Which law says a black body's emitted power is proportional to temperature to the fourth power?

The Stefan–Boltzmann law says that a black body’s emitted power per unit area is proportional to the fourth power of its absolute temperature.

For an ideal black body, the radiant exitance is M = σT⁴, where T is measured in kelvins and σ is the Stefan–Boltzmann constant. The fourth-power dependence is powerful: doubling absolute temperature increases emitted power by a factor of 16. For a real surface, emissivity is included, giving M = εσT⁴.

Josef Stefan inferred the relationship from experimental work in 1877. Ludwig Boltzmann derived it theoretically in 1884 using thermodynamics and electromagnetic radiation pressure. The law later emerged naturally from Planck’s radiation law, which describes the full black-body spectrum.

The law concerns total emitted power across all wavelengths, not the wavelength at which emission peaks. That distinction separates it from Wien’s displacement law. In climate science, the Stefan–Boltzmann relationship helps describe how Earth emits infrared energy and why a warmer surface radiates disproportionately more energy.