International System of Units 
The International System of Units (SI, abbreviated from the
The base units are defined in terms of invariant constants of nature, such as the
Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the
The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.
The motivation for the development of the SI was the diversity of units that had sprung up within the
Since then, the SI has officially been
The International System of Units consists of a set of
Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example,
The SI base units are the building blocks of the system and all the other units are derived from them.
Unit name 
Unit symbol 
symbol 
name 
Definition 

^{[n 1]} 
s  T  The duration of 9192631770 periods of the radiation corresponding to the transition between the two  
m  L  The distance travelled by light in vacuum in 1/299792458 second.  
^{[n 2]} 
kg  M  The kilogram is defined by setting the  
A  I  The flow of 1/1.602176634×10^{−19} times the  
K  Θ  temperature 
The kelvin is defined by setting the fixed numerical value of the  
mol  N  substance 
The amount of substance of exactly 6.02214076×10^{23} elementary entities.^{[n 3]} This number is the fixed numerical value of the  
cd  J  intensity 
The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×10^{14} hertz and that has a radiant intensity in that direction of 1/683 watt per  

The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number.^{[3]}^{:103}^{[4]}^{:9} Derived units are associated with derived quantities; for example,
Combinations of base and derived units may be used to express other derived units. For example, the SI unit of
Name  Symbol  Quantity  In SI base units  In other SI units 

rad  m/m  1  
sr  m^{2}/m^{2}  1  
Hz  s^{−1}  
N  kg⋅m⋅s^{−2}  
Pa  kg⋅m^{−1}⋅s^{−2}  N/m^{2}  
J  kg⋅m^{2}⋅s^{−2}  N⋅m = Pa⋅m^{3}  
W  kg⋅m^{2}⋅s^{−3}  J/s  
C  s⋅A  
V  kg⋅m^{2}⋅s^{−3}⋅A^{−1}  W/A = J/C  
F  kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2}  C/V  
Ω  kg⋅m^{2}⋅s^{−3}⋅A^{−2}  V/A  
S  kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2}  Ω^{−1}  
Wb  kg⋅m^{2}⋅s^{−2}⋅A^{−1}  V⋅s  
T  kg⋅s^{−2}⋅A^{−1}  Wb/m^{2}  
H  kg⋅m^{2}⋅s^{−2}⋅A^{−2}  Wb/A  
°C  K  
lm  cd⋅sr  cd⋅sr  
lx  m^{−2}⋅cd  lm/m^{2}  
Bq  s^{−1}  
Gy  m^{2}⋅s^{−2}  J/kg  
Sv  m^{2}⋅s^{−2}  J/kg  
kat  mol⋅s^{−1}  
Notes 1. The radian and steradian are defined as dimensionless derived units. 
SI derived unit  Symbol  Derived quantity  Typical symbol 

m^{2}  A  
m^{3}  V  
m/s  v  
m/s^{2}  a  
m^{−1}  σ, ṽ  
kg/m^{3}  ρ  
kilogram per square metre  kg/m^{2}  ρ_{A}  
cubic metre per kilogram  m^{3}/kg  v  
ampere per square metre  A/m^{2}  j  
A/m  H  
mole per cubic metre  mol/m^{3}  c  
kg/m^{3}  ρ, γ  
cd/m^{2}  L_{v} 
Name  Symbol  Quantity  In SI base units 

Pa⋅s  m^{−1}⋅kg⋅s^{−1}  
N⋅m  m^{2}⋅kg⋅s^{−2}  
newton per metre  N/m  kg⋅s^{−2}  
rad/s  s^{−1}  
rad/s^{2}  s^{−2}  
W/m^{2}  heat flux density  kg⋅s^{−3}  
joule per kelvin  J/K  m^{2}⋅kg⋅s^{−2}⋅K^{−1}  
joule per kilogram kelvin  J/(kg⋅K)  m^{2}⋅s^{−2}⋅K^{−1}  
joule per kilogram  J/kg  m^{2}⋅s^{−2}  
watt per metre kelvin  W/(m⋅K)  m⋅kg⋅s^{−3}⋅K^{−1}  
joule per cubic metre  J/m^{3}  m^{−1}⋅kg⋅s^{−2}  
volt per metre  V/m  m⋅kg⋅s^{−3}⋅A^{−1}  
coulomb per cubic metre  C/m^{3}  m^{−3}⋅s⋅A  
coulomb per square metre  C/m^{2}  m^{−2}⋅s⋅A  
farad per metre  F/m  m^{−3}⋅kg^{−1}⋅s^{4}⋅A^{2}  
henry per metre  H/m  m⋅kg⋅s^{−2}⋅A^{−2}  
joule per mole  J/mol  m^{2}⋅kg⋅s^{−2}⋅mol^{−1}  
joule per mole kelvin  J/(mol⋅K)  m^{2}⋅kg⋅s^{−2}⋅K^{−1}⋅mol^{−1}  
coulomb per kilogram  C/kg  kg^{−1}⋅s⋅A  
gray per second  Gy/s  m^{2}⋅s^{−3}  
watt per steradian  W/sr  m^{2}⋅kg⋅s^{−3}  
watt per square metre steradian  W/(m^{2}⋅sr)  kg⋅s^{−3}  
katal per cubic metre  kat/m^{3}  m^{−3}⋅s^{−1}⋅mol 
Prefixes are added to unit names to produce multiples and submultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo denotes a multiple of a thousand and milli denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.^{[3]}^{:122}^{[8]}^{:14} When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent.^{[3]}^{:7}
The BIPM specifies 20 prefixes for the International System of Units (SI):
Prefix  Base 1000  Base 10  English word  Adoption^{[nb 1]}  

Name  Symbol  
Y  1000^{8}  
1000000000000000000000000  septillion  quadrillion  1991  
Z  1000^{7}  
1000000000000000000000  sextillion  trilliard  1991  
E  1000^{6}  
1000000000000000000  quintillion  trillion  1975  
P  1000^{5}  
1000000000000000  quadrillion  billiard  1975  
T  1000^{4}  
1000000000000  trillion  billion  1960  
G  1000^{3}  
1000000000  billion  milliard  1960  
M  1000^{2}  
1000000  million  1873  
k  1000^{1}  
1000  thousand  1795  
h  1000^{2/3}  
100  hundred  1795  
da  1000^{1/3}  
10  ten  1795  
1000^{0}  
1  one  –  
d  1000^{−1/3}  
0.1  tenth  1795  
c  1000^{−2/3}  
0.01  hundredth  1795  
m  1000^{−1}  
0.001  thousandth  1795  
μ  1000^{−2}  
0.000001  millionth  1873  
n  1000^{−3}  
0.000000001  billionth  milliardth  1960  
p  1000^{−4}  
0.000000000001  trillionth  billionth  1960  
f  1000^{−5}  
0.000000000000001  quadrillionth  billiardth  1964  
a  1000^{−6}  
0.000000000000000001  quintillionth  trillionth  1964  
z  1000^{−7}  
0.000000000000000000001  sextillionth  trilliardth  1991  
y  1000^{−8}  
0.000000000000000000000001  septillionth  quadrillionth  1991  

Many nonSI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of
Some units of time, angle, and legacy nonSI units have a long history of use. Most societies have used the solar day and its nondecimal subdivisions as a basis of time and, unlike the
Name  Value in SI units  

min  1 min = 60 s  
h  1 h = 60 min = 3600 s  
d  1 d = 24 h = 86400 s  
au  1 au = 149597870700 m  
phase angle 
°  1° = (π/180) rad  
′  1′ = (1/60)° = (π/10800) rad  
″  1″ = (1/60)′ = (π/648000) rad  
ha  1 ha = 1 hm^{2} = 10^{4} m^{2}  
l, L  1 l = 1 L = 1 dm^{3} = 10^{3} cm^{3} = 10^{−3} m^{3}  
t  1 t = 1000 kg  
Da  1 Da = 1.660539040(20)×10^{−27} kg  
eV  1 eV = 1.602176634×10^{−19} J  
logarithmic ratio quantities 
Np  In using these units it is important that the nature of the quantity be specified and that any reference value used be specified.  
bel  B  
dB 
The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.^{[Note 3]}