Blackbody Radiation Calculator
Enter a temperature and surface area to instantly calculate peak emission wavelength via Wien's displacement law, total radiated power via the Stefan-Boltzmann law, and the spectral radiance at any chosen wavelength via Planck's law. The spectral-power chart shows the full emission curve so you can see where most of the energy falls across the electromagnetic spectrum.
What is blackbody radiation?
A blackbody is an idealised object that absorbs all incoming electromagnetic radiation and re-emits energy solely as a function of its temperature. Real objects are graded by emissivity (0 to 1): a perfect blackbody has emissivity 1, polished metals can be as low as 0.02. The spectrum of radiation emitted by a blackbody is described by Planck's law, which gives the power per unit area per unit wavelength (spectral radiance) at any temperature. Integrating that spectrum over all wavelengths gives the Stefan-Boltzmann law, and the wavelength at which the spectrum peaks is given by Wien's displacement law. Together, these three laws underpin thermal imaging, astrophysics, climate science, and lighting design.
Wien's displacement law and spectral regions
Wien's displacement law states that the peak wavelength of emission is inversely proportional to absolute temperature: lambda_peak = b / T, where b = 2.898 x 10^-3 m·K. A human body at 310 K peaks around 9350 nm (long-wave infrared, invisible to the eye). The Sun at 5778 K peaks near 500 nm (green light), which is why sunlight appears white-yellowish and our eyes evolved peak sensitivity there. Stars hotter than about 30 000 K peak in the ultraviolet. The law immediately explains why objects glow red before they glow orange then white as they heat up: the peak shifts from the infrared through red into the blue end of the visible spectrum.
Stefan-Boltzmann law and total emitted power
The Stefan-Boltzmann law gives the total power radiated per unit area by a blackbody: M = sigma * T^4, where sigma = 5.670 x 10^-8 W/(m^2·K^4). Power scales as the fourth power of temperature, so doubling the temperature multiplies the radiated power by 2^4 = 16. For a real object with emissivity e, the formula becomes M = e * sigma * T^4. The total power from the full surface is P = M * A. The Sun radiates about 3.83 x 10^26 W from its surface at 5778 K over a radius of 696 000 km.
Planck's law and the full emission spectrum
Planck's law (1900) describes how much power is emitted at each specific wavelength: B_lambda(lambda, T) = 2hc^2 / lambda^5 × 1 / (exp(hc/(lambda·kB·T)) - 1), where h is Planck's constant, c the speed of light, and kB the Boltzmann constant. The spectral radiance peaks exactly at the wavelength predicted by Wien's law, falls steeply to zero at short wavelengths, and decays gradually at long wavelengths. This calculator evaluates Planck's law at whatever wavelength you specify and also plots the full curve in the chart below, letting you see the entire emission profile at a glance.
Blackbody temperatures of common objects
| Object / source | Temperature (K) | Peak wavelength (nm) | Spectral region |
|---|---|---|---|
| Human body (skin) | 310 | 9,355 | Long-wave infrared |
| Incandescent bulb filament | 2,700 | 1,074 | Near-infrared |
| Halogen lamp filament | 3,200 | 906 | Near-infrared |
| Sun (effective surface) | 5,778 | 502 | Visible (green) |
| Blue-white star (Sirius A) | 9,940 | 292 | Ultraviolet |
| Hot fusion plasma (tokamak) | 1e8 | 0.029 | X-ray |
Approximate effective blackbody temperatures and corresponding peak emission wavelengths for common radiation sources.
Frequently asked questions
What is Wien's displacement law?
Wien's displacement law states that the peak emission wavelength of a blackbody is inversely proportional to its absolute temperature: lambda_peak = 2.898 x 10^-3 m·K / T. Hotter objects peak at shorter wavelengths. The Sun (5778 K) peaks at about 500 nm (visible green), while a human body (310 K) peaks at about 9350 nm (long-wave infrared, invisible to the eye).
What is the Stefan-Boltzmann law?
The Stefan-Boltzmann law relates the total power radiated by a blackbody to the fourth power of its temperature: M = sigma * T^4, with sigma = 5.670 x 10^-8 W/(m^2·K^4). For a real object with emissivity e the law becomes M = e * sigma * T^4. Doubling the temperature multiplies radiated power by 2^4 = 16. Multiply M by the surface area to get the total emitted power in watts.
What does Planck's law calculate?
Planck's law gives the spectral radiance of a blackbody at a specific wavelength and temperature: B_lambda = 2hc^2 / lambda^5 × 1 / (exp(hc / (lambda·kB·T)) - 1). The result is power per unit area per unit solid angle per unit wavelength (W/sr/m^2/nm). Planck introduced this formula in 1900 to match experimental measurements, and it was the birth of quantum mechanics.
What is emissivity and how does it affect the result?
Emissivity (e) is a dimensionless number between 0 and 1 that measures how closely a real object approximates an ideal blackbody. A value of 1 means perfect emission; polished metals can be as low as 0.02. All emissive power outputs scale linearly with e: a surface with e = 0.9 radiates 90% of what a blackbody at the same temperature would. The peak wavelength from Wien's law is independent of emissivity.
Why does the Sun look white or yellow if it peaks in green?
The Sun's effective surface temperature is about 5778 K, which peaks near 502 nm (green). However, it emits strongly across the entire visible spectrum from violet to red, and the combination of all those colours produces near-white light. The slightly yellow-orange appearance when the Sun is near the horizon is caused by atmospheric scattering, which removes shorter (blue/green) wavelengths, not by the blackbody spectrum itself.
Can I use this for a non-ideal (real) object?
Yes. Enter the emissivity of the material (e.g. 0.95 for human skin, 0.9 for concrete, 0.02 for polished aluminium). The emissive power and total power outputs are scaled by your emissivity value. Wien's peak wavelength calculation is not affected by emissivity - it depends only on temperature.
What units does this calculator use?
Temperature can be entered in Kelvin, Celsius, or Fahrenheit - the calculator converts to Kelvin internally. Peak wavelength is in nanometres (nm). Emissive power is in watts per square metre (W/m^2). Total power is in watts (W). Spectral radiance is in W/sr/m^2/nm, which is the standard photometric unit for spectral intensity per unit wavelength.