Stefan-Boltzmann Law

Also known as radiated power · blackbody radiation

P = \varepsilon \sigma A T^4

P =

ε =

A =

T =

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Constant used — built into this formula, no need to enter

\sigma = 5.670374419 \times 10^{-8}\ \text{W/(m}^{2}{\cdot}\text{K}^{4}\text{)}

Stefan-Boltzmann constant · exact

Learning zone

Every surface radiates power proportional to the fourth power of its absolute temperature — double the kelvin temperature and the glow grows sixteenfold, which is how astronomers size stars from brightness alone. The Stefan–Boltzmann constant σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴) is exact in the 2019 SI, and emissivity ε runs from 0 to 1 (a perfect black body). Solving for T takes the positive real fourth root — the only physical branch, since absolute temperature cannot be negative.

Stefan-Boltzmann Law

P = \varepsilon \sigma A T^4

Where

$P$ = Radiated power
$\varepsilon$ = Emissivity
$A$ = Surface area
$T$ = Surface temperature

Missing one of these? Work it out first, then come back

Radiated power — Power (P = W/t), Power from Force and Velocity (P = Fv)
Emissivity — Net Radiation Exchange Between Surfaces, Combined Convection and Radiation Coefficient
Surface area — Newton's Law of Cooling (Q = hAΔT), Lumped Capacitance Time Constant
Surface temperature — Net Radiation Exchange Between Surfaces, Wien's Displacement Law