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.

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.

1. 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.
2. 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