Stefan-Boltzmann constant

Physical constant
Surname	Stefan-Boltzmann constant
Formula symbol	${\displaystyle \sigma }$
value
SI	5.670 374 419 ...e-8th ${\displaystyle \textstyle {\frac {\mathrm {W} }{\mathrm {m^{2}K^{4}} }}}$
Uncertainty  (rel.)	(exactly)
Relation to other constants
${\displaystyle \sigma ={\frac {2\pi ^{5}k_{\mathrm {B} }^{4}}{15h^{3}c^{2}}}}$ ${\displaystyle k_{\mathrm {B} }}$: Boltzmann constant : Planck's quantum of action : speed of light ${\displaystyle h}$ ${\displaystyle c}$
Sources and Notes
Source SI value: CODATA 2018 ( direct link )

The Stefan-Boltzmann constant , after Josef Stefan and Ludwig Boltzmann , not to be confused with the Boltzmann constant , is a physical constant that occurs as a proportionality constant in the Stefan-Boltzmann law . According to this, the power of a black body emitted in the form of electromagnetic radiation is proportional to its surface area and the fourth power of its temperature : ${\displaystyle \sigma }$ ${\displaystyle P}$ ${\displaystyle A}$ ${\displaystyle T}$

${\displaystyle P=\sigma AT^{4}}$

With

${\displaystyle \sigma ={\frac {2\pi ^{5}k_{\mathrm {B} }^{4}}{15h^{3}c^{2}}}=5{,}670\,374\,419\ldots \cdot 10^{-8}\;\mathrm {\frac {W}{m^{2}K^{4}}} }$

The constants k _B ( Boltzmann constant ), h ( Planck's quantum of action ) and c ( speed of light ) are used in the SI system to define the units of measurement and are assigned exact numerical values. This means that the Stefan-Boltzmann constant also has an exact value in the SI.

Remarks

1. ↑ ^{a b} The value of the Stefan-Boltzmann constant in SI units is exact , i.e. H. without measurement uncertainty, but due to the factor π ^{5 it has} no finite representation of decimal places.