Stefan-Boltzmann law

The Stefan-Boltzmann law, also known as Stefan's Law, is a law that expresses the total power per unit surface area (otherwise known as the intensity) that is radiated by an object, often taken to be a blackbody.[1] The formula used to determine at what wavelength the power peaks at is Wien's Law. The Stefan-Boltzmann Law explains how much power the Sun gives off given its temperature (or allows scientists to figure out how hot the sun is based on how much power strikes the Earth in a square metre). The law also predicts how much heat the Earth radiates into space. The Stefan-Boltzmann law doesn't say anything about the wavelength of light emitted, that is described by the Plank radiation formula.

This law is expressed as:

[math] \frac{P}{A} = e\sigma T^4 [/math]


  • [math]P[/math] is the total power radiated (energy per unit time) per unit surface area
  • [math]A[/math] is the surface area
  • [math]e[/math] is the emissivity (how good of a radiator/absorber the object is). For most objects this is taken to be 1, although the Earth's atmosphere is an interesting exception.
  • [math]\sigma[/math] is the Stefan-Boltzmann constant.
  • [math]T[/math] is the temperature of the object expressed in degrees Kelvin

The total radiated energy increases as temperature is increased. Based on a common observation wherein a heated object glows brighter as temperature increases, it should not be too surprising that objects radiate more energy with an increase in temperature.[2] As well, by manipulating the Stefan-Boltzmann equation, the temperature of the Earth without the greenhouse effect can be determined when values for power from the Sun and surface area of the Earth are used.[3]

To read more about the physics of the Stefan-Boltzmann law please see hyperphysics.


  1. Marc L. Kutner. Astronomy: A Physical Perspective, 2nd ed. New York, USA: Cambridge University Press, 2003.
  2. Kenneth Krane. Modern Physics, 3rd ed. Hoboken, NJ, USA: John Wiley & Sons, 2012.
  3. R. Wolfson, (May 8, 2015). Energy, Environment and Climate, 2nd ed. New York, U.S.A.: Norton, 2012.

Authors and Editors

Jordan Hanania, Kailyn Stenhouse, Jason Donev
Last updated: August 29, 2017
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