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Stefan Boltzmann Law Calculator

Work out stefan boltzmann law instantly with clear inputs, formula shown and shareable results.

About Stefan Boltzmann Law Calculator

The Stefan-Boltzmann law says radiated power per unit area is e.sigma.T^4. A 2 m2 surface at 500 K with emissivity 0.9 radiates about 6.4 kW. The fourth power dominates everything: doubling absolute temperature multiplies emission sixteenfold, which is why radiation overtakes convection in furnaces.

Formulas

Stefan-Boltzmann law

P = e sigma A T^4, sigma = 5.6704e-8 W/(m2 K4)

Net exchange

P(net) = e sigma A (T^4 - T(surroundings)^4)

Worked example

With the default values below, Stefan Boltzmann Law Calculator returns Radiated Power of 6,379.17. Change any input above and every figure here is recalculated in your browser.

Inputs used

Absolute temperatureminimum 0 K
500 K
Radiating areaminimum 0 m2
2 m2
Emissivityaccepts 0–1
0.9

Results

Radiated Power
6,379.17 W
Emissive Power Per Unit Area
3,189.59 W/m2
Perfect Black Body Flux At That Temperature
3,543.98 W/m2
Power If Temperature Doubled
102,066.7 W

Step by step

  1. 1Values used
  2. 2Stefan-Boltzmann law
  3. 3Net exchange
  4. 4Radiated Power= 6,379.17 W
  5. 5Emissive Power Per Unit Area= 3,189.59 W/m2
  6. 6Perfect Black Body Flux At That Temperature= 3,543.98 W/m2
  7. 7Power If Temperature Doubled= 102,066.7 W

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Must the temperature be in kelvin?

Absolutely - the fourth power makes any offset scale meaningless. Using Celsius would be badly wrong.

What emissivity should I use?

About 0.95 for matt paint, brick and skin, 0.9 for oxidised metal, and as low as 0.03 for polished aluminium.

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Stefan Boltzmann Law Calculator – Calculate Radiated Power