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Measurement FundamentalsInternational System of Units (SI)

The principle behind the International System of Units is to provide the same values for measurements such as length, weight, and time no matter where in the world measurement is performed. The units used in this system are referred to as “SI units.” The system was established at the 1960 General Conferences on Weights and Measures (CGPM). The abbreviation “SI” stands for “Le Système International d'Unités.”

The International System of Units comprises the following three categories.

  • Base units
  • Supplementary units
  • Derived units

Base Units

Amount Unit name Unit symbol Definition
Length Metre m The distance traveled by light in a vacuum in 1/299792458 second.
Weight Kilogram kg This is the unit for weight. The mass of the international prototype kilogram.
Time Second s The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
Current Ampere A The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10-7 newtons per metre of length.
Thermodynamic temperature Kelvin K 1/273.16 of the thermodynamic temperature of the triple point of water.
Substance amount Mole mol The amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (Limited to objects with clarified composition.) Elementary entities are subatomic particles that compose matter and energy.
Luminosity Candela cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Supplementary Units

Amount Unit name Unit symbol Definition
Plane angle Radian rad Radian describes the plane angle subtended by an arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian.
Solid angle Steradian sr A steradian is a solid angle at the centre of a sphere subtending a section on the surface equal in area to the square of the radius of the sphere.

Derived Units

Derived units are a combination of base units and supplementary units and the mathematical symbols of multiplication and division.

Amount Unit name Unit symbol
Area Square metre m2
Volume Cubic metre m3
Speed Metre per second m/s
Acceleration Metre per second squared m/s2
Wavenumber Reciprocal metre m-1
Density Kilogram per cubic metre kg/m3
Current density Ampere per square metre A/m2
Magnetic field strength Ampere per metre A/m
Concentration (of amount of substance) Mole per cubic metre mol/m3
Specific volume Cubic metre per kilogram m3/kg
Luminance Candela per square metre cd/m2

Some derived units are given unique names.

Amount Unit name Unit symbol Composition
Frequency Hertz Hz 1Hz=1s-1
Force Newton N 1N=1kg・m/s2
Pressure, stress Pascal Pa 1Pa=1N/m2
Energy, work, amount of heat Joule J 1J=1N・m
Power, radiant flux Watt W W=1J/s
Electric charge, amount of electricity Coulomb C 1C=1A・s
Electric potential/electric potential difference, voltage, electromotive force Volt V 1V=1J/C
Resistance (electrical) Ohm Ω 1Ω=1V/A
Conductance (electrical) Siemens S 1S=1Ω-1
Magnetic Weber Wb 1Wb=1V・s
Magnetic flux density, magnetic induction Tesla T 1T=1Wb/m2
Inductance Henry H 1H=1Wb/A
Celsius temperature Degree Celsius 1t=T-To
Luminous flux Lumen lm 1lm=1cd・sr
Illuminance Lux lx 1lx=1lm/m2

Reference Information

SI unit prefixes indicating integer powers of ten

Factor Prefix Symbol Factor Prefix Symbol
1018 exa E 10-1 deci d
1015 peta P 10-2 centi c
1012 tera T 10-3 milli m
109 giga G 10-6 micro µ
106 mega M 10-9 nano n
103 kilo k 10-12 pico p
102 hecto h 10-15 femto f
10 deka da 10-18 atto a

Non-SI units

Amount Unit name Unit symbol Definition
Time Minute min 1min=60s
Hour h 1h=60min
Day d 1d=24h
Plane angle Degree ° 1°= (π/180) rad
Minute 1′= (1/60) °
Second 1″= (1/60) ′
Volume Litre l, L 1l=7dm3
Weight Metric ton t 1t=103kg

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