About the Blackbody Radiation Calculator
An ideal blackbody absorbs all radiation that strikes it and re-emits energy purely as a function of its temperature. This calculator applies the two classical results that describe that emission: the Stefan-Boltzmann law, which gives the total power radiated per unit area, and Wien's displacement law, which gives the wavelength where that emission peaks.
The Stefan-Boltzmann law
The radiant exitance (power emitted per unit surface area) of a surface at absolute temperature T is M = εσT⁴, where σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant and ε is the surface's emissivity — 1 for an ideal blackbody, less than 1 for real materials. Multiplying M by the surface area A gives the total radiated power, P = εσAT⁴. Because power scales with the fourth power of temperature, doubling T multiplies the output by 16.
Real surfaces also absorb radiation emitted by their surroundings. If the environment sits at temperature Tsurr, the net radiative power exchanged is Pnet = εσA(T⁴ − Tsurr⁴). A positive value means the object is a net emitter and loses heat by radiation; a negative value means it is a net absorber because the surroundings are warmer.
Wien's displacement law
The wavelength at which emission is strongest is λmax = b / T, where b = 2.897771955 × 10⁻³ m·K is Wien's displacement constant. Cool objects around a few hundred kelvin peak in the infrared; the Sun's roughly 5,778 K surface peaks near 500 nanometers, in visible light; very hot plasmas peak in the ultraviolet or beyond.
Assumptions and limits
- The object is treated as a gray body with a single, wavelength-independent emissivity ε — real materials can have emissivity that varies with wavelength, angle, and surface finish.
- Temperature must be entered in kelvin (K); convert from Celsius with K = °C + 273.15.
- The net power formula assumes the object is fully surrounded by an isothermal environment at Tsurr, with no reflected or transmitted radiation from other sources.