# 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.