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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.

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 1012 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.

QuantityName of UnitSymbolExpression in terms of SI base unitsExpression in terms of other units
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-1s3A2 A/V
Electrical inductance henry H m2 kg s-2 A-2
Electrical potential volt V m2 kg s-3 A-1 W/A
Electrical resistance ohm Ω m2 kg s-3 A-2 V/A
Force newton N kg ms-2
Frequency hertz Hz s-1
Illuminance lux lx m-2cd sr lm/m2
Luminous flux lumen lm cd sr
Magnetic flux weber Wb m2 kg 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 m2 s-3 J/s
Pressure pascal Pa kg/(m s2) = (N/m2)
Temperature relative to 273.15 K degree Celsius °C K
Work, energy, heat joule J m2 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.

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/(m2 K) kg s-3K-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 m2 kg s-2 K-1
heat flow rate (often used symbol Q or q) watt W or J/s m2 kg 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 10-9 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 m2 kg 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 m2 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 m2 s-2
specific heat capacity (or specific entropy, often used symbol c,p,cv or s) joule per kilogram Kelvin J/(kg K) m2 s-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 m2 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 m2/s m2 s-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 m2 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.

PrefixSymbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 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 = 10-9 m
• 1 mm3 = (10-3 m)3 = 10-9 m3

## Related Topics

• Basics - The SI-system, unit converters, physical constants, drawing scales and more.

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## Citation

• Engineering ToolBox, (2003). SI System. [online] Available at: https://www.engineeringtoolbox.com/si-unit-system-d_30.html [Accessed Day Mo. Year].

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