# Stefan-Boltzmann law for blackbody radiation

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### Energy Flux from a Blackbody: Stefan-Boltzmann Law for Blackbody Radiation

The Stefan-Boltzmann law for blackbody radiation is a formula for the emitted energy flux ($F$) per unit area (integrated over all frequencies), and depends only on the blackbody temperature, $T$.

\[

F = \sigma T^{4}

\]

where $\sigma = 5.67 \times 10^{-5} \ {\rm erg \ cm^{-2} \ deg^{-4} \ s^{-1}}$ is the Stefan-Boltzmann constant.

To get the energy density ($u$) instead of flux, replace $\sigma$ by $a$, where $\sigma =(1/4)ac$:

\[

u=aT^{4}

\]

($a \sim 7.56 \times 10^{-15} \ {\rm erg \ cm^{-3} \ deg^{-4}}$.)