Stefan-Boltzmann Law Calculator: P = sigma e A T^4

The heat a hot surface radiates away.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • P = \sigma\varepsilon AT^4
  • T = \left(\frac{P}{\sigma\varepsilon A}\right)^{1/4}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the radiated power: radiated power = 5.670e-8 x emissivity x surface area x absolute temperature^4
  2. Put the values in (every value in its SI unit): radiated power = 5.670e-8 x 0.9 x 1.5 x 310^4
  3. The answer: radiated power: 706.956 W
  4. The same answer in other units: 0.706956 kW

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Absolute temperature; Radiated power (leave it as it is if this is what you are finding) 706.8 W; Emissivity (leave it as it is if this is what you are finding) 0.9; Surface area (leave it as it is if this is what you are finding) 1.5 m2.

  1. The formula, arranged to find the absolute temperature: absolute temperature = ((radiated power) / (5.670e-8 x emissivity x surface area))^0.25
  2. Put the values in (every value in its SI unit): absolute temperature = ((706.8) / (5.670e-8 x 0.9 x 1.5))^0.25
  3. The answer: absolute temperature: 309.983 K

Common questions

What is the Stefan-Boltzmann law?

The power radiated by a surface is proportional to its area, its emissivity and the fourth power of its absolute temperature.

What is the Stefan-Boltzmann constant?

5.670e-8 watts per square metre per kelvin to the fourth.

How much does a person radiate?

About 700 W for a skin area of 1.5 m2 at 37 C, though they absorb nearly as much back from their surroundings.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics or heat transfer text (thermal radiation). Constant from the 2019 SI values.

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