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Thermodynamics
Thermodynamics

Stefan-Boltzmann Law

P=ϵσAT4P = \epsilon\sigma AT^4

Power radiated by a body due to its temperature. The emissivity ε covers real (gray) surfaces; setting ε = 1 gives the ideal blackbody form P = σAT⁴. This is the comprehensive, general form of the law.

Variables

P
Radiated power
Energy per second
W
ε
Emissivity
0 to 1 (1 for blackbody)
unitless
σ
Stefan-Boltzmann constant
5.67×10⁻⁸
W/(m²·K⁴)
A
Surface area
Radiating surface
m²
T
Temperature
Absolute temperature
K

Derivation

Derived from Planck blackbody radiation law.

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Common questions

What is the Stefan-Boltzmann Law formula?

Stefan-Boltzmann Law is written P = εσAT⁴. Power radiated by a body due to its temperature. The emissivity ε covers real (gray) surfaces; setting ε = 1 gives the ideal blackbody form P = σAT⁴. This is the comprehensive, general form of the law. It belongs to Thermodynamics, under Heat & Temperature.

What are the units in P = εσAT⁴?

In SI units, P is radiated power, measured in kg·m²/s³; ε is emissivity (dimensionless); σ is stefan-boltzmann constant, measured in kg/(s³·K⁴); A is surface area, measured in m²; T is temperature, measured in K.

How is the Stefan-Boltzmann Law formula derived?

Derived from Planck blackbody radiation law. The result is P = εσAT⁴.