Black-Body Radiation Calculator
See the light a hot object gives off. Plot the Planck spectrum for any temperature, find the peak wavelength with Wien’s law and the power with the Stefan–Boltzmann law, see the colour of the glow, and work out a star’s luminosity.
How to Use
- Pick a mode: the Spectrum of a temperature, the temperature From a peak wavelength, the Power an object radiates, or a Star’s luminosity.
- Enter the temperature in kelvin, °C or °F. Everything below absolute zero is rejected.
- Read the Planck curve: the coloured area under it is the part emitted as visible light, and the dot marks the Wien peak.
- For power, enter the area and emissivity (1 for a perfect black body), and optionally the temperature of the surroundings to get the net heat loss.
- For a star, enter two of radius, temperature and luminosity in solar units, kilometres or watts; the Find menu picks the third.
Worked Example
The Sun. At T = 5,772 K, Wien’s law gives λmax = 2.897771955 × 10⁻³ ÷ 5,772 = 5.020 × 10⁻⁷ m = 502.0 nm, in the blue-green. Each square metre of the surface radiates σT⁴ = 5.670374419 × 10⁻⁸ × 5,772⁴ = 6.294 × 10⁷ W. Over a sphere of radius 6.957 × 10⁸ m that is L = 4πR²σT⁴ = 3.828 × 10²⁶ W, which spread over a sphere 1 au across gives the 1,361 W/m² that reaches the top of Earth’s atmosphere.
A person. Skin at 33 °C is 306.15 K. With an emissivity of 0.98 and 1.8 m² of skin, P = 0.98 × 5.670374419 × 10⁻⁸ × 1.8 × 306.15⁴ = 878.7 W. In a 20 °C room the walls send 738.7 W back, so the net loss is about 140 W.
The common mistake: using °C instead of kelvin. Put 33 straight into σT⁴ and skin seems to radiate 0.0659 W/m²; with 306.15 K it is 488.2 W/m², about 7,400 times more. The Stefan–Boltzmann and Wien laws only work with absolute temperature, so always add 273.15 to a Celsius value first.
Show Work
Formulas
The Curve That Started Quantum Physics
Gustav Kirchhoff coined the term “black body” in 1860 for a perfect absorber, and showed that its glow depends on temperature alone. Josef Stefan found the fourth-power law from measurements in 1879, and his former student Ludwig Boltzmann derived it from thermodynamics in 1884. Wilhelm Wien showed in 1893 that the peak moves to shorter wavelengths as the temperature rises.
Classical physics could not get the whole curve right: the Rayleigh–Jeans formula worked at long wavelengths but predicted infinite energy at short ones, later called the ultraviolet catastrophe. In 1900 Max Planck found a formula that matched the measurements of Otto Lummer, Ernst Pringsheim, Heinrich Rubens and Ferdinand Kurlbaum at every wavelength, and could only justify it by supposing energy is emitted in packets of hf. That assumption began quantum theory.
The most perfect black-body spectrum ever measured is the cosmic microwave background: the COBE satellite’s FIRAS instrument found it matches Planck’s curve to better than one part in 10,000, at 2.7255 K. The star values used here are the IAU 2015 nominal solar values; colours are computed from the CIE 1931 colour-matching functions and shown as approximate sRGB.
About This Tool
This calculator draws the Planck spectrum for any temperature from a fraction of a kelvin to millions, marks the Wien peak, shades the part that falls in visible light and tells you what share of the power that is, using the exact integral of Planck’s law rather than a numerical guess. It also gives the colour of the glow, worked out by weighting the spectrum with the CIE colour-matching functions (an approximate on-screen rendering: brightness is scaled up, and 6,500 K counts as white). The power and star modes solve the Stefan–Boltzmann law for any one unknown.
Real objects are not perfect black bodies; an emissivity below 1 scales the power, but real spectra also have lines and bands this model leaves out. Everything runs in your browser; nothing you enter is sent anywhere.
Related tools: Photon Energy & Wavelength Calculator, Inverse-Square Law Calculator, and Frequency & Wavelength Converter.
Frequently Asked Questions
What is Wien’s displacement law?
The peak of a black body’s spectrum sits at λmax = b ÷ T, with b = 2.897771955 × 10⁻³ m·K. The Sun at 5,772 K peaks at 502.0 nm, a 2,700 K filament at 1.073 µm (in the infrared), a human body at 310 K at 9.348 µm, and the cosmic microwave background at 2.7255 K at 1.063 mm.
How much power does a hot object radiate?
P = εσAT⁴ with σ = 5.670374419 × 10⁻⁸ W/m²K⁴. A perfect black body at 310 K gives off 523.7 W per square metre; the Sun’s surface gives 6.294 × 10⁷ W/m². Because of the fourth power, doubling the temperature multiplies the power by 16.
If the Sun peaks in green light, why does it look white?
The curve is broad: 43.77% of a 5,772 K black body’s output falls between 380 and 750 nm, spread across every colour, and our eyes see that mix as white. The peak also depends on how you plot it: per unit of frequency the peak is at 339.3 THz, which is 883.5 nm in the infrared.
How hot does something have to be to glow?
Things start to glow a dull red at about 800 K (525 °C), which is why a stove ring at a few hundred degrees looks black even though it radiates strongly in the infrared. By 2,700 K, a filament glows warm white, but only 7.02% of its output is visible light; the rest is heat.
How is a star’s luminosity worked out?
Treating the star as a black body, L = 4πR²σT⁴. With the IAU’s nominal solar radius 6.957 × 10⁸ m and temperature 5,772 K this gives 3.828 × 10²⁶ W, the nominal solar luminosity. Sirius A, about 1.711 times the Sun’s radius at about 9,940 K, comes out at 25.75 times the Sun.
How do I use the Black-Body Radiation Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Astronomy
Find a star’s luminosity from its radius and temperature: Sirius A (1.711 R☉, 9,940 K) is 25.75 L☉, absolute bolometric magnitude 1.21.
Thermal imaging
A human body at 310 K peaks at 9.348 µm, which is why thermal cameras work in the 8–14 µm band.
Lighting
A 2,700 K black body puts only 7.02% of its power into visible light, peaking at 1.073 µm in the infrared.
Heat loss
A person with 1.8 m² of skin at 33 °C (emissivity 0.98) radiates 878.7 W but absorbs 738.7 W back from a 20 °C room: a net loss of 140 W.
Cosmology
The cosmic microwave background at 2.7255 K peaks at 1.063 mm in wavelength and at 160.2 GHz in frequency.
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