`sigma = 5.670373 * 10^-8 W/(m^2 K^4)`

5.670373E-8

The Stefan–Boltzmann constant, σ = 5.6703 10^-8 (W/m²K⁴) , is the constant of proportionality in the Stefan–Boltzmann law. The Stefan–Boltzmann law states that the total energy radiated per unit surface area of a black body in unit time is proportional to the fourth power of the thermodynamic temperature. This is not the same as the Boltzman constant. The Stefan-Boltzman constant is expressed in units of watts per square meter kelvin to the fourth (`W/(m^2K^4)`)

DERIVATION

The constant of proportionality σ, called the Stefan–Boltzmann constant or Stefan's constant, derives from other known constants of nature. The value of the constant is

$\sigma=\frac{2\pi^5 k^4}{15c^2h^3}= 5.670373 \times 10^{-8}\, \mathrm{J\, s^{-1}m^{-2}K^{-4}},$ = 5.670373⋅10⁻⁸ W/(m²K⁴)

where k is the Boltzmann constant, h is Planck's constant, and c is the speed of light in a vacuum. Thus at 100 K the energy flux is 5.67 W/m², at 1000 K 56,700 W/m², etc.

Notes

The Stefan-Boltzmann constant is specified with a standard uncertainty (standard deviation) of `0.000021 * 10^(-8)W/(m^2*K^4)`

See Uncertainty of Measurement Results, a discussion provided by NIST of the application of uncertainty to the documented constants.