Stefan-Boltzmann constant

\sigma = 5.670374419 \times 10^{-8}\ \text{W/(m}^{2}{\cdot}\text{K}^{4}\text{)}

Value	5.670374419e-8 W/(m²·K⁴)
Status	Exact by definition — no uncertainty
Source	CODATA 2022 (exact in the 2019 SI)
Categories	Thermodynamic Universal & Atomic

Learning zone

A blackbody at absolute temperature T radiates σT⁴ watts from every square metre of its surface. The fourth power is brutal: double the temperature and the radiated power goes up sixteenfold, which is why a glowing element sheds heat so much faster than a warm one and why radiant losses dominate above a few hundred degrees.

Josef Stefan inferred the fourth-power law empirically in 1879 from John Tyndall's measurements of glowing platinum wire, and used it almost immediately to make the first sensible estimate of the Sun's surface temperature, around 5700 K. His student Ludwig Boltzmann derived it thermodynamically in 1884 from Maxwell's radiation pressure, which is why the law carries both names. σ is not independent: it equals 2π⁵k⁴/(15h³c²), so once the 2019 SI fixed k, h and c, σ became exact too.

Used by these solvers

Stefan-Boltzmann Law

P = \varepsilon \sigma A T^4

Wien's Displacement Law

\lambda_{max} = \frac{b}{T}