The SI unit of the Stefan-Boltzmann constant is

According to the Stefan-Boltzmann law, the power radiated by a black body is given by:

$P = \sigma A T^4$

Where $P$ is the power (in Watts, $\mathrm{W}$), $A$ is the surface area (in $\mathrm{m}^2$), $T$ is the absolute temperature (in $\mathrm{K}$), and $\sigma$ is the Stefan-Boltzmann constant.

Rearranging for $\sigma$:

$\sigma = \dfrac{P}{A T^4}$

Substituting the SI units for each quantity:

Unit of $\sigma = \dfrac{\mathrm{W}}{\mathrm{m}^2 \mathrm{K}^4} = \mathrm{W}\ \mathrm{m}^{-2}\ \mathrm{K}^{-4}$

Answer: $\mathrm{W}\ \mathrm{m}^{-2}\ \mathrm{K}^{-4}$