Stefan-Boltzmann Calculator
Enter a surface area and an absolute temperature to get the power an ideal blackbody radiates in watts — and see why output climbs with the fourth power of temperature.
Radiated power in watts
Enter the surface area and the absolute temperature and the calculator returns the power an ideal blackbody radiates (P = σAT⁴) in watts.
Use kelvin
Temperature must be absolute — use kelvin, not Celsius. Add 273.15 to a Celsius reading before you enter it, so room temperature becomes about 300 K.
What is the Stefan-Boltzmann law?
How temperature drives radiated power
The Stefan-Boltzmann calculator applies the Stefan-Boltzmann law, which says that an ideal blackbody radiates thermal energy at a rate proportional to the fourth power of its absolute temperature. Every warm object emits radiation, and the hotter it is the more it sheds — but the relationship is steep, not gentle. Give the calculator a surface area in square metres and a temperature in kelvin and it returns the total radiated power in watts. It is the number behind a star's luminosity, the heat a glowing filament loses, and the radiative cooling of any warm surface.
Enter a surface area in square metres and an absolute temperature in kelvin to get the radiated power of an ideal blackbody in watts instantly.
The radiated power is the Stefan-Boltzmann constant σ multiplied by the surface area and by the absolute temperature raised to the fourth power.
P = σ × A × T⁴Here σ is the Stefan-Boltzmann constant, 5.670374419 × 10⁻⁸ W/(m²·K⁴), a fixed constant of nature. Because the temperature is raised to the fourth power, it dominates the result: a small rise in temperature produces a large rise in radiated power. Suppose a 1 m² blackbody sits at 300 K. Raise 300 to the fourth power to get 8.1 × 10⁹, multiply by σ and by the 1 m² area, and the radiated power comes to about 459.3 W. Use square metres and kelvin and the answer comes back in watts.
The law is exact for an idealised surface, but a couple of practical points matter.
Ideal blackbody, absolute temperature, net flux
This calculator assumes an ideal blackbody with emissivity ε = 1 — the maximum any surface can emit. Real surfaces emit less, so multiply the result by their emissivity ε (between 0 and 1): P = ε × σ × A × T⁴. The temperature must be absolute, in kelvin, or T⁴ is meaningless. The figure is the power radiated outward; to find the net heat loss you must subtract the radiation the object absorbs from its surroundings, which depends on the surrounding temperature.