### 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, which are now all given exact values (i.e., form part of the basis of SI units) and give the Stefan-Boltzmann constant the above exact value. 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 if spherical.

(physics,constant)