Stefan-Boltzmann Calculator
Radiated power as T⁴, with Wien's peak wavelength.
Work out Stefan-Boltzmann. Radiated power as T⁴, with Wien's peak wavelength. Free, with no account and nothing to download.
Absolute. The Sun's surface is 5778 K, a human body 310 K, a filament about 2800 K.
1 is a perfect black body. Human skin 0.98, polished aluminium 0.04.
Radiated power
6.3201e+7 W
Peaks at 501.5 nm — Visible
Stefan-Boltzmann gives P = εσAT⁴ and Wien gives the peak wavelength as 2.898 × 10⁻³ / T. They describe the same radiating body, so both are here. The fourth power is severe: doubling the absolute temperature raises output sixteenfold, which is why a filament goes from invisible to blinding over a small voltage range. And the peak shifts shorter as things heat, which is why red hot, white hot and blue hot is a genuine temperature sequence rather than a figure of speech. A human body at 310 K peaks around 9,300 nm, deep in the infrared — which is exactly what thermal cameras are built to see.
How the Stefan-Boltzmann Calculator works
Enter temperature, area and emissivity for the radiated power, plus the wavelength the emission peaks at. Both laws describe the same radiating body, so both are on one page rather than split for page count.
Also known as: blackbody radiation calculator · wien's displacement law calculator · radiated power calculator · peak wavelength calculator
Frequently asked questions
What is the Stefan-Boltzmann law?
P = εσAT⁴, with σ at 5.670 × 10⁻⁸ W/(m²·K⁴). Radiated power rises with the fourth power of absolute temperature.
What is Wien's displacement law?
λmax = 2.898 × 10⁻³ / T. The peak wavelength shifts shorter as temperature rises, which is why hot objects go red, then white, then blue.
Why does a filament brighten so suddenly?
The fourth power. A modest voltage rise raises the temperature enough to multiply the output several times over, and at the same time shifts the peak from infrared into visible.
What does emissivity change?
It scales the power linearly, from 1 for a perfect black body down to 0.04 for polished aluminium. It is why a shiny thermos radiates so little and why thermal cameras need the emissivity set correctly to read temperatures.
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