Stefan-Boltzmann constant, σ
The constant in the Stefan-Boltzmann law: an ideal black body radiates σT⁴ watts from every square metre of its surface. It has been exact since 2019, because it is built entirely from exact constants.
σ = 5.670374419… × 10⁻⁸ W/(m²·K⁴)
Exact, derived. The decimal runs on past ten significant figures, so it is cut off there and marked …, the way NIST prints it, rather than rounded.
In other units
| Quantity | Value |
|---|---|
| σ | 5.670374419… × 10⁻⁸ W/(m²·K⁴) |
| σ | 5.670374419… × 10⁻¹² W/(cm²·K⁴) |
| σT⁴ at 300 K | 459.3003279… W/m² |
σ in W/(cm²·K⁴)
- 5.670374419… × 10⁻⁸ W/(m²·K⁴) × 10⁻⁴ m²/cm²
- = 5.670374419… × 10⁻¹² W/(cm²·K⁴)
σT⁴ at 300 K in W/m²
- 5.670374419… × 10⁻⁸ W/(m²·K⁴) × (300 K)⁴
- = 5.670374419… × 10⁻⁸ × 8.1 × 10⁹
- = 459.3003279… W/m²
The power an ideal black body at room temperature radiates from each square metre.
Where the value comes from
Integrating Planck’s law for black-body radiation over every wavelength and every direction leaving a surface gives a total power per area of σT⁴, with σ = 2π⁵k⁴/(15h³c²). Every term is exact, so σ is exact; the π⁵ is what makes its decimal run on for ever.
Josef Stefan found the fourth-power law from measurements in 1879, and Ludwig Boltzmann derived it from thermodynamics in 1884, both long before Planck’s law of 1900 explained the constant in front of it.
σ from k, h and c
- σ = 2π⁵k⁴ ÷ (15h³c²)
- = 2 × 306.0196847… × (1.380649 × 10⁻²³)⁴ ÷ (15 × (6.62607015 × 10⁻³⁴)³ × 299,792,458²)
- = 5.670374419… × 10⁻⁸ W/(m²·K⁴)
Which form to use
Use 5.67 × 10⁻⁸ W/(m²·K⁴) with the area in square metres and the temperature in kelvin. A real surface radiates εσAT⁴, where the emissivity ε lies between 0 and 1 and equals 1 only for an ideal black body.
For an object exchanging radiation with its surroundings, the net power is εσA(T⁴ − Tₛ⁴), with both temperatures absolute.
The fourth power makes it steep: doubling the absolute temperature multiplies the radiated power by 16. At 300 K, around room temperature, a black body gives off 459.3 W from each square metre.
Common mistakes
- Using degrees Celsius. The law needs absolute temperature, and a Celsius value raised to the fourth power is not slightly off, it is meaningless.
- Subtracting before raising to the fourth power. The net exchange goes as
T⁴ − Tₛ⁴, not(T − Tₛ)⁴. - Forgetting the area or the emissivity. σT⁴ is the power from one square metre of a perfect black body, not the power from the object in front of you.
Related constants
- Boltzmann constant, k = 1.380649 × 10⁻²³ J/K
- Planck constant, h = 6.62607015 × 10⁻³⁴ J·s
- Speed of light in vacuum, c = 299,792,458 m/s
- Wien’s displacement constant, b = 2.897771955… × 10⁻³ m·K
See also
- The physical constants table, every constant side by side
- Stefan-Boltzmann constant on Wikipedia
Source: BIPM, The International System of Units (SI Brochure), 9th edition. The same value in NIST’s CODATA listing.
The values are facts and free to use; this page’s selection and presentation are © 2026 ScienceQuest.