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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

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.

SI Base Units
QuantityName of UnitSymbol
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 caesium-133 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 carbon-12
  • 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.

SI Derived Units with Special Names and Symbols acceptable in SI
QuantityName of UnitSymbolExpression in terms of SI base unitsExpression in terms of other units
Plane angle radian rad
Solid angle steradian sr
Adsorbed radiation gray Gy m2s-2 J/kg
Electrical capacitance farad F m-2 kg-1 s4 A2 C/V
Electrical charge coulomb C A s
Electrical conductance siemens S m-2 kg-1 s3 A2 A/V
Electrical inductance henry H m2kg s-2 A-2
Electrical potential volt V m2kg s-3 A-1 W/A
Electrical resistance ohm Ω m2kg 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/m2
Luminous flux lumen lm cd sr
Magnetic flux weber Wb m2kg s-2 A-1 V s
Magnetic flux density tesla T kg s-2 A-1 Wb/m2
Power or radiant flux watt W kg m2s-3 J/s
Pressure pascal Pa kg/(m s2) = (N/m2)
Radioactivity becquerel Bq s-1
Temperature relative to 273.15 K degree Celsius °C K
Work, energy, heat joule J m2kg 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.

SI Derived Units described in Terms of acceptable SI Units
QuantityDescriptionSymbolExpression in terms of SI base units
acceleration meter per second squared m/s2 m s-2
area square meter m2 m2
coefficient of heat transfer (often used symbol h or U ) watt per square meter Kelvin W/(m2K) kg s-3 K-1
concentration (of amount of substance) mole per cubic meter mol/m3 mol m-3
current density (often used symbol r ) ampere per square meter A/m2 A m-2
density (mass density) kilogram per cubic meter kg/m3 kg m-3
electrical charge density coulomb per cubic meter C/m3 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/m2 m-2 s A
energy density joule per cubic meter J/m3 m-1 kg s-2
force Newton N or J/M m kg s-2
heat capacity joule per Kelvin J/K m2kg s-2 K-1
heat flow rate (often used symbol Q or q ) watt W or J/s m2kg s-3
heat flux density or irradiance watt per square meter W/m2 kg s-3
luminance candela per square meter cd/m2 cd m-2
magnetic field strength ampere per meter A/m A m-1
modulus of elasticity (or Young's modulus) giga Pascal GPa 10-9m-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 m2kg s-2
moment of inertia kilogram meter squared kg m2 kg m2
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 s4 A2
power kilowatt kW 10-3 m2kg 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 m2s-2
specific heat capacity (or specific entropy, often used symbol c ,p , cv or s ) joule per kilogram Kelvin J/(kg K) m2s-2 K-1
specific volume cubic meter per kilogram m3 /kg m3 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 m2kg 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 m2/s m2s-1
volume cubic meter m3 m3
wave number 1 per meter 1/m m-1
work (or energy heat, often used symbol W ) joule J or N m m2kg s-2

SI Prefixes

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.

SI Prefix Symbols
PrefixSymbol
10 24 yotta Y
1021 zetta Z
1018 exa E
10 15 peta P
10 12 tera T
109 giga G
106 mega M
103 kilo k
102 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 = 16.6 103 m = 16.6 km
  • 1 centimeter = 10-2 m
  • 1 millimeter = 10-3 m
  • 1 micrometer = 10-6 m
  • 1 nanometer = 10-9m
  • 1 mm3 = (10-3 m)3 = 10-9m3

Non-Si Units Accepted for Use with the International System

Non-Si Units Accepted for Use with the International System
NameSymbolValue 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 dm3 = 10-3 m3
metric ton t 1 t = 103 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 = 102m2
hectare ha 1 ha = 1 hm2= 104 m2
bar bar 1 bar = 0.1 MPa = 100 kPa = 105 Pa
ångström Å 1 Å = 0.1 nm = 10 -10 m
barn b 1 b = 100 fm2= 10 -28 m2
  • neper and bel is used to express values of logarithmic quantities like power level, field level and so on

Related Topics

  • Basics

    Basic engineering data. SI-system, unit converters, physical constants, drawing scales and more.

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