Stefan-Boltzmann Law Calculator — Radiated Power
Enter the surface temperature, emissivity, and area to compute total emitted radiant power and net heat loss to the surroundings using the Stefan-Boltzmann law.
°C
°C
m²
Radiated power from the entire surface: P = ε σ A T⁴
- 1
Surface temperature in Kelvin
1,000 + 273.15 = 1,273.15 - 2
T⁴
1,273.15⁴ = 2,627,352,218,679.802 - 3
Irradiance: ε × σ × T⁴
0.95 × 5.670×10⁻⁸ × 2,627,352,218,679.802 = 141,531.673 - 4
Total power: irradiance × A
141,531.673 × 1 = 141,531.67
How does this calculator work?
Radiated power P = ε × σ × A × T⁴ where σ = 5.670 × 10⁻⁸ W/(m²·K⁴) and T is in Kelvin. Net loss to ambient = ε × σ × A × (T⁴ − T_amb⁴). At 500°C with ε = 0.95 and 1 m², a surface emits roughly 20 kW. The T⁴ dependence means small temperature rises cause large power jumps.
Formula
How this is calculated
Every object above absolute zero emits electromagnetic radiation proportional to the fourth power of its absolute temperature. The Stefan-Boltzmann law quantifies this: P = ε σ A T⁴, where ε is emissivity (how closely the surface behaves like an ideal black body, ranging from 0 to 1), σ is the Stefan-Boltzmann constant (5.670374419 × 10⁻⁸ W m⁻² K⁻⁴), A is the emitting area in m², and T is the absolute temperature in Kelvin (°C + 273.15).
The T⁴ dependence makes radiation extremely sensitive to temperature: doubling the temperature increases radiated power by a factor of 16. This is why furnaces and stars radiate so intensely — a surface at 1,000°C (1,273 K) emits about 74 kW/m² for a black body, versus only 419 W/m² at 100°C.
In most real applications a surface also absorbs radiation from its surroundings. The net power lost is P_net = ε σ A (T_surface⁴ − T_ambient⁴). The ambient temperature defaults to 20°C (room temperature). Emissivity values for common materials: polished metals ≈ 0.02–0.1 (poor radiators), painted surfaces ≈ 0.9–0.95, human skin ≈ 0.97–0.99. The formula assumes a convex surface radiating to a large enclosure; view-factor corrections are required for enclosed geometries.
Frequently asked questions
Emissivity (ε) is a dimensionless ratio from 0 to 1 expressing how efficiently a surface radiates compared to an ideal black body. Polished metals have low emissivity (0.02–0.1), while painted surfaces, oxidised metals, skin and most non-metals have high emissivity (0.85–0.99). When in doubt, 0.95 is a good default for engineering estimates of non-metallic surfaces.
The T⁴ dependence follows from quantum statistical mechanics (Planck's law integrated over all wavelengths). It means small temperature changes have a large effect on radiation: a 10% increase in absolute temperature raises emitted power by about 46%. This is why radiation dominates heat transfer at high temperatures while convection and conduction dominate at low temperatures.
Yes — stars are excellent approximations of black bodies (ε ≈ 1). The Sun's photosphere temperature is about 5,778 K, giving a surface irradiance of approximately 63.2 MW/m². Multiplied by the Sun's surface area, this yields the solar luminosity of about 3.83 × 10²⁶ W.
Also known as
TG we-Calculate Editorial Team. (2026). Stefan-Boltzmann Law Calculator — Radiated Power [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/stefan-boltzmann-law-calculator
TG we-Calculate Editorial Team. "Stefan-Boltzmann Law Calculator — Radiated Power." TG we-Calculate. 2026. https://we-calculate.com/calculator/stefan-boltzmann-law-calculator.
TG we-Calculate Editorial Team, "Stefan-Boltzmann Law Calculator — Radiated Power," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/stefan-boltzmann-law-calculator
@misc{wecalculate_stefan_boltzmann_law_calculator, title = {Stefan-Boltzmann Law Calculator — Radiated Power}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/stefan-boltzmann-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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