for use with the SI.
1 min = 60 s
Hour
Hour (h) is accepted for use with the SI.
1 h = 60 min = 3600 s
Day
Day (d) is accepted for use with the SI.
1 d = 24 h = 86 400 s
Note that there are several different days and a definition may be required for clarity.
Speed, velocity
Metre per second
Metre per second (m/s) is a derived SI unit.
Knot
Knot should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 knot = 1 nautical mile per hour = (1852/3600) m/s (exactly)
Frequency
Hertz
Hertz (Hz) is a derived SI unit with a special name and symbol.
Hz = s–1
Quantities of Electricity and Magnetism
Ampere
Ampere (A) is an SI base unit.
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 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per metre of length.
Note that the effect of this definition is to fix the permeability of vacuum at exactly 4π x 10-7 H · m-1.
Volt
Volt (V) is a derived SI unit.
V = W/A = m2·kg·s-3·A-1
Ampere per square metre
Ampere per square metre (A/m2) is a derived SI unit.
Ampere per metre
Ampere per square metre (A/m) is a derived SI unit.
Force
Newton
Newton (N) is a derived SI unit.
N = m·kg·s-2
Mass
In science and technology, weight is a force, for which the SI unit is the newton; in commerce and everyday use, weight is usually a synonym for mass, for which the SI unit is the kilogram.
Kilogram
Kilogram (kg) is an SI base unit.
The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
Unified atomic mass unit
Unified atomic mass unit (u) is accepted for use with the SI and is obtained experimentally.
The unified atomic mass unit is equal to 1/12 of the mass of an atom of the nuclide 12 C
1 u = 1.660 540 2 x 1027 kg with a combined standard uncertainty of 0.000 001 0 x 1027 kg
Tonne
Tonne (t) is a non-SI unit accepted for use with the International System.
1 t = 103 kg
Temperature
Kelvin
Kelvin (K) is an SI base unit.
It is the unit of thermodynamic temperature and is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
0 K is the lowest thermodynamic temperature obtainable.
Degree Celsius
Degree Celcius (°C) is a derived SI unit and is by definition equal in magnitude to the kelvin.
Because of the way temperature scales used to be defined, it remains common practice to express thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation
- t = T - T0.
A difference or interval of temperature may be expressed in kelvins or in degrees Celsius. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by
- t/°C = T/K - 273.15.
Zero degrees C is defined as the freezing point of water at one atmosphere of pressure. 100°C is the boiling point of water at 1 atm.
Pressure
Pascal
Pascal (Pa) is a derived SI unit.
1 Pa = 1 N/m2 = m-1·kg·s-2
Bar
Bar (bar) is a non-SI unit currently accepted for use with the International System. It should be defined in relation to the SI in every document in which it is used. Its use is not encouraged.
1 bar = 0.1 MPa = 100 kPa = 1000 hPa = 105 Pa (exactly)
Amount of substance
Mole
Mole (mol) is an SI base unit.
- 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.
- When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole.
Quantities of light
Candela
Candela (cd) is an SI base unit.
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.
Angle
Radian
Radian (rad), the derived quantity is plane angle.
rad = m · m-1 = 1
Steradian
Steradian (sr), The derived quantity is solid angle.
sr = m2 · m-2 = 1
Degree
Degree (°) is a non-SI unit accepted for use with the International System.
1° = (π/180) rad
Minute
Minute (') is a non-SI unit accepted for use with the International System.
1' = (1/60)° = (π/10 800) rad
Second
Second ('') is a non-SI unit accepted for use with the International System.
1'' = (1/60)' = (π/648 000) rad
Energy
Joule
Joule (J) is a derived SI unit.
J = N · m = m2 · kg · s-2
Electronvolt
Electronvolt (eV) is accepted for use with the IS and the value is obtained experimentally.
1 eV = 1.602 177 33(49) x 10–19 J