Stefan-Boltzmann Law Calculator
The Stefan-Boltzmann law is the cornerstone of thermal radiation: it tells you how much power a hot surface gives off purely from its temperature and area. A black body radiates power equal to the Stefan-Boltzmann constant multiplied by the emitting area and by the fourth power of the absolute temperature. That fourth power is the headline: double the temperature and the radiated power rises by a factor of sixteen, which is why filaments, stars and furnaces glow so fiercely as they heat. This calculator takes the emitting area in square meters and the absolute temperature in kelvin, holds the Stefan-Boltzmann constant sigma fixed at 5.670374419e-8 W/(m^2 K^4), and returns the radiated power in watts. The defaults describe one square meter of an ideal black body at 1,000 kelvin, a convenient round case for checking your own numbers. Remember that temperature must be in kelvin because the fourth-power relationship only holds on an absolute scale, and that the result assumes a perfect emitter, so a real surface radiates less in proportion to its emissivity. Every figure here is computed deterministically from the standard physics formula shown below, with a worked example that reconciles exactly to the calculator so you can follow each step of the arithmetic.
The Stefan-Boltzmann law gives radiated power as the constant sigma times the area times temperature to the fourth power: P = sigma A T^4, with sigma fixed at 5.670374419e-8 W/(m^2 K^4). For an area of 1 m^2 at 1,000 K, the radiated power is 56,703.74 W.
Stefan-Boltzmann formula
P = sigma A T^4
P = radiated power in watts
A = emitting area in square meters
T = absolute temperature in kelvin
sigma = 5.670374419e-8 W/(m^2 K^4) (fixed constant)
The Stefan-Boltzmann constant sigma is held fixed at 5.670374419e-8 W/(m^2 K^4). Raise the absolute temperature to the fourth power, multiply by the emitting area, then multiply by sigma. Temperature must be in kelvin for the fourth-power law to hold.
Worked example
A black body has an emitting area of 1 square meter and an absolute temperature of 1,000 kelvin, with sigma fixed at 5.670374419e-8 W/(m^2 K^4).
- T^4 = 1,000^4 = 1e12
- sigma x A = 5.670374419e-8 x 1 = 5.670374419e-8
- P = 5.670374419e-8 x 1e12 = 56,703.74 W
The radiated power is 56,703.74 watts. These are the calculator's default inputs, so the result above matches the widget exactly.
Power at sample temperatures
| Temperature (K) | Area (m^2) | Radiated power (W) |
|---|---|---|
| 500 | 1 | 3,543.98 |
| 1,000 | 1 | 56,703.74 |
| 2,000 | 1 | 907,259.91 |
Each row uses sigma fixed at 5.670374419e-8 W/(m^2 K^4). Note how the power jumps sixteen-fold when the temperature doubles.
Stefan-Boltzmann law calculator: frequently asked questions
What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law states that the power radiated by a black body equals the Stefan-Boltzmann constant sigma multiplied by the emitting area and by the fourth power of the absolute temperature. Because temperature enters to the fourth power, even a modest rise in temperature produces a large jump in radiated power. The law underpins how we model thermal radiation from stars, filaments and heated surfaces.
What value of sigma does this calculator use?
It uses the Stefan-Boltzmann constant sigma fixed at 5.670374419e-8 W/(m^2 K^4), the standard accepted value. The constant is held fixed inside the calculation, so you enter only the emitting area in square meters and the absolute temperature in kelvin. The output is the radiated power in watts.
Why must temperature be in kelvin?
The fourth-power dependence only makes physical sense on an absolute temperature scale that starts at absolute zero. Kelvin is that scale. Entering temperature in Celsius or Fahrenheit would give a wrong answer, so convert first: add 273.15 to a Celsius reading to get kelvin before using this calculator.
What does the default case represent?
The defaults are an emitting area of 1 square meter at an absolute temperature of 1,000 kelvin. Plugging those into P = sigma A T^4 gives 5.670374419e-8 multiplied by 1 and by 1,000 to the fourth power, which is 1e12, for a radiated power of 56,703.74 watts. That is the power leaving one square meter of an ideal black body at 1,000 K.
Does this assume a perfect black body?
Yes. The formula here gives the power for an ideal black body with an emissivity of one. A real surface radiates less, in proportion to its emissivity, which ranges from zero to one. To model a real surface, multiply the result by its emissivity. This calculator reports the ideal upper bound.
Official sources
- Physical constants and the Stefan-Boltzmann constant: US National Institute of Standards and Technology (NIST). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.