# Boltzmann constant

A natural constant relating energy to temperature. Symbol, *k*. As part of the redefinition of the
kelvin, in 2018 the CGPM assigned it an exact numerical value within SI, of 1.380 649 × 10⁻²³ joules per 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}.

Resolutions Adopted.

Resolution 1, appendix 3.

26 CGPM, Versailles 13-16 November 2018.

BIPM.

Here *h* is the Planck constant, *c* is the speed of light, and Δν_{cs} refers to the frequency of light emitted by a cesium atom under specified conditions.

It is named for the German physicist Ludwig Boltzmann.

Boltzmann himself (and his mentor Stefan) did not regard this number as a
constant, but as a conversion factor. Apparently Max Planck was the first person
to refer to it as a constant. By the 1920's the usage “Boltzmann constant” was thoroughly established.

## Recent history

At its 24^{th} meeting (Paris, October 2011), the CGPM declared its intention to make the value of the Boltzmann constant a matter of definition, rather than something to be determined experimentally. The new value was to be *exactly* 1.380 6X × 10⁻²³ joule per kelvin, where X stood for one or more yet to be determined digits. The new definition was not be adopted before 2014. For comparison, the 2006 CODATA recommended values give *k* = 1.380 6504 × 10⁻²³ joule per kelvin, with a standard uncertainty of 0.000 0024 × 10⁻²³ joule per kelvin.

Work on refining the value of the Boltzmann constant has continued at such centers as the Physikalisch-Technische Bundesanstalt.

Photograph courtesy Physikalisch-Technische Bundesanstalt

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Last revised: 1 January 2007.