Stefan–Boltzmann Radiation Calculator

All objects with T > 0 K emit electromagnetic thermal radiation. The Stefan–Boltzmann law (Stefan 1879; Boltzmann 1884) gives the total power radiated per unit time from a surface: P = εσAT⁴, where σ = 5.670374×10⁻⁸ W/(m²·K⁴) is the Stefan–Boltzmann constant, A is surface area (m²), T is absolute temperature (K), and ε is emissivity (0 ≤ ε ≤ 1).

A perfect blackbody has ε = 1 and emits the maximum possible thermal radiation at temperature T. Real surfaces have ε < 1: polished aluminum ~0.05, oxidized iron ~0.8, human skin ~0.98, matte black paint ~0.95. Emissivity equals absorptivity at thermal equilibrium (Kirchhoff's law).

The T⁴ dependence is extremely strong: doubling absolute temperature multiplies radiated power by 2⁴ = 16. A 500 K object radiates roughly 16× more power than at 250 K (same area and ε). This explains why hot objects glow visibly and cool rapidly at high T.

Net radiative heat transfer between an object at T and large surroundings at T_env: P_net = εσA(T⁴ − T_env⁴). If surroundings are colder, net power is positive (object cools by radiation). In a vacuum, radiation is often the only heat loss mode (spacecraft, thermos flask silvering reduces ε).

Stefan–Boltzmann gives total power across all wavelengths. Wien's displacement law λ_max T = b (b ≈ 2.898×10⁻³ m·K) gives the peak emission wavelength. Planck's law describes the full spectrum; integrating Planck over all λ yields σT⁴.

Applications range from stellar astrophysics (luminosity L ∝ R²T⁴ for stars) to building energy loss, infrared cameras, and furnace design. At room temperature (~300 K), radiation is often smaller than convection; above ~500 K it dominates cooling.