SI Units
Standards and Units (abbreviated as SI Units): Laws of physics are expressed in terms of physical quantities such as time, force, temperature, density and numerous other parameters. Physical quantities are often divided into fundamental and derived quantities. Derived quantities arc those whose definitions are based on other physical quantities, e.g., speed, area, density, etc. Fundamental quantities are not defined of other physical quantities, e.g., length, mass and time.
The International System of Units, inspired by the metric system, is the most widely used system of units in the world; but it is not officially used in the United States, Liberia, and Burma.
Fundamental SI Units
Base quantity  Name  Symbol 

Length  Meter  M 
Mass  kilogram  kg 
Time  Second  S 
Electric current  Ampere  A 
ThermodynamicTemperature  Kelvin  K 
Amount of substance  Mole  mol 
Luminous intensity  Candela  cd 
Derived SI Units
Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in the following table, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.
Examples of SI Derived Units
SI derived unit  

Derived quantity  Name  Symbol 
Area  Square meter  m^{2} 
Volume  Cubic meter  m^{3} 
Speed, velocity  Meter per second  m/s 
Acceleration  Meter per second squared  m/s^{2} 
Wave number  Reciprocal meter  m^{1} 
Mass density  Kilogram per cubic meter  Kg/m^{3} 
Specific volume  Cubic meter per kilogram  m^{3}/kg 
Current density  Ampere per square meter  A/m^{2} 
Magnetic field strength  Ampere per meter  A/m 
Amountofsubstance concentration  Mole per cubic meter  mol/m^{3} 
Luminance  Candela per square meter  cd/m^{2} 
Mass fraction  Kilogram per kilogram, which may be represented by the number 1  kg/kg=1 
For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in the following table.
SI derived units with special names and symbols
Derived quantity  Name  Symbol  Expression in terms of other SI units 

Plane angle  radian  rad  – 
Solid angle  steradian  sr  – 
Frequency  hertz  Hz  – 
Force  newton  N  – 
Pressure, stress  pascal  Pa  N/m^{2} 
Energy, work, quantity of heat  joule  J  N.M 
Power, radiant flux  watt  W  J/s 
Electric charge, quantity of electricity  coulomb  C  – 
Electric potential difference, electromotive force  Volt  V  W/A 
Capacitance  farad  F  C/V 
Electric resistance  ohm  Ω  V/A 
Electric conductance  siemens  S  A/V 
Magnetic flux  weber  Wb  V.s 
Magnetic flux density  tesla  T  Wb/m^{2} 
Inductance  henry  H  Wb/a^{2} 
Celsius temperature  degree Celsius  ^{o}C  – 
Luminous flux  lumen  lm  cd.sr 
Illuminance  lux  lx  lm/m^{2} 
Activity (of a radionuclide)  becquerel  Bq  – 
Absorbed dose, specific energy (imparted), kerma  gray  Gy  J/kh 
Dose equivalent  sievert  Sv  J/kg 
Catalytic  katal  kat 
Some commonly used units other than SI units
 Light years: the light year is a unit of length and is equal to the distance travelled by light in one year. It is used to express large astronomical distance like the distance between the sun and earth etc. 1 light year = 9.46 x 10^{15}m
 An Astronomical Unit (A.U) is the mean distance from the centre of the earth to centre of the sun. 1 A. U = 1.495 x 10^{11} m.
 F. P. S system is used in Britain, where length is measured in Foots, mass in pounds and time in Seconds.
 In C.G.S system, length is measured in Centimeter, mass in Grams and time in Seconds.
 Barrel is the internationally used unit for measuring the volume of crude oil. 1 Barrel = 159 Litres.
Base Units
The SI base units are the building blocks of the system and all the other units are derived from them.
The base units of the International System are the seven independent units of measurement (or fundamental units) of the International System from which all other units, called derived units, are obtained by dimensional analysis.
These units are assumed to be independent insofar as they make it possible to measure independent physical quantities. However, the definition of a unit may involve that of other units.
Unit name  Unit symbol  Dimension symbol  Quantity name  Definition 

second ^{}  s  T  time  The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium133 atom. 
metre  m  L  length  The distance travelled by light in vacuum in 1/299792458 second. 
kilogram ^{}  kg  M  mass  The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10^{−34} J⋅s (J = kg⋅m^{2}⋅s^{−2}), given the definitions of the metre and the second.^{} 
ampere  A  I  electric current  The flow of exactly 1/1.602176634×10^{−19} times the elementary charge e per second.Equalling approximately 6.2415090744×10^{18} elementary charges per second. 
kelvin  K  Θ  thermodynamic temperature  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⋅m^{2}⋅s^{−2}), given the definition of the kilogram, the metre, and the second. 
mole  mol  N  amount of substance  The amount of substance of exactly 6.02214076×10^{23} elementary entities.^{[n 3]} This number is the fixed numerical value of the Avogadro constant, N_{A}, when expressed in the unit mol^{−1}. 
candela  cd  J  luminous 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 steradian. 

Derived units
Name  Symbol  Quantity  In SI base units  In other SI units 

radian^{}  rad  plane angle  m/m  1 
steradian^{}  sr  solid angle  m^{2}/m^{2}  1 
hertz  Hz  frequency  s^{−1}  
newton  N  force, weight  kg⋅m⋅s^{−2}  
pascal  Pa  pressure, stress  kg⋅m^{−1}⋅s^{−2}  N/m^{2} 
joule  J  energy, work, heat  kg⋅m^{2}⋅s^{−2}  N⋅m = Pa⋅m^{3} 
watt  W  power, radiant flux  kg⋅m^{2}⋅s^{−3}  J/s 
coulomb  C  electric charge  s⋅A  
volt  V  electrical potential difference (voltage), emf  kg⋅m^{2}⋅s^{−3}⋅A^{−1}  W/A = J/C 
farad  F  capacitance  kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2}  C/V 
ohm  Ω  resistance, impedance, reactance  kg⋅m^{2}⋅s^{−3}⋅A^{−2}  V/A 
siemens  S  electrical conductance  kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2}  Ω^{−1} 
weber  Wb  magnetic flux  kg⋅m^{2}⋅s^{−2}⋅A^{−1}  V⋅s 
tesla  T  magnetic flux density  kg⋅s^{−2}⋅A^{−1}  Wb/m^{2} 
henry  H  inductance  kg⋅m^{2}⋅s^{−2}⋅A^{−2}  Wb/A 
degree Celsius  °C  temperature relative to 273.15 K  K  
lumen  lm  luminous flux  cd⋅sr  cd⋅sr 
lux  lx  illuminance  cd⋅sr⋅m^{−2}  lm/m^{2} 
becquerel  Bq  radioactivity (decays per unit time)  s^{−1}  
gray  Gy  absorbed dose (of ionising radiation)  m^{2}⋅s^{−2}  J/kg 
sievert  Sv  equivalent dose (of ionising radiation)  m^{2}⋅s^{−2}  J/kg 
katal  kat  catalytic activity  mol⋅s^{−1}  
Notes

Name  Symbol  Derived quantity  Typical symbol 

square metre  m^{2}  area  A 
cubic metre  m^{3}  volume  V 
metre per second  m/s  speed, velocity  v 
metre per second squared  m/s^{2}  acceleration  a 
reciprocal metre  m^{−1}  wavenumber  σ, ṽ 
vergence (optics)  V, 1/f  
kilogram per cubic metre  kg/m^{3}  density  ρ 
kilogram per square metre  kg/m^{2}  surface density  ρ_{A} 
cubic metre per kilogram  m^{3}/kg  specific volume  v 
ampere per square metre  A/m^{2}  current density  j 
ampere per metre  A/m  magnetic field strength  H 
mole per cubic metre  mol/m^{3}  concentration  c 
kilogram per cubic metre  kg/m^{3}  mass concentration  ρ, γ 
candela per square metre  cd/m^{2}  luminance  L_{v} 
Name  Symbol  Quantity  In SI base units 

pascalsecond  Pa⋅s  dynamic viscosity  m^{−1}⋅kg⋅s^{−1} 
newtonmetre  N⋅m  moment of force  m^{2}⋅kg⋅s^{−2} 
newton per metre  N/m  surface tension  kg⋅s^{−2} 
radian per second  rad/s  angular velocity, angular frequency  s^{−1} 
radian per second squared  rad/s^{2}  angular acceleration  s^{−2} 
watt per square metre  W/m^{2}  heat flux density, irradiance  kg⋅s^{−3} 
joule per kelvin  J/K  entropy, heat capacity  m^{2}⋅kg⋅s^{−2}⋅K^{−1} 
joule per kilogramkelvin  J/(kg⋅K)  specific heat capacity, specific entropy  m^{2}⋅s^{−2}⋅K^{−1} 
joule per kilogram  J/kg  specific energy  m^{2}⋅s^{−2} 
watt per metrekelvin  W/(m⋅K)  thermal conductivity  m⋅kg⋅s^{−3}⋅K^{−1} 
joule per cubic metre  J/m^{3}  energy density  m^{−1}⋅kg⋅s^{−2} 
volt per metre  V/m  electric field strength  m⋅kg⋅s^{−3}⋅A^{−1} 
coulomb per cubic metre  C/m^{3}  electric charge density  m^{−3}⋅s⋅A 
coulomb per square metre  C/m^{2}  surface charge density, electric flux density, electric displacement  m^{−2}⋅s⋅A 
farad per metre  F/m  permittivity  m^{−3}⋅kg^{−1}⋅s^{4}⋅A^{2} 
henry per metre  H/m  permeability  m⋅kg⋅s^{−2}⋅A^{−2} 
joule per mole  J/mol  molar energy  m^{2}⋅kg⋅s^{−2}⋅mol^{−1} 
joule per molekelvin  J/(mol⋅K)  molar entropy, molar heat capacity  m^{2}⋅kg⋅s^{−2}⋅K^{−1}⋅mol^{−1} 
coulomb per kilogram  C/kg  exposure (x and γrays)  kg^{−1}⋅s⋅A 
gray per second  Gy/s  absorbed dose rate  m^{2}⋅s^{−3} 
watt per steradian  W/sr  radiant intensity  m^{2}⋅kg⋅s^{−3} 
watt per square metresteradian  W/(m^{2}⋅sr)  radiance  kg⋅s^{−3} 
katal per cubic metre  kat/m^{3}  catalytic activity concentration  m^{−3}⋅s^{−1}⋅mol 
Prefixes
The BIPM specifies 20 prefixes for the International System of Units (SI):
Prefix  Base 10  Decimal  English word  Adoption^{}  

Name  Symbol  Short scale  Long scale  
yotta  Y  10^{24}  1000000000000000000000000  septillion  quadrillion  1991  
zetta  Z  10^{21}  1000000000000000000000  sextillion  trilliard  1991  
exa  E  10^{18}  1000000000000000000  quintillion  trillion  1975  
peta  P  10^{15}  1000000000000000  quadrillion  billiard  1975  
tera  T  10^{12}  1000000000000  trillion  billion  1960  
giga  G  10^{9}  1000000000  billion  milliard  1960  
mega  M  10^{6}  1000000  million  1873  
kilo  k  10^{3}  1000  thousand  1795  
hecto  h  10^{2}  100  hundred  1795  
deca  da  10^{1}  10  ten  1795  
10^{0}  1  one  –  
deci  d  10^{−1}  0.1  tenth  1795  
centi  c  10^{−2}  0.01  hundredth  1795  
milli  m  10^{−3}  0.001  thousandth  1795  
micro  μ  10^{−6}  0.000001  millionth  1873  
nano  n  10^{−9}  0.000000001  billionth  milliardth  1960  
pico  p  10^{−12}  0.000000000001  trillionth  billionth  1960  
femto  f  10^{−15}  0.000000000000001  quadrillionth  billiardth  1964  
atto  a  10^{−18}  0.000000000000000001  quintillionth  trillionth  1964  
zepto  z  10^{−21}  0.000000000000000000001  sextillionth  trilliardth  1991  
yocto  y  10^{−24}  0.000000000000000000000001  septillionth  quadrillionth  1991  

 Examples
 5 cm = 5×10^{−2} m = 5 × 0.01 m = 0.05 m.
 9 km^{2} = 9 × (10^{3} m)^{2} = 9 × (10^{3})^{2} × m^{2} = 9×10^{6} m^{2} = 9 × 1000000 m^{2} = 9000000 m^{2}.
 3 MW = 3×10^{6} W = 3 × 1000000 W = 3000000 W.
NonSI units accepted for use with SI
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 nonSI units accepted for use with SI:^{}
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 foot or the pound, these were the same regardless of where they were being measured. The radian, being 1/2π of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. The tonne, litre, and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are given below:
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 
plane and phase angle  degree  °  1° = (π/180) rad 
minute  ′  1′ = (1/60)° = (π/10800) rad  
second  ″  1″ = (1/60)′ = (π/648000) rad  
area  hectare  ha  1 ha = 1 hm^{2} = 10^{4} m^{2} 
volume  litre  l, L  1 l = 1 L = 1 dm^{3} = 10^{3} cm^{3} = 10^{−3} m^{3} 
mass  tonne (metric ton)  t  1 t = 1 000 kg 
dalton  Da  1 Da = 1.660539040(20)×10^{−27} kg  
energy  electronvolt  eV  1 eV = 1.602176634×10^{−19} J 
logarithmic ratio quantities  neper  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  
decibel  dB 
These units are used in combination with SI units in common units such as the kilowatthour (1 kW⋅h = 3.6 MJ).
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