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The International System of Units

The International System of Units

Published by: Kamila Szulc

The International System of Units (SI) on the BIPM website:

 

The definition of the SI units is established in terms of a set of seven defining constants. The complete system of units can be derived from the fixed values of these defining constants, expressed in the units of the SI. These seven defining constants are the most fundamental feature of the definition of the entire system of units.

 

The seven defining constants of the SI and the seven corresponding units they define:

Defining constant Symbol Numerical value Unit
hyperfine transition frequency of Cs DeltanuCs 9 192 631 770 Hz
speed of light in vacuum c 299 792 458 m s–1
Planck constant h 6.626 070 15 x 10–34 J s
elementary charge e 1.602 176 634 x 10–19 C
Boltzmann constant k 1.380 649 x 10–23 J K–1
Avogadro constant NA 6.022 140 76 x 1023 mol–1
luminous efficacy Kcd 683 lm W–1

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These particular constants were chosen after having been identified as being the best choice, taking into account the previous definition of the SI, which was based on seven base units, and progress in science.

The definitions below specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit. By fixing the exact numerical value the unit becomes defined, since the product of the numerical value and the unit has to equal the value of the constant, which is postulated to be invariant. The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or quotients of defining constants.

The International System of Units, the SI, is the system of units in which

  • the unperturbed ground state hyperfine transition frequency of the caesium 133 atom DeltanuCs is 9 192 631 770 Hz,
  • the speed of light in vacuum c is 299 792 458 m/s,
  • the Planck constant h is 6.626 070 15 x 10–34 J s,
  • the elementary charge e is 1.602 176 634 x 10–19 C,
  • the Boltzmann constant k is 1.380 649 x 10–23 J/K,
  • the Avogadro constant NA is 6.022 140 76 x 1023 mol–1,
  • the luminous efficacy of monochromatic radiation of frequency 540 x 1012 Hz, Kcd, is 683 lm/W.

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to Hz = s–1, J = kg m2 s–2, C = A s, lm = cd m2 m–2 = cd sr, and W = kg m2 s–3.

The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or quotients of defining constants.

The numerical values of the seven defining constants have no uncertainty.

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