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

   =  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.