\[P=\varepsilon\sigma AT^4\]
Variables
Pradiated power (W)
epsilon[ε]emissivity (dimensionless)
sigma[σ]Stefan-Boltzmann constant (5.670374419E-8 W/m²·K⁴)
Aradiating surface area (m²)
Tabsolute temperature (K)
Description
What is this formula?
The Stefan-Boltzmann law calculates the total thermal radiation power emitted by a surface due to its temperature. The emitted power increases rapidly with temperature because it is proportional to the fourth power of absolute temperature.
When to use it
Use this formula when analyzing thermal radiation from hot surfaces, furnaces, stars, heaters, electronic equipment, or any object exchanging heat by radiation.
Example
Given:
epsilon = 0.90
sigma = 5.670374419×10^-8 W/m²·K⁴
A = 2.0 m²
T = 500 K
Formula:
P = εσAT⁴
Substitution:
P = 0.90 × 5.670374419×10^-8 × 2.0 × 500⁴
Result:
P = 6380 W
Applications
Thermal radiation analysis, furnace design, spacecraft thermal control, infrared engineering, heat transfer calculations, astrophysics, and high-temperature process engineering.