Reference sheets · 2019

The SI Base Units

Bureau International des Poids et Mesures

Reference sheet · SI Brochure, 9th edition 2019 · Version 4.01, June 2026

The SI Brochure, Sections 2.2 and 2.3.1

Source: bipm.org
Retrieved: 27 September 2026
License: MIT (compilation); data: SI Brochure, BIPM (CC BY 4.0)
Rights holder: Bureau International des Poids et Mesures (text); one-page-papers (compilation)
Language: English

The SI Brochure is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

About this edition and its rights

Edition

The SI Brochure, The International System of Units (SI), 9th edition 2019, English PDF SI-Brochure-9-EN.pdf, V4.01 of June 2026 (https://doi.org/10.59161/AUEZ1291), pages 123 to 131. Kept: from Section 2.2, the statement “The International System of Units, the SI, is the system of units in which” with its seven items, the paragraph “where the hertz, joule, ...” and the sentence on the uncertainty of the constants; from Section 2.3.1, its first sentence, Table 2, the sentence that introduces the definitions, and for each of the seven base units its title, its definition (for the mole, its two paragraphs), the paragraph “This definition implies the exact relation...”, its equations, “which is equal to” where the brochure has a second equation, and the paragraph “The effect of this definition...”. Left out: the other paragraphs of those sections (previous definitions, realization, the Celsius temperature, the molar mass, Table 1, which repeats the seven constants) and the margin notes. The text was taken from the PDF with pdftotext and its superscripts and subscripts restored by script, checked against the pages: powers of ten and unit exponents are superscript, 133 before Cs is superscript, and the symbols are set in italic with their subscripts (the caesium frequency, N with subscript A, K with subscript cd, c, h, e, k, n, kT and the frequency nu), as the brochure prints them; the definitions are in bold, as printed. The brochure writes some minus signs of exponents with an en dash character (s–1, s–2, s–3 in the paragraph “where the hertz...”) and others with a minus sign: each is kept as it is. The increment sign (U+2206) of the caesium frequency, which no bundled font has, is set as the Greek capital delta (U+0394), which the printed page shows. The equations are set with KaTeX from the printed pages; the long ones, which the brochure sets on one line (on two for the candela), are broken before the “approximately equal” sign to fit the columns. The spaces between groups of digits and around the multiplication sign are set as no-break spaces. Table 2 is set as a table, its typical symbols in italic as printed. The header and the footer are written for the poster.

Rights

License notice: “The SI Brochure is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.”

Copyright statement of the SI Brochure, 9th edition, V4.01 (June 2026), on the page after its title page, https://www.bipm.org/en/publications/si-brochure. The footer credits the BIPM, names the brochure, its version and sections, links the license and says that the text is excerpted and the equations reset. The selection and layout are an original compilation under the MIT license of this repository.

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, Δν_Cs, 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 × 10⁻³⁴ J s,
the elementary charge, e, is 1.602 176 634 × 10⁻¹⁹ C,
the Boltzmann constant, k, is 1.380 649 × 10⁻²³ J/K,
the Avogadro constant, N_A, is 6.022 140 76 × 10²³ mol⁻¹,
the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, K_cd, 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 sr, and W = kg m² s^–3.

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

The base units of the SI are listed in Table 2.

Table 2. SI base units
Base quantity		Base unit
Name	Typical symbol	Name	Symbol
time	t	second	s
length	l, x, r, etc.	metre	m
mass	m	kilogram	kg
electric current	I, i	ampere	A
thermodynamic temperature	T	kelvin	K
amount of substance	n	mole	mol
luminous intensity	I_v	candela	cd

Starting from the 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 using, as appropriate, one or more of these defining constants to give the following set of definitions:

The second#

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

This definition implies the exact relation Δν_Cs = 9 192 631 770 Hz. Inverting this relation gives an expression for the unit second in terms of the defining constant Δν_Cs:

1 Hz = \frac{Δ ν _{Cs}}{9 192 631 770} or 1 s = \frac{9 192 631 770}{Δ ν _{Cs}} .

The effect of this definition is that the second is equal to the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ¹³³Cs atom.

The metre#

The metre, 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 caesium frequency Δν_Cs.

This definition implies the exact relation c = 299 792 458 m s⁻¹. Inverting this relation gives an exact expression for the metre in terms of the defining constants c and Δν_Cs:

1 m = (\frac{c}{299 792 458}) s = \frac{9 192 631 770}{299 792 458} \frac{c}{Δ ν _{Cs}} \approx 30.663 319 \frac{c}{Δ ν _{Cs}} .

The effect of this definition is that one metre is the length of the path travelled by light in vacuum during a time interval with duration of 1/299 792 458 of a second.

The kilogram#

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 metre and the second are defined in terms of c and Δν_Cs.

This definition implies the exact relation h = 6.626 070 15 × 10⁻³⁴ kg m² s⁻¹. Inverting this relation gives an exact expression for the kilogram in terms of the three defining constants h, Δν_Cs and c:

1 kg = (\frac{h}{6.626 070 15 \times 1 0 ^{- 34}}) m^{- 2} s

which is equal to

1 kg = \frac{( 299 792 458 ) ^{2}}{( 6.626 070 15 \times 1 0 ^{- 34} ) ( 9 192 631 770 )} \frac{h Δ ν _{Cs}}{c ^{2}} \approx 1.475 5214 \times 1 0^{40} \frac{h Δ ν _{Cs}}{c ^{2}} .

The effect of this definition is to define the unit kg m² s⁻¹ (the unit of both the physical quantities action and angular momentum). Together with the definitions of the second and the metre this leads to a definition of the unit of mass expressed in terms of the Planck constant h.

The ampere#

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.

This definition implies the exact relation e = 1.602 176 634 × 10⁻¹⁹ A s. Inverting this relation gives an exact expression for the unit ampere in terms of the defining constants e and Δν_Cs:

1 A = (\frac{e}{1.602 176 634 \times 1 0 ^{- 19}}) s^{- 1}

which is equal to

1 A = \frac{1}{( 9 192 631 770 ) ( 1.602 176 634 \times 1 0 ^{- 19} )} Δ ν_{Cs} e \approx 6.789 6868 \times 1 0^{8} Δ ν_{Cs} e .

The effect of this definition is that one ampere is the electric current corresponding to the flow of 1/(1.602 176 634 × 10⁻¹⁹) elementary charges per second.

The kelvin#

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, metre and second are defined in terms of h, c and Δν_Cs.

This definition implies the exact relation k = 1.380 649 × 10⁻²³ kg m² s⁻² K⁻¹. Inverting this relation gives an exact expression for the kelvin in terms of the defining constants k, h and Δν_Cs:

1 K = (\frac{1.380 649 \times 1 0 ^{- 23}}{k}) kg m^{2} s^{- 2}

which is equal to

1 K = \frac{1.380 649 \times 1 0 ^{- 23}}{( 6.626 070 15 \times 1 0 ^{- 34} ) ( 9 192 631 770 )} \frac{Δ ν _{Cs} h}{k} \approx 2.266 6653 \frac{Δ ν _{Cs} h}{k} .

The effect of this definition is that one kelvin is equal to the change of thermodynamic temperature that results in a change of thermal energy kT by 1.380 649 × 10⁻²³ J.

The mole#

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.

This definition implies the exact relation N_A = 6.022 140 76 × 10²³ mol⁻¹. Inverting this relation gives an exact expression for the mole in terms of the defining constant N_A:

1 mol = (\frac{6.022 140 76 \times 1 0 ^{23}}{N _{A}}) .

The effect of this definition is that the mole is the amount of substance of a system that contains 6.022 140 76 × 10²³ specified elementary entities.

The candela#

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, metre and second are defined in terms of h, c and Δν_Cs.

This definition implies the exact relation K_cd = 683 cd sr kg⁻¹ m⁻² s³ for monochromatic radiation of frequency ν = 540 × 10¹² Hz. Inverting this relation gives an exact expression for the candela in terms of the defining constants K_cd, h and Δν_Cs:

1 cd = (\frac{K _{cd}}{683}) kg m^{2} s^{- 3} s r^{- 1}

which is equal to

1 cd = \frac{1}{( 6.626 070 15 \times 1 0 ^{- 34} ) ( 9 192 631 770 ) ^{2} 683} (Δ ν_{Cs})^{2} h K_{cd} \approx 2.614 8305 \times 1 0^{10} (Δ ν_{Cs})^{2} h K_{cd} .

The effect of this definition is that one candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10¹² Hz and has a radiant intensity in that direction of (1/683) W sr⁻¹. The definition of the steradian is given below Table 4.