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The International System of Units (SI) and the corresponding system of quantities
Version française
Summary
Quantities and units
The International System of Units (SI) and the corresponding system of quantities
Dimensions of quantities
Coherent units, derived units with special names, and the SI prefixes
SI units in the framework of general relativity
Units for quantities that describe biological effects
Legislation on units
Historical note

Search the SI brochure
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SI brochure, Section 1.2


This Brochure is concerned with presenting the information necessary to define and use the International System of Units, universally known as the SI (from the French Système International d'Unités). The SI was established by and is defined by the General Conference on Weights and Measures, the CGPM, as described in the Historical note in Section 1.8*.

The system of quantities, including the equations relating the quantities, to be used with the SI, is in fact just the quantities and equations of physics that are familiar to all scientists, technologists, and engineers. They are listed in many textbooks and in many references, but any such list can only be a selection of the possible quantities and equations, which is without limit. Many of the quantities, their recommended names and symbols, and the equations relating them, are listed in the International Standards ISO 31 and IEC 60027 produced by Technical Committee 12 of the International Organization for Standardization, ISO/TC 12, and by Technical Committee 25 of the International Electrotechnical Commission, IEC/TC 25. The ISO 31 and IEC 60027 Standards are at present being revised by the two standardization organizations in collaboration. The revised harmonized standard will be known as ISO/IEC 80000, Quantities and Units, in which it is proposed that the quantities and equations used with the SI will be known as the International System of Quantities.

The base quantities used in the SI are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The base quantities are by convention assumed to be independent. The corresponding base units of the SI were chosen by the CGPM to be the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. The definitions of these base units are presented in Section 2.1.1 in the following chapter. The derived units of the SI are then formed as products of powers of the base units, according to the algebraic relations that define the corresponding derived quantities in terms of the base quantities, see Section 1.4.

On rare occasions a choice may arise between different forms of the relations between the quantities. An important example occurs in defining the electromagnetic quantities. In this case the rationalized four-quantity electromagnetic equations used with the SI are based on length, mass, time, and electric current. In these equations, the electric constant epsilon0 (the permittivity of vacuum) and the magnetic constant mu0 (the permeability of vacuum) have dimensions and values such that epsilon0mu0 = 1/c02, where c0 is the speed of light in vacuum. The Coulomb law of electrostatic force between two particles with charges q1 and q2 separated by a distance r is written**

F =
q1q2 r
4piepsilon0 r3

and the corresponding equation for the magnetic force between two thin wire elements carrying electric currents, i1dl1 and i2dl2, is written

d2F =
mu0
i1dl1 x (i2dl2 x r)
4pi
r3

where d2F is the double differential of the force F. These equations, on which the SI is based, are different from those used in the CGS-ESU, CGS-EMU, and CGS-Gaussian systems, where epsilon0 and mu0 are dimensionless quantities, chosen to be equal to one, and where the rationalizing factors of 4pi are omitted.



* Acronyms used in this Brochure are listed with their meaning here.
** Symbols in bold print are used to denote vectors.
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Note: For the official text, please refer to the PDF files available at:
  • http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf (in English) and
  • http://www.bipm.org/utils/common/pdf/si_brochure_8_fr.pdf (in French).
  •