Stefan Boltzmann Law Calculator

Created by Luis Hoyos
Last updated: Sep 05, 2022

Welcome to the Stefan-Boltzmann law calculator, a tool created to calculate the radiation heat transfer from a surface. The Stefan-Boltzmann law of radiation initially applies to a blackbody, but this calculator allows the selection of different emissivities so that you can use it in two ways:

  • Blackbody calculator; and
  • Radiation heat transfer calculator of any surface material.

Keep reading this article to learn more about Stefan-Boltzmann law and its formula.

The Stefan-Boltzmann law of radiation

Radiation is the emission of energy in the form of waves or photons. Within the types of radiation, we can find electromagnetic radiation, in which energy is in the form of waves of the electromagnetic field. One of the most common ways of electromagnetic radiation is thermal radiation, which occurs because of the temperature of the particles of an object. Any object with a temperature above absolute zero (zero kelvin or Rankine degrees) will emit thermal radiation.

The Stefan-Boltzmann law calculates the maximum rate of thermal radiation (power radiated) a surface can emit, as a function of its temperature, using the following formula:

P = σAT

, where:

  • P — Rate of thermal radiation, in watts (W) or Btu per hour (Btu/h).
  • A — Surface area, in square meters () or square feet (ft²).
  • T — Surface absolute temperature, in kelvin (K) or Rankine degrees (°R); and
  • σ — Stefan–Boltzmann constant, whose value equals 5.670 × 10⁻⁸ W/(m² K⁴) or 0.1714 × 10⁻⁸ Btu/(h ft² R⁴).

The Stefan-Boltzmann law calculates the maximum rate of thermal radiation any surface can emit. The only surface that emits that amount is a hypothetic surface called a blackbody. Real surfaces will differ from the blackbody behavior and emit less thermal radiation. To calculate how much less, we must consider a material property called emissivity.

🙋 You must input the thermodynamic or absolute temperature in the formula. If it is in celsius degrees (°C) or degrees Fahrenheit (°F), you must convert it to kelvin or degrees Rankine. This Stefan Boltzmann law calculator converts it for you, but you can also do it using our temperature converter.

The Stefan-Boltzmann law formula with emissivity

For a surface other than a blackbody, to calculate the rate of thermal radiation, we include the emissivity (ε) in the original Stefan-Boltzmann law:

P = σεAT

The surface emissivity measures how close the surface is to the blackbody behavior, and its value goes in the range 0 ≤ ε ≤ 1. For the theoretical blackbody, ε = 1, and for other surfaces, the value is lower.

Apart from calculating the radiation heat transfer rate, this calculator provides the emissivity of the most common materials.

Luis Hoyos
Black body
Radiated power
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