# 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.[1]

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
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

### 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 (mean distance of Earth from Sun)
lane and
phase angle
degree ° 1° = π/180 rad
arcminute 1′ = 1/60 ° = π/10800 rad
arcsecond 1″ = 1/60 ′ = π/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 1 Da = 1.660539040 x 10-27 kg
energy electronvolt eV 1 eV = 1.602176634 x 10-19 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
zetta Z 1021 sextillion trilliard
exa E 1018 quintillion trillion
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
atto a 10−18 quintillionth trillionth
zepto z 10−21 sextillionth trilliardth
quecto* q* 10−30 nonillionth quintillionth

The prefixes quetta, ronna, quecto and ronto have been proposed and are under consideration as of 2022[2]. 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)[3]. 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.