Stefan-Boltzmann Law Calculator

At a glance:The Stefan-Boltzmann law (Josef Stefan 1879, Ludwig Boltzmann 1884) describes the power a body radiates due to its temperature. For a grey surface: P=ε·σ·A·T⁴, where P is radiated power (W), ε is emissivity (0 to 1, dimensionless), σ is the Stefan-Boltzmann constant =5.670374419×10⁻⁸ W/(m²·K⁴), A is the radiating area (m²) and T is the absolute temperature (K — must be Kelvin). This law's most important feature is that radiated power is proportional to the fourth power of absolute temperature: a small temperature rise sharply increases radiation — double T and radiation becomes 16× larger. Emissivity ε describes how much a real surface radiates relative to an ideal blackbody: blackbody ε=1 (strongest), leaves/soil/water are near 0.9–0.98, polished metals as low as 0.05 (barely radiate). Example: ε=0.9, A=1 m², T=300 K (≈27°C) → P=0.9×5.670e-8×1×300⁴ ≈ 413.37 W, radiating about 413 J per second. At T=500 K (blackbody ε=1): P≈3543.75 W — the fourth-power effect makes radiation surge. The actual net exchange must consider ambient T_env: P_net=εσA(T⁴−T_env⁴). Uses: (1) long-wave crop canopy radiation and night radiative cooling (frost warning); (2) Earth energy balance and greenhouse effect, planetary equilibrium temperature; (3) heatsink, solar-collector and insulation radiation loss; (4) infrared thermometry (infer temperature from radiation). Notes: (1) T must be absolute K (°C+273.15), Celsius badly breaks it; (2) ε depends on material and surface, range 0–1; (3) this tool gives emitted power — net exchange subtracts εσA·T_env⁴; (4) keep SI units consistent. In short, thermal radiation power is given by P=εσA·T⁴; the fourth-power law is the core of thermal radiation, energy balance and radiative cooling.