Metric system

The metric system is an international system of measurement that was first introduced in France in the 1790s, and has since undergone revision. In the mid-20th century, it was standardized by an international standards body, and became officially known by the French abbreviation SI (System International), or the International System of Units.

The metric system is built around the basic units of the meter, liter, gram, Kelvin (for temperature) and a few other core units. The system is based on several core principles. The units are based on natural, physical, and scientific principles, that is, they are defined precisely and scientifically based on scientific phenomena in the natural world that can always be measured consistently. This stands in contrast to older systems like the imperial system used in the US, consisting of units like inches, miles, and gallons, which are arbitrary and not defined by natural principles. Another principle of the metric system is that the units are related to each other consistently, and they are coherent, that is, based on natural orders of magnitude, or factors of ten (e.g., 1 meter = 100 centimeters, 1 centimeter = 10 millimeters), and this is expressed with regular prefixes (e.g., centi-, milli-).

This system serves as the official system of weights and measures internationally, except in Myanmar, Liberia, and the United States.

1 Base units and derived units

The following are the base units of the metric system and their formal scientific definitions.

SI base units

Unit name	Symbol	Dimension	Definition
second	s	time (T)	The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
meter	m	length (L)	The distance travelled by light in a vacuum in 1/299792458 seconds.
kilogram	kg	mass (M)	The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10−34 J⋅s (J = kg⋅m2⋅s−2), given the definitions of the metre and the second.
ampere	A	electric current (I)	The flow of exactly 1/1.602176634×10−19 times the elementary charge e per second, equalling approximately 6.2415090744×1018 elementary charges per second.
kelvin	K	thermodynamic temperature (Θ)	The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10−23 J⋅K−1, (J = kg⋅m2⋅s−2), given the definition of the kilogram, the meter, and the second.
mole	mol	amount of substance (N))	The amount of substance of exactly 6.02214076×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1.
candela	cd	luminous intensity (J)	The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

1.1 Derived units

The following units are commonly used derived units, often formed from combinations of base units.

SI derived units with special names and symbols

Name	Symbol	Quantity	In SI base units	In other SI units
radian*	rad	plane angle	m/m	*
steradian*	sr	solid angle	m2/m2	*
hertz	Hz	frequency	s−1
newton	N	force, weight	kg⋅m⋅s−2
pascal	Pa	stress	kg⋅m−1⋅s−2	N/m2
joule	J	work, heat	kg⋅m2⋅s−2	N⋅m = Pa⋅m3
watt	W	power, radiant flux	kg⋅m2⋅s−3	J/s
coulomb	C	electric charge	s⋅A
volt	V	emf	kg⋅m2⋅s−3⋅A−1	W/A = J/C
farad	F	capacitance	kg−1⋅m−2⋅s4⋅A2	C/V = C2/J
ohm	Ω	resistance, electrical impedance, (electronics) reactance	kg⋅m2⋅s−3⋅A−2	V/A = J⋅s/C2
siemens	S	electrical conductance	kg−1⋅m−2⋅s3⋅A2	Ω−1
weber	Wb	magnetic flux	kg⋅m2⋅s−2⋅A−1	V⋅s
tesla	T	magnetic flux density	kg⋅s−2⋅A−1	Wb/m2
henry	H	inductance	kg⋅m2⋅s−2⋅A−2	Wb/A
degree Celsius	°C or ℃	temperature relative to 273.15 K	K
lumen	lm	luminous flux	cd⋅sr	cd⋅sr
lux	lx	illuminance	cd⋅sr⋅m−2	lm/m2
becquerel	Bq	activity referred to a radionuclide (decays per unit time)	s−1
gray	Gy	absorbed dose (of ionising radiation)	m2⋅s−2	J/kg
sievert	Sv	equivalent dose (of ionising radiation)	m2⋅s−2	J/kg
katal	kat	catalytic activity	mol⋅s−1
*Note: The radian and steradian are defined as dimensionless derived units.

1.2 Unofficial SI units

A number of units are accepted and commonly used in science and other fields, though these are not officially part of the SI system. However, these units are defined according to official SI units.

Non-SI units accepted for use with SI 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
length	astronomical unit	au	1 au = 149597870700 m
Angle|plane and phase angle	degree	°	1° = pi/180 rad
	arcminute	′	1′ = 1/60 ° = pi/10800 rad
	arcsecond	″	1″ = 1/60 ′ = pi/648000 rad
area	hectare	ha	1 ha = 1 hm2 = 104 m2
volume	litre	l, L	1 l = 1 L = 1 dm3 = 103 cm3 = 10−3 m3
mass	tonne (metric ton)	t	1 t = 1 Mg = 103 kg
	dalton	Da	(20)|e=-27 kg
energy	electronvolt	eV	e=-19 J
logarithmic ratio quantities	neper	Np	For these units, the type of quantity should be specified, with appropriate reference values.
	bel	B
	decibel	dB

2 Prefixes

The following are official SI prefixes that are attached to SI units, along with several proposed new prefixes.

SI prefixes

Prefix		Base 10	English equivalent
Name	Symbol		Short scale	Long scale (UK)
quetta*	Q*	1030	nonillion	quintillion
ronna*	R*	1027	octillion	quadrilliard
yotta	Y	1024	septillion	quadrillion
zetta	Z	1021	sextillion	trilliard
exa	E	1018	quintillion	trillion
peta	P	1015	quadrillion	billiard
tera	T	1012	trillion	billion
giga	G	109	billion	milliard
mega	M	106	million
kilo	k	103	thousand
hecto	h	102	hundred
deca	da	101	ten
		100	one
deci	d	10−1	tenth
centi	c	10−2	hundredth
milli	m	10−3	thousandth
micro	μ	10−6	millionth
nano	n	10−9	billionth	milliardth
pico	p	10−12	trillionth	billionth
femto	f	10−15	quadrillionth	billiardth
atto	a	10−18	quintillionth	trillionth
zepto	z	10−21	sextillionth	trilliardth
yocto	y	10−24	septillionth	quadrillionth
ronto*	r*	10−27	octillionth	quadrilliard
quecto*	q*	10−30	nonillionth	quintillionth

The prefixes quetta, ronna, quecto and ronto have been proposed and are under consideration as of 2022. For newer prefixes beyond sextillion and sextillionth, the names large scale and fractional orders of magnitude are deliberately named to be similar to each other, e.g., yotto (septillion) and yocto (septillionth). The prefixes yotta, yocto, zetta, and zepto are the most recently added official prefixes, which were added in 1991. The prefix deca is nowadays less commonly used. One might see a few older prefixes, namely, myria for 10,000, but this never became popular, and was removed from the SI system in 1960.

The long scale numerals are those traditionally used in the UK and British Commonwealth nations, but are increasingly less common, especially in math, science and engineering, where the North American short scale is more common. In the long scale, 10⁹ is one million, while 10¹² is one milliard, corresponding to one billion in the short scale; thus, 10¹⁵ is one billion in the long scale and one trillion in the short scale, and 10¹⁸ is one billiard in the long scale, and one quadrillion in the short scale, and so on.

3 See also

• Large numbers