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The International System of Units (SI Units)

28th Mar 2019 @ 20 min read

Basic Chemistry

The International System of Units or in short SI (in French Le Systeme International d’Unités) is the currently accepted system of measurement. It originated from France. The SI was established in 1960 by the 11th CGPM (General Conference on Weights and Measures or Conférence Générale des Poids et Mesures in French). The SI system is the updated version of the metric system. It is presently accepted worldwide; though, certain countries like the USA still follows traditional English units. The SI system includes the seven base units, names of 22 derived units, and a set of prefixes.

The SI units comprise of the base units and derived units.

SI base units

There are seven fundamental or base units. According to Inter International System of Units, they are metre, kilogram, second, ampere, kelvin, mole and candela. From these base units, we can derive any other SI units; in other words, all rest SI Units are the combination of these seven base units.

The seven SI base units: second, metre, kilogram, ampere, kelvin, mole, and candela.
The SI Base Units

Each SI base unit is associated with a basic physical quantity. Physical quantities with its respective SI units are length with metre, mass with kilogram, time with second, current with ampere, temperature with kelvin, amount of substance with mole, and luminous intensity with candela. The table below explains the same.

Seven SI Base Units with Their Physical Quantities
Physical QuantityQuantity SymbolSI UnitSI Unit Symbol
Amount of substancenmolemol
Luminous intensityIvcandelacd

The General Conference on Weights and Measures (CGPM) is responsible for the maintenance and improvisation of SI units. The CGPM keeps improving the SI system, including definitions of the SI units, for better accuracy and precision. The base SI units are defined from constants of nature like the speed of light in vacuum, the triple point of water. Their definitions keep modifying with time. Thus, the SI system is an evolving system. The table below lists the definitions as of 2019.

Definition of the SI Base Units
SI UnitSymbolDefinition
metremA metre is distance travelled by light in vacuum in 1299 792 458 of a second.
kilogramkgThe definition of kilogram is based on three parameters: the Planck constant (6.626 070 15 × 10−34 J·s), the speed of light and the natural microwave radiation of the caesium atom.
secondsThe duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
ampereAAn ampere is the flow of 11.602 176 634 × 10−19 times the elementary charge per second.
kelvinKThe kelvin is defined by fixing the value of the Boltzmann constant to 1.380 649 × 10−23 J·K−1.
molemolA mole represents 6.022 140 76 × 1023 elementary entities. This number is also called the Avogadro constant, NA
candelacdIt is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.40 × 1014 hertz and that has a radiant intensity in that direction of 1683 watt per steradian.

Note: Earlier the base SI unit of temperature was °K or Kelvin (with “K” capital), but now it is revised to K or kelvin.

SI derived units

SI derived units are units derived from various combinations (product, power, and quotient) of 7 SI base units. They may be dimensionless or express in terms of the above SI base units or other SI derived units. Consider an example of pressure; pressure is force per unit area. The unit of pressure is pascal or Pa; The pascal can be expressed in another SI derived unit, N·m−2 or in the base unit, kg·m−1·s−2.

There is no limit to SI derived units; they are unlimited. The below table mentions various SI derived units in the form of the SI base units.

Various SI Derived Units with Their Physical Quantities
Physical QuantityQuantity SymbolSI UnitSI Unit Symbol
AreaAsquare metrem2
VolumeVcubic metrem3
Densityρkilogram per cubic metrekg⋅m−3
Specific volumeVspcubic metre per kilogramm3⋅kg−1
ConcentrationCmole per cubic metremol⋅m−3
Velocityvmetre per secondm⋅s−1
Accelerationametre per second squaredm⋅s−2
Magnetic field strengthHampere per metreA⋅m−1
LuminanceLvcandela per square metrecd⋅m−2
Refractive indexnone1

In the International System of Units, there are special names and symbols of 22 SI derived units. They are listed in the below table.

Special Names and Symbols of 22 SI Derived Units
Physical QuantityNameSymbolSI UnitsEquivalent Units
Solid anglesteradiansr1m2/m2
Force, weightnewtonNkg⋅m⋅s−2kg⋅m/s2
Pressure, stresspascalPakg⋅m−1⋅s−2N/m2
Work, energyjouleJkg⋅m2⋅s−2N⋅m, W⋅s, C⋅V
PowerwattWkg⋅m2⋅s−3J/s, V⋅A
Electric chargecoulombCs⋅As⋅A, F⋅V
Voltage, e.m.fvoltVkg⋅m2⋅s−3⋅A−1W/A, J/C
CapacitancefaradFkg−1⋅m−2⋅s4⋅A2s/Ω, C/V
Electrical resistance, impedanceohmΩkg⋅m2⋅s−3⋅A−2V/A, 1/S
Electrical conductancesiemensSkg−1⋅m−2⋅s3⋅A21/Ω, A/V
Magnetic fluxweberWbkg⋅m2⋅s−2⋅A−1J/A, T⋅m2
Magnetic induction, magnetic flux densityteslaTkg⋅s−2⋅A−1Wb/m2, V⋅s/m2 N/(A⋅m)
Electrical inductancehenryHkg⋅m2⋅s−2⋅A−2Ω⋅s, Wb/A, V⋅s/A
Temperaturedegree CelsiusKK
Luminous fluxlumenlmcdcd⋅sr
Absorbed dosegrayGym2⋅s−2J/kg
Equivalent dosesievertSvm2⋅s−2J/kg
Catalytic activitykatalkats−1⋅molmol/s

Note: Angle and steradian are the only dimensionless SI derived units in the above table. They are together known as supplementary units. Relation between the SI base units and SI derived units

22 SI derived units and 7 SI base units
Relation between the SI base units and SI derived units
[Image source: NIST]

SI Prefixes

Prefixes precede the original unit. They are used to create the multiple or fraction of the original units. These prefixes are all decadic. The SI prefixes are adopted by the International System of Quantities. The table below lists them.

SI Units Prefixes
PrefixesSymbolFactor (Base 10)English WordExample
yottaY1024SeptillionEarth’s mass is 5972.6 Yg
zettaZ1021SextillionAtmosphere’s mass is 2 Zg
exaE1018Quintillion1 EeV is 0.1602 J
petaP1015Quadrillion9.461 Pm is 1 light-year
teraT1012Trillion1 TB of storage
gigaG109Billion4 GHz of clock rate (CPU)
megaM106Million50 MW of electricity
kilok103Thousand5 kg of sugar
hectoh102Hundred2 hm2 farm area
decada101Ten1 dam wide road
  100OneOne dollar
decid10−1Tenth1 dm is one-tenth metre
centic10−2HundredthA typical ruler is 15 cm long.
millim10−3Thousandth10 mg of salt
microμ10−6Millionth2.5 μm of bacteria
nanon10−9Billionthwavelengths of visible light range from 380 nm to 740 nm
picop10−12Trillionth25 pm is the radius of a Hydrogen atom
femtof10−15QuadrillionthProton’s diameter is 1.6 fm
attoa10−18QuintillionthMass of the virus is 1510 ag
zeptoz10−21Sextillionth160.21 zC is charge on an electron
yoctoy10−24Septillionth1.674 yg is the rest mass of a neutron

Accepted non-SI units

Many traditional units are still in practice and are difficult to replace with their respective SI alternatives. This is because of the long history of usage of these non-SI units. The international committee does recognise these traditional units. These units are mentioned below.

Accepted Non-SI Units
QuantityUnitSymbolValue in SI
Plane angledegree°1° = (π180) rad
Plane angleminute1′ = (160
Plane anglesecond1″ = (160)′
Timeminutemin1 min = 60 s
Timehourh1 h = 60 min
Timedayd1 d = 24 h
VolumelitreL, l1 L = 10−3 m3
Massgramg1 g = 10−3 kg
Masstont1 t = 103 kg
Areahectareha1 ha = 104 m2
RatioNeperNp1 Np = 1
RatioBelB1 B = 12 ln(10) Np
ElectronvoltenergyeV1 eV = 1.602 176 53(14) × 10−19 J
Astronomical unitlengthau1 au = 1.495 978 707 00 × 1011 m
Atomic mass unitmassu1 u = 1.660 538 86(28) × 10−27 kg

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