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Wien Displacement Law

Peak emission wavelength of a blackbody.

Formula

λmax=bT\lambda_{max} = \frac{b}{T}

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Variables

bWien constant
TTemperature

Example

Hotter stars glow bluer

How it works

A blackbody does not emit the same amount of radiation at all wavelengths; its spectrum has a single peak that shifts as the temperature changes. Wien Displacement Law says that as temperature increases, the peak moves to shorter wavelengths, because hotter objects populate higher-energy electromagnetic modes more strongly. The constant b is an empirically measured constant that comes out of the full blackbody radiation spectrum derived from quantum theory.

When to use it

Use this law when you want to estimate the temperature of an object from the wavelength where its emission is strongest, such as stars, planets, dust clouds, or heated lab objects. It is also useful for predicting whether the peak will lie in infrared, visible, or ultraviolet light.

Worked example, step by step

A heated tungsten filament has a temperature of 2500 K. Use Wien's law: \lambda_{max} = b / T Take b = 2.898 × 10^-3 m·K Substitute: \lambda_{max} = (2.898 × 10^-3 m·K) / (2500 K) Calculate: \lambda_{max} = 1.1592 × 10^-6 m Convert to micrometres: 1.1592 × 10^-6 m = 1.16 \u03bcm Final answer: the peak emission wavelength is about 1.16 \u03bcm, which is in the infrared.

Common mistakes to avoid

  • Using the temperature in Celsius instead of Kelvin
  • Confusing the peak wavelength with the wavelength where the object looks brightest to the eye
  • Forgetting that the formula gives the peak of the spectrum, not the total emitted power

Did You Know?

Wien's law lets astronomers read a star's temperature straight from its colour, blue being hottest.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026