Resource: The SI unit system

1 The SI unit system (abbreviated from French ‘Système international d’unités’) defines an official international collection of units that can and is recommended to be used for all properties. Until 2018, the SI system defined a set of SI base units:

Former SI base units2
LengthMetre$\mathrm m$
TimeSecond$\mathrm s$
Electrical currentAmpere$\mathrm A$
TemperatureKelvin$\mathrm K$
Amount of substanceMole$\mathrm{mol}$

They were chosen for historical reasons[2] or after what was easier to measure and verify universally (so-called ‘operational definitions’),[3] and not from how fundamental they “felt”.

Since 2018, all units are instead defined from a set of defining constants. These are universal constants2 whose values are not necessarily clean or obvious by far, but nevertheless reliable and always the same (as far as we know).

Defining constants in the SI system6
Caesium transition frequency5$\Delta \nu_\text{Cs}=9\,192\,631\,770\,\mathrm{Hz}$
Speed of light$c=299\,792\,458\,\mathrm{m/s}$
Planck constant$h=6.626\,070\,15\times10^{-34}\,\mathrm{J\,s}$
Elementary charge$e=1.602\,176\,634\times10^{-19}\,\mathrm{C}$
Boltzmann's constant$k_B=1.380\,649\times10^{-23}\,\mathrm{J/K}$
Avogadro's constant$N_A=6.022\,140\,76\times10^{23}\,\mathrm{mol^{-1}}$
Luminous efficacy4$K_\mathrm{cd}=683\,\mathrm{lm/W}$

Since the units involved in these constants can be converted into all of the former base units, these defining constants can derive those base units and thus all units possible:

  • the ‘Hertz’ is a term for ‘per second’: $\mathrm{[Hz]=[s^{-1}]}$,
  • the ‘Joule’ covers: $\mathrm{[J]=[kg\,m^2/s^2]}$,
  • Coulomb-per-second is Amperes: $\mathrm{[C/s]=[A]}$,
  • the ‘lumen’ translates to the ‘candela’: $\mathrm{[lm]=[cd\,m^2/m^2]=[cd]}$, and
  • the ‘Watt’ is a term for Joules-per-second: $\mathrm{[W]=[J/s]=[kg\,m^2/s^3]}$.

The SI unit system is being revised continuously by the Metre Convention consisting of and supported by a bunch of countries worldwide (101 as of 2019). Their goal is to universally define a unit system to ‘provide a fundamental, stable and universal reference that simultaneously allows for practical realisations with the smallest uncertainties’ as well as to ‘disconnect definition from realisation3 so that the invention of better measurement technologies in the future will not require the definitions to be changed.

The above defining constants have taken over gradually after decades with less optimal definitions, such as definitions based on specific objects.4 Such objects would gradually deteriorate and are not universally accessible. So, the change to purely universal constants should future-proof the SI system.


  1. The International System of Units (SI)’ (book), B. Inglis, J. Ullrich and others, Bureau International des Poids et Mesures (BIPM), 9th ed., 2019, www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf, chapter 3
  2. The name “kilogram”: a historical quirk’ (web page), Bureau International des Poids et Mesures (BIPM), www.bipm.org/en/measurement-units/history-si/name-kg.html (accessed Sep. 11th, 2019)
  3. Variables and Operational Definitions’ (web page), Grand Canyon University, Center for Innovation in Research and Teaching (CIRT), cirt.gcu.edu/research/developmentresources/research_ready/quantresearch/variables_def (accessed Aug. 6th, 2019)
  4. (Former) International Prototype of the Kilogram’ (web page), Bureau International des Poids et Mesures (BIPM), 2019, www.bipm.org/en/bipm/mass/ipk (accessed Sep. 11th, 2019)
  5. Physical kilogram is officially dead’ (web page), Elizabeth Gibney, Nature, 2019, www.nature.com/articles/d41586-019-01614-8, DOI 10.1038/d41586-019-01614-8
  6. The former Prototype Metre’ (web page), Bureau International des Poids et Mesures (BIPM), www.bipm.org/en/measurement-units/history-si/former-prototype-metre.html (accessed Sep. 11th, 2019)