SI Seven Constants and Base Units

1. The SI

The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), informally known as the metric system, is the dominant measurement system used around the world as the preferred system of units, the basic language for science, technology, industry and international commerce.

The SI was established in 1960 by the 11th CGPM (from the French Conférence Générale des Poids et Mesures, known in English as the General Conference on Weights and Measures). The SI has always been a practical and dynamic system that has evolved to exploit the latest scientific and technological developments. The most recent revision of the SI was made by the 26th CGPM (2018) and effected from May 20th 2019. This new revision is the first time, a complete set of definitions is available that does not make reference to any artefact standards, material properties or measurement descriptions. The new definitions enable the realization of all units with an accuracy that is ultimately limited only by the quantum structure of nature and our technical abilities but not by the definitions themselves. 

2. The Seven SI Defining Constants

The definition of the entire system of SI units is established in terms of a set of seven defining constants. The seven defining constants are listed in Table 1.

Table 1. The seven defining constants of the SI and the seven corresponding units they define

The set of seven defining constants has been chosen to provide a fundamental, stable and universal reference that simultaneously allows for practical realizations with the smallest uncertainties. The technical conventions and specifications also take historical developments into account.

3. The Seven SI Base Units

In the revised SI, the values of the seven defining constants are the same everywhere in the universe, and these constants completely define the seven base SI units. The seven SI base units are listed in Table 2.

Table 2. SI base units

Starting from the new definition of the SI in terms of fixed numerical values of the defining constants, definitions of each of the seven base units are deduced by taking, as appropriate, one or more of these defining constants to give the following set of definitions.

The second – symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the cesium frequency Δν_Cs, the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹.

The conversion is: 1 Hz = Δν_Cs / 9 192 631 770 or 1 s = 9 192 631 770 / Δν_Cs

The meter – symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c, to be 299 792 458 when expressed in the unit m s⁻¹, where the second is defined in terms of the cesium frequency Δν_Cs.

The conversion is: 1 m = (c / 299 792 458) s = 30.663 318… c / Δν_Cs

The kilogram – symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h, to be 6.626 070 15 × 10⁻³⁴ when expressed in the unit J s, which is equal to kg m² s⁻¹, where the meter and the second are defined in terms of c and Δν_Cs.

The conversion is: 1 kg = (h / 6.626 070 15 × 10^–34) m^–2 s = 1.475 521... × 10⁴⁰ h Δν_Cs / c²

The ampere – symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e, to be 1.602 176 634 × 10⁻¹⁹ when expressed in the unit C, which is equal to A s, where the second is defined in terms of Δν_Cs.

The conversion is: 1 A = e / (1.602 176 634 × 10^–19) s^–1 = 6.789 686... × 10⁸ Δν_Cs e

The kelvin - symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k, to be 1.380 649 × 10⁻²³ when expressed in the unit J K⁻¹, which is equal to kg m² s⁻² K⁻¹, where the kilogram, meter and second are defined in terms of h, c and Δν_Cs.

The conversion is: 1 K = (1.380 649 × 10^–23 / k) kg m² s^–2 = 2.266 665… Δν_Cs h / k

The mole - symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number.

The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.

The conversion is: 1 mol = 6.022 140 76 × 10²³ / N_A

The candela - symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, K_cd, to be 683 when expressed in the unit lm W⁻¹, which is equal to cd sr W⁻¹, or cd sr kg⁻¹ m⁻² s³, where the kilogram, meter and second are defined in terms of h, c and Δν_Cs.

The conversion is: 1 cd = (K_cd / 683) kg m² s^–3 sr^–1 = 2.614 830... × 10¹⁰ (Δν_Cs)² h K_cd

In illuminating engineering, radiometry is the measurement of quantities associated with entire optical radiation in a broad spectrum, the radiometric quantities are purely physical quantities; photometry is the measurement of quantities associated with light as perceived by the human visual system, the photometric quantities are human-oriented quantities. They are different quantities as human eyes cannot see all optical radiation, and the eyes do not see all wavelengths equally. The SI defining constant luminous efficacy K_cd and the SI base unit candela establish relation between the radiometric quantities and the photometric quantities. More details about radiometry, photometry, SI luminous efficacy constant K_cd, and the SI base unit candela are described in other articles.

4. SI Derived units

The SI derived units are defined as products of powers of the seven SI base units. 22 derived units in the SI are given special names. Together with the seven base units, these 29 units form the core of the set of SI units. The 22 SI derived units with special names are listed in Table 3.

Table 3. The 22 SI units with special names and symbols

All other SI units can be derived from these core units by multiplying together different powers.

Last Update: August 25, 2020