Stefan-Boltzmann Radiated Power Calculator
Every surface above absolute zero radiates thermal energy, and the Stefan-Boltzmann law gives how much: power equals emissivity times the Stefan-Boltzmann constant times area times the absolute temperature to the fourth power. Because of that fourth-power dependence, radiated power climbs steeply with temperature. This calculator returns the radiated power from the temperature, surface area and emissivity you enter, plus the radiant exitance per unit area. Enter temperature in Celsius and it converts to kelvin. The Stefan-Boltzmann constant is an editable input set to the NIST value.
Stefan-Boltzmann formula
T (K) = temperature in Celsius + 273.15
Radiant exitance = emissivity * sigma * T^4
Radiated power = radiant exitance * area
kW = radiated power / 1,000
Radiant exitance is the power per unit area; multiply by the surface area for total power. The fourth-power term means doubling the absolute temperature increases radiated power by a factor of sixteen.
Using the result
- This is gross emitted power; net radiative loss subtracts the radiation absorbed from the surroundings at their temperature.
- Emissivity strongly affects the result: polished metals radiate far less than matte surfaces at the same temperature.
- Always work in kelvin; the Celsius conversion is built in.
- Small values may display in scientific notation for clarity.
Stefan-Boltzmann law: frequently asked questions
What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law gives the power a surface radiates as thermal radiation: P = emissivity * sigma * area * T^4, where sigma is the Stefan-Boltzmann constant and T is the absolute temperature in kelvin. Radiated power rises with the fourth power of temperature, so even modest temperature increases sharply increase emission.
What is the Stefan-Boltzmann constant?
The Stefan-Boltzmann constant, sigma, is approximately 5.670374419e-8 watts per square metre per kelvin to the fourth power. It is a defined constant in the SI system following the 2019 redefinition and is published by NIST. It is an editable input here so you can use the exact value.
What is emissivity?
Emissivity is how effectively a surface radiates compared with an ideal black body, on a scale from 0 to 1. A perfect black body has emissivity 1; real surfaces are lower (polished metals can be well below 0.1, while matte and oxidised surfaces are closer to 1). Enter the emissivity for your surface.
Why must temperature be in kelvin?
The law uses absolute temperature raised to the fourth power, so it only works in kelvin. This calculator lets you enter the temperature in Celsius and converts it to kelvin (Celsius plus 273.15) before applying the fourth-power law.
Official sources
- U.S. National Institute of Standards and Technology: Stefan-Boltzmann constant.
- NASA Earth Observatory: Climate and Earth's Energy Budget.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.