Blackbody Wien's Law Calculator

Frequently Asked Questions

What is the displacement law?

The displacement law states that the wavelength of peak emission from a blackbody is inversely proportional to its absolute temperature, so hotter objects glow at shorter wavelengths.

Why does radiated power rise so steeply with temperature?

The Stefan-Boltzmann law makes total radiant exitance proportional to the fourth power of temperature, so doubling the temperature increases radiated power sixteen-fold.

What temperature unit does this calculator use?

Enter the temperature in kelvin, the absolute scale, because both Wien's law and the Stefan-Boltzmann law require an absolute temperature. To convert from Celsius, add 273.15. For example, room temperature of about 27 degrees Celsius is 300 K, where the blackbody peak falls in the thermal infrared near 9.7 micrometers.

What is a blackbody?

A blackbody is an idealized object that absorbs all radiation falling on it and re-emits energy purely as a function of its temperature, independent of its material or surface finish. Real objects only approximate this, but stars, glowing metal, and a small hole in a heated cavity all behave much like blackbodies. Because the spectrum depends only on temperature, measuring the peak wavelength (Wien's law) or the total output (Stefan-Boltzmann) tells you how hot the object is.

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How This Calculator Works

An ideal blackbody glows with a spectrum set entirely by its temperature. Wien's displacement law states that the wavelength of peak emission is inversely proportional to temperature, using the constant 2.8978 times ten to the minus three meter kelvin. Hotter objects peak at shorter wavelengths, which is why a heated metal goes from red to white to blue as it gets hotter. This calculator uses the wavelength form of Wien's law (λ_peak = b ÷ T); the frequency form of the law peaks at a different point, which is why the cosmic microwave background is quoted as ~1.06 mm from the wavelength form but ~1.9 mm from the frequency form.

The total energy radiated per unit area follows the Stefan-Boltzmann law, where the radiant exitance rises with the fourth power of temperature. A small rise in temperature therefore produces a large jump in radiated power.

How To Use It

Enter the absolute temperature in kelvin. The result gives the peak wavelength in nanometers and the total radiant exitance in watts per square meter.

Which Band The Peak Falls In

Near room temperature, around 300 K, the peak lies in the infrared.

The Sun, near 5800 K, peaks in visible green-yellow light.

Above roughly 10,000 K the peak moves into the ultraviolet.

Worked Example

Take a Sun-like blackbody at T = 5800 K. Wien's law gives the peak wavelength: λ_peak = b ÷ T = (2.8978 × 10⁻³ m·K) ÷ 5800 K ≈ 4.996 × 10⁻⁷ m ≈ 500 nm, which is green-yellow light. The Stefan-Boltzmann law gives the radiant exitance: M = σT⁴ = (5.670 × 10⁻⁸) × (5800)⁴. Since 5800⁴ ≈ 1.132 × 10¹⁵, M ≈ 5.670 × 10⁻⁸ × 1.132 × 10¹⁵ ≈ 6.42 × 10⁷ W/m². That is roughly 64 megawatts radiated from every square meter of the surface.

Temperature Benchmarks

300 K (27°C / 80°F) - Room temperature. Peak emission at ~9.7 µm (thermal infrared). Thermal cameras detect this range.

800 K (527°C) - Dull red glow. Steel begins to visibly radiate. Peak near 3.6 µm.

3,000 K - Incandescent bulb filament. Warm white light, peak near 966 nm (near-infrared). Only ~5% of emitted energy is visible light.

5,778 K - Sun's photospheric temperature. Peak near 501 nm (green), but the full visible spectrum makes sunlight appear white.

10,000-30,000 K - Hot blue-white stars (type O/B). Peak shifts into UV; the visible blue color is the tail of the distribution.

2.725 K - Cosmic Microwave Background. Peak at ~1.06 mm (microwave). The afterglow of the Big Bang.

The Stefan-Boltzmann law (P = σT⁴) means a star twice as hot as the Sun radiates 16 times more power per unit area - the fourth-power dependence makes temperature the dominant driver of stellar luminosity.

Blackbody Wien's Law Calculator

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