SI System
An introduction to the SI metric system.
The SI system (International System of Units) is the modern metric system of measurement and the dominant system of international commerce and trade. SI units are gradually replacing Imperial and USCS units.
The SI is maintained by the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures) in Paris.
The SI system is founded on the
 SI base units
 SI derived units described in terms of acceptable SI units
 SI derived units with special names and symbols acceptable in SI
 SI Prefixes
SI Base Units
The core of the SI system is a short list of base units defined in an absolute way without referring to any other units. The base units are consistent with the part of the metric system called the MKS system. The International System of Units (SI) is founded on seven base units.
Quantity  Name of Unit  Symbol 

Length  metre  m 
Mass  kilogram  kg 
Time  second  s 
Electrical current  ampere  A 
Thermodynamic temperature  kelvin  K 
Luminous intensity  candela  cd 
Amount of substance  mole  mole 
 Metre  is the length of a path traveled by light in vacuum during a time interval of 1/299792458 of a second
 Kilogram  is equal to the mass of the international prototype of the kilogram
 Second  is the duration of 9192631770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of caesium133 atom
 Ampere  is the constant current in two parallel conductors of infinite length with negligible circular cross section and placed 1 metre apart in vacuum  that produces a force equal to 2 10^{7} newton per metre of length between the conductors
 Kelvin  is the 1/273.16 fraction of the thermodynamic temperature of the triple point of water
 Mole  is the amount of substance which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon12
 Candela  is the luminous intensity in a given direction of a source that emits monochromatic radiations of 540 10^{12} hertz frequency with a radiant intensity of 1/683 watt per steradian in the direction
SI Derived Units with Special Names and Symbols acceptable in SI
Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.
Quantity  Name of Unit  Symbol  Expression in terms of SI base units  Expression in terms of other units 

Plane angle  radian  rad  
Solid angle  steradian  sr  
Adsorbed radiation  gray  Gy  m^{2} s^{2}  J/kg 
Electrical capacitance  farad  F  m^{2} kg^{1} s^{4} A^{2}  C/V 
Electrical charge  coulomb  C  A s  
Electrical conductance  siemens  S  m^{2} kg^{1}s^{3}A^{2}  A/V 
Electrical inductance  henry  H  m^{2} kg s^{2} A^{2}  
Electrical potential  volt  V  m^{2} kg s^{3} A^{1}  W/A 
Electrical resistance  ohm  Ω  m^{2} kg s^{3} A^{2}  V/A 
Force  newton  N  kg ms^{2}  
Frequency  hertz  Hz  s^{1}  
Illuminance  lux  lx  m^{2}cd sr  lm/m^{2} 
Luminous flux  lumen  lm  cd sr  
Magnetic flux  weber  Wb  m^{2} kg s^{2} A^{1}  V s 
Magnetic flux density  tesla  T  kg s^{2} A^{1}  Wb/m^{2} 
Power or radiant flux  watt  W  kg m^{2} s^{3}  J/s 
Pressure  pascal  Pa  kg/(m s^{2}) = (N/m^{2})  
Radioactivity  becquerel  Bq  s^{1}  
Temperature relative to 273.15 K  degree Celsius  °C  K  
Work, energy, heat  joule  J  m^{2} kg s^{2}  N m 
SI Derived Units described in Terms of acceptable SI Units
Derived units are algebraic combinations of the seven base units and the two supplementary units with some of the combinations being assigned special names and symbols.
Quantity  Description  Symbol  Expression in terms of SI base units 

acceleration  meter per second squared  m/s^{2}  m s^{2} 
area  square meter  m^{2}  m^{2} 
coefficient of heat transfer (often used symbol h or U)  watt per square meter Kelvin  W/(m^{2} K)  kg s^{3}K^{1} 
concentration (of amount of substance)  mole per cubic meter  mol/m^{3}  mol m^{3} 
current density (often used symbol r)  ampere per square meter  A/m^{2}  A m^{2} 
density (mass density)  kilogram per cubic meter  kg/m^{3}  kg m^{3} 
electrical charge density  coulomb per cubic meter  C/m^{3}  m^{3} s A 
electric field strength  volt per meter  V/m  m kg s^{3} A^{1} 
electric flux density  coulomb per square meter  C/m^{2}  m^{2} s A 
energy density  joule per cubic meter  J/m^{3}  m^{1} kg s^{2} 
force  Newton  N or J/M  m kg s^{2} 
heat capacity  joule per Kelvin  J/K  m^{2} kg s^{2} K^{1} 
heat flow rate (often used symbol Q or q)  watt  W or J/s  m^{2} kg s^{3} 
heat flux density or irradiance  watt per square meter  W/m^{2}  kg s^{3} 
luminance  candela per square meter  cd/m^{2}  cd m^{2} 
magnetic field strength  ampere per meter  A/m  A m^{1} 
modulus of elasticity (or Young's modulus)  giga Pascal  GPa  10^{9} m^{1} kg s^{2} 
molar energy  joule per mole  J/mole  m^{2} kg s^{2} mol^{1} 
molar entropy (or molar heat capacity)  joule per mole Kelvin  J/(mole K)  m^{2} kg s^{2} K^{1} mol^{1} 
moment of force (or torque)  Newton meter  N m  m^{2} kg s^{2} 
moment of inertia  kilogram meter squared  kg m^{2}  kg m^{2} 
momentum  kilogram meter per second  kg m/s  kg m s^{1} 
permeability  Henry per meter  H/m  m kg s^{2} A^{2} 
permitivity  farad per meter  F/m  m^{3} kg^{1} s^{4} A^{2} 
power  kilowatt  kW  10^{3} m^{2} kg s^{3} 
pressure (often used symbol P or p)  kilo Pascal  kPa  10^{3} m^{1} kg s^{2} 
specific energy  joule per kilogram  J/kg  m^{2} s^{2} 
specific heat capacity (or specific entropy, often used symbol c_{,p},c_{v} or s)  joule per kilogram Kelvin  J/(kg K)  m^{2} s^{2} K^{1} 
specific volume  cubic meter per kilogram  m^{3}/kg  m^{3} kg^{1} 
stress  mega Pascal  MPa  10^{6} m^{1} kg s^{2} 
surface tension  Newton per meter  N/m  kg s^{2} 
thermal conductivity (often used symbol k)  watt per meter Kelvin  W/(m K)  m kg s^{3} K^{1} 
torque  Newton meter  N m  m^{2} kg s^{2} 
velocity (or speed)  meters per second  m/s  m s^{1} 
viscosity, absolute or dynamic (often used symbol m)  Pascal second  Pa s  m^{1} kg s^{1} 
viscosity, kinematic (often used symbol n)  square meter per second  m^{2}/s  m^{2} s^{1} 
volume  cubic meter  m^{3}  m^{3} 
wave number  1 per meter  1/m  m^{1} 
work (or energy heat, often used symbol W)  joule  J or N m  m^{2} kg s^{2} 
SI Prefixes
Number  Greek  Latin 
½  hemi  semi 
1  mono  uni 
1½  sesqui  
2  di  bi 
3  tri  ter 
4  tetra  quandri 
5  penta  quinque 
6  hexa  sexi 
7  hepta  septi 
8  octa  octo 
9  ennea  nona 
10  deca  deci 
11  hendeca  undec 
12  dodeca  duodec 
13  trideca  tridec 
14  tetradeca  quatuordec 
15  pentadeca  quindec 
16  hexadeca  sedec 
17  heptadeca  septendec 
20  eicosane  vige, vice 
30  triaconta  trige, trice 
40  tetraconta  quadrage 
50  pentaconta  quincuage 
60  hexaconta  sexage 
70  heptaconta  septuage 
80  octaconta  octage 
90  enneaconta  nonage 
100  hecto  cente 
many  poly  multi 
A strength of the SI system is the use of prefixes to indicate multiples or submultiples of units as indicated below.
Prefix  Symbol  

10^{24}  yotta  Y 
10^{21}  zetta  Z 
10^{18}  exa  E 
10^{15}  peta  P 
10^{12}  tera  T 
10^{9}  giga  G 
10^{6}  mega  M 
10^{3}  kilo  k 
10^{2}  hecto  h 
10^{1}  deca  da 
10^{1}  deci  d 
10^{2}  centi  c 
10^{3}  milli  m 
10^{6}  micro  μ 
10^{9}  nano  n 
10^{12}  pico  p 
10^{15}  femto  f 
10^{18}  atto  a 
10^{21}  zepto  z 
10^{24}  yocto  y 
The prefixes provide an order of magnitude: Ex.
 16600 m = 16.6 10^{3} m = 16.6 km
 1 centimeter = 10^{2} m
 1 millimeter = 10^{3} m
 1 micrometer = 10^{6} m
 1 nanometer = 10^{9} m
 1 mm^{3} = (10^{3} m)^{3} = 10^{9} m^{3}
NonSi Units Accepted for Use with the International System
Name  Symbol  Value in SI Units 

minute  min  1 min = 60 s 
hour  h  1 h = 60 min = 3600 s 
day  d  1 d = 24 h = 86400 s 
degree  °  1° = (π/180) rad 
minute  '  1' = (1/60)° = (π/10800) rad 
second  ''  1'' = (1/60)' = (π/648000) rad 
liter  l, L  1 L = 1 dm^{3} = 10^{3} m^{3} 
metric ton  t  1 t = 10^{3} kg 
neper  Np  1 Np = 1 
bel  B  1 B = (1/2) ln 10 Np 
nautical mile  1 nautical mile = 1852 m  
knot  knot  1 knot = 1 nautical mile per hour = (1852/3600) m/s 
are  a  1 a = 1 dam^{2 = }10^{2} m^{2} 
hectare  ha  1 ha = 1 hm^{2} = 10^{4} m^{2} 
bar  bar  1 bar = 0.1 MPa = 100 kPa = 10^{5} Pa 
ångström  Å  1 Å = 0.1 nm = 10^{10} m 
barn  b  1 b = 100 fm^{2} = 10^{28} m^{2} 
 neper and bel is used to express values of logarithmic quantities like power level, field level and so on
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