Last updated: 2026-06-15

Wien's Displacement Law

Heat something up and its colour changes — a poker glows dull red, then orange, then white as it gets hotter. Wien's displacement law puts a number on that everyday observation. It gives the exact wavelength at which a hot body's thermal radiation is most intense, and shows that this peak slides toward shorter (bluer) wavelengths as the temperature rises. This calculator returns the peak wavelength for any temperature and tells you which part of the electromagnetic spectrum it lands in.

Where the formula comes from

A black body radiates across a continuous band of wavelengths, described by Planck's law. That spectrum has a single peak. If you find where the peak sits and ask how it moves with temperature, the answer is strikingly simple: the peak wavelength times the temperature is a constant. That constant is Wien's displacement constant, $b$, so $\lambda_\text{max} = b/T$. The peak is displaced to shorter wavelengths as $T$ grows — hence the name.

Formula

The temperature must be absolute. Because the relationship is an inverse one, hotter means a shorter peak wavelength.

Worked example

The Sun's photosphere is about $T = 5778\ \text{K}$:

That is green light, near the centre of the visible band — which is why sunlight appears white and why our eyes are most sensitive there.

Reading the spectrum

The peak wavelength tells you the character of the radiation. A body near room temperature (300 K) peaks around 10 µm, deep in the infrared, so it radiates warmth you feel but cannot see. A tungsten filament at 3000 K peaks in the near-infrared, spilling just enough into the visible to glow yellow-white. A blue star at 30000 K peaks in the ultraviolet. The calculator labels the band for whatever temperature you enter.

Limitations

Wien's law locates the peak of a black-body spectrum; it does not describe a surface that emits strongly at one specific wavelength, like a laser or a gas-discharge lamp. Real objects are also only approximately black bodies, and their emissivity can vary with wavelength, nudging the apparent peak. Finally, the law gives the peak of the spectrum plotted against wavelength; plotting the same radiation against frequency puts the peak at a different place, because the two are related non-linearly.