Stefan-Boltzmann Calculator

How it is calculated

The Stefan-Boltzmann law gives the heat a hot surface radiates: P = ε × σ × A × T4. Here P is the radiated power in watts (W), ε is the emissivity between 0 and 1, σ = 5.670374 × 10^-8 W/(m²·K⁴) is the Stefan-Boltzmann constant, A is the surface area in square metres, and T is the absolute temperature in kelvin. Because of the fourth power, doubling the temperature increases the output by 16 times. If emissivity is left empty or is zero or less, the tool uses 1, an ideal black body. The result is printed in scientific notation with four significant digits. Area and temperature cannot be negative. This is the power emitted, not the net loss: a surface also absorbs radiation from its surroundings.

Common mistakes

• Entering the temperature in degrees Celsius or Fahrenheit; it must be in kelvin, and the fourth power magnifies the error.
• Typing the area in cm² instead of m², which gives a result 10,000 times too small.
• Entering emissivity as a percentage such as 90 instead of 0.9.
• Reading the output as the net heat loss; a surface in a warm room also receives radiation, so the net flow depends on the surroundings' temperature as well.
• Not noticing that a blank emissivity is treated as 1, which gives the maximum possible output.