Systems of Units and the International System (SI)

Units And Measurements • Physics

Concept Summary

In earlier times scientists of different countries used different systems of units. Three systems were widely used: the CGS system (centimetre, gram, second), the FPS or British system (foot, pound, second) and the MKS system (metre, kilogram, second). Today the internationally accepted system is the Système International d'Unités, abbreviated SI. Its standard scheme of symbols, units and abbreviations was developed by the Bureau International des Poids et Mesures (BIPM) in 1971 and was recently revised by the General Conference on Weights and Measures in November 2018. SI is used in scientific, technical, industrial and commercial work, and because it is a decimal system, conversions within it are simple and convenient. SI has seven base units: metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance and candela (cd) for luminous intensity. In the revised definitions each base unit is fixed by assigning an exact numerical value to a constant of nature, such as the speed of light, the Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant. Besides these, the radian (plane angle) and steradian (solid angle) are dimensionless supplementary units. Some units outside SI, such as litre, tonne, hectare and bar, are retained for general use.

Key Notes
  • CGS base units: centimetre, gram, second. FPS: foot, pound, second. MKS: metre, kilogram, second.
  • SI is the internationally accepted system; it was developed by BIPM in 1971 and revised in November 2018.
  • SI has seven base units: m, kg, s, A, K, mol, cd.
  • Plane angle: \(d\theta = ds/r\), unit radian (rad). Solid angle: \(d\Omega = dA/r^2\), unit steradian (sr). Both are dimensionless.
  • Revised definitions fix exact values of constants: \(c\), \(h\), \(e\), \(k\), \(N_A\), \(\Delta\nu_{Cs}\) and \(K_{cd}\).
  • One mole contains exactly \(6.02214076\times10^{23}\) elementary entities, which must be specified (atoms, molecules, ions, electrons, etc.).
  • The second is defined using the caesium-133 hyperfine transition frequency, 9192631770 Hz.
  • Units retained for general use (outside SI) include minute, hour, day, year, litre, tonne, bar, hectare and atm.
  • The exact values in the definitions need not be remembered; they only show the accuracy of measurement.
Important Equations
\[ c = 299792458\ \mathrm{m\,s^{-1}} \qquad h = 6.62607015\times10^{-34}\ \mathrm{J\,s} \] \[ e = 1.602176634\times10^{-19}\ \mathrm{C} \qquad k = 1.380649\times10^{-23}\ \mathrm{J\,K^{-1}} \] \[ N_A = 6.02214076\times10^{23}\ \mathrm{mol^{-1}} \qquad \Delta\nu_{Cs} = 9192631770\ \mathrm{Hz} \] \[ d\theta = \frac{ds}{r}\ \text{(radian)} \qquad d\Omega = \frac{dA}{r^2}\ \text{(steradian)} \]

Conversions: \(1\ \mathrm{h} = 3600\ \mathrm{s}\), \(1\ \mathrm{L} = 10^{-3}\ \mathrm{m^3}\), \(1\ \mathrm{t} = 10^{3}\ \mathrm{kg}\), \(1\ \mathrm{bar} = 10^{5}\ \mathrm{Pa}\), \(1\ \mathrm{atm} = 101325\ \mathrm{Pa}\).

Flow Chart
Different countries used CGS, FPS, MKS
Mind Map
  • Systems of Units
    • CGS: cm, g, s
    • FPS: foot, pound, s
    • MKS: m, kg, s
    • SI
      • Base: m, kg, s, A, K, mol, cd
      • Supplementary: rad, sr
      • Derived: N, J, W, Pa, etc.
      • Decimal, so easy conversion
    • Retained outside SI
      • min, h, d, y, L, t, bar, ha, atm
Graphic Organiser
Base QuantitySI UnitSymbolDefined by fixing
Lengthmetremspeed of light \(c\)
MasskilogramkgPlanck constant \(h\)
Timesecondscaesium frequency \(\Delta\nu_{Cs}\)
Electric currentampereAelementary charge \(e\)
Thermodynamic temperaturekelvinKBoltzmann constant \(k\)
Amount of substancemolemolAvogadro constant \(N_A\)
Luminous intensitycandelacdluminous efficacy \(K_{cd}\) = 683 lm W-1
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