Science & engineering · Heat
Stefan-Boltzmann law calculator.
Thermal radiation emitted by a surface, and the net loss to its surroundings.
Inputs
Radiated power
Enter a temperature.
How do you calculate thermal radiation with the Stefan-Boltzmann law?
A surface at absolute temperature T, area A and emissivity ε radiates P = σ ε A T⁴, where σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴). With surroundings at Tₛ the net loss is σ ε A (T⁴ − Tₛ⁴). Temperatures must be in kelvin, which the tool converts for you. Emissivity is 1 for an ideal black body and 0 for a perfect reflector.
Worked example. An unclothed person with skin at 306 K (33°C), area 1.50 m² and skin emissivity 0.97 in a room at 295 K loses about 99 W by radiation (OpenStax Example 14.9, which uses σ = 5.67 × 10⁻⁸; this tool gives 98.5 W).
Because power scales with T⁴, doubling the absolute temperature raises the radiated power sixteen-fold. The simple net formula assumes the surroundings fully enclose the object; there is no view-factor correction.
Frequently asked questions
What is the Stefan-Boltzmann constant?
σ = 5.670374419 × 10⁻⁸ W m⁻² K⁻⁴, an exact value in the CODATA 2022 release published by NIST.
What emissivity should I use?
1 for an ideal black body, about 0.97 for human skin in the infrared and about 0.5 for a tungsten filament per OpenStax. Measure or look up the value for your material and finish.
Why does the formula need kelvin?
Radiated power depends on absolute temperature to the fourth power, so Celsius values would give wrong results. This tool converts Celsius and Fahrenheit for you.
What is net radiation?
The power a surface emits minus what it absorbs from surroundings at their own temperature, σεA(T⁴ − Tₛ⁴). Positive means net heat loss.
Sources
Checked
Constant from NIST; formulas, emissivity examples and the worked example from OpenStax. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Education and engineering reference. Treats the surroundings as fully enclosing the surface (view factor 1) and emissivity as constant; real surfaces vary with wavelength and temperature.