Blackbody Radiation Calculator
Calculate blackbody radiation power using the Stefan-Boltzmann law and peak wavelength.
Stefan-Boltzmann: P = εσT⁴ | Wien: λ_max = b/T
What Is the Blackbody Radiation Calculator?
The Blackbody Radiation Calculator computes the peak emission wavelength, total radiated power, and spectral radiance of an ideal blackbody at a given temperature. It uses Wien's displacement law and the Stefan-Boltzmann law, and plots the Planck radiation spectrum.
Formula
How to Use
Enter the temperature of the blackbody in Kelvin (K). The calculator outputs the peak wavelength (where radiation is most intense), the total radiated power per unit area, and the color of visible light emitted if the temperature is in the visible range.
Example Calculation
Sun's surface T = 5778 K: λ_max = 2.898×10⁻³/5778 = 501 nm (green-yellow visible light). Power = σT⁴ = 5.67×10⁻⁸ × 5778⁴ = 6.33×10⁷ W/m². Human body T = 310 K: λ_max = 2.898×10⁻³/310 = 9.35 μm (mid-infrared).
Understanding Blackbody Radiation
Blackbody radiation describes the electromagnetic spectrum emitted by a perfect absorber and emitter in thermal equilibrium. Planck's radiation law, derived in 1900, was a revolutionary result that launched quantum mechanics by showing that energy is emitted in discrete quanta (photons) rather than continuously.
As temperature increases, a blackbody radiates more intensely at all wavelengths, and the peak wavelength shifts to shorter (bluer) wavelengths — a phenomenon quantified by Wien's displacement law. This is why heated metal glows red at lower temperatures and shifts toward white-blue at very high temperatures.
Blackbody radiation underpins many technologies: infrared thermometers measure temperature from emitted IR radiation, thermal cameras image heat distributions, stellar spectroscopy determines star temperatures and compositions, and the cosmic microwave background (CMB) is the thermal radiation of the universe itself at 2.725 K.
Frequently Asked Questions
What is a blackbody?
A blackbody is an idealized object that absorbs all incident radiation and re-emits it as thermal radiation dependent only on its temperature. Real objects approximate blackbody behavior — the ratio of actual to ideal emission is called emissivity (ε ≤ 1).
Why does the Sun appear yellow/white?
The Sun's surface is ~5778 K, giving peak emission at ~501 nm (green). But it emits across the entire visible spectrum, so the combination appears white. Atmospheric scattering makes it appear yellow from Earth's surface.
What is Wien's displacement law?
Wien's law states that the peak emission wavelength of a blackbody is inversely proportional to its temperature: λ_max × T = 2.898×10⁻³ m·K. Hotter objects emit peak radiation at shorter wavelengths (bluer light).
What is the Stefan-Boltzmann law?
It states that total radiated power per unit area is proportional to the fourth power of temperature: P/A = σT⁴. Doubling temperature increases total emitted power by 16×.
Is this calculator free?
Yes, completely free with no account required.
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