### Stefan-Boltzmann constant

(σ, Stefan's constant)
(relates radiation power to temperature and surface area)

The Stefan-Boltzmann constant is a physical constant relating the power radiated from a black body to its temperature according to the Stefan-Boltzmann law (i.e., Stefan-Boltzmann equation, which is not the same as the Boltzmann equation): the energy radiated by a black body is proportional to its surface and the fourth power of its temperature:

```j* = σT4
```
• j* - energy radiated per unit surface area.
• T - temperature.
• σ - Stefan-Boltzmann constant.

In SI units, it is:

```σ = 5.670374419×10-8 W m-2 K-4
```

It can be derived from the Boltzmann constant, Planck constant, and the speed of light. A consequence of the Stefan-Boltzmann equation: the bolometric luminosity of a black body (which approximates real astronomical objects) is j* times the surface area:

```Lbol = AσT4
```
• Lbol - bolometric (i.e., total) luminosity.
• A - surface area of the object, π r²

(physics,constant)