What is Wien's displacement law?

Wien's displacement law relates the peak wavelength of blackbody radiation to its absolute temperature: λ_max = b / T, where b ≈ 2.898 × 10⁻³ m·K is Wien's displacement constant. As temperature increases, the peak wavelength shifts to shorter (bluer) wavelengths.

What units should I use for temperature?

The formula requires absolute temperature in Kelvin (K). This calculator accepts Kelvin directly. 0 K is absolute zero; room temperature is about 293 K; the Sun's surface is about 5778 K.

Why is this relevant to stars?

Stars approximate blackbodies. By measuring the wavelength at which a star emits most intensely, astronomers can estimate its surface temperature using Wien's law. Hot blue stars peak in the UV; cool red dwarfs peak in the infrared.

Does this only apply to perfect blackbodies?

Wien's law is exact only for ideal blackbodies. Real objects have emissivities less than 1 and may not follow a perfect Planck spectrum, so the peak wavelength can differ slightly. However, the law is a very useful approximation for many hot objects like stellar surfaces, incandescent bulbs, and glowing metals.

What is the peak wavelength of the human body?

The human body surface is about 307 K (34 °C / 93 °F). Plugging in: λ_max = 2.898×10⁻³ / 307 ≈ 9440 nm, which is in the mid-infrared — the range used by thermal cameras.

What is Wien's displacement constant?

The constant b = 2.897771955 × 10⁻³ m·K (CODATA 2018 value). It is derived from fundamental constants: b = hc / (k_B × x_max), where x_max ≈ 4.965 is the solution to the transcendental equation arising from Planck's law.

Wien's Law Calculator

Enter a temperature (K) to find the peak emission wavelength of a blackbody, or enter a wavelength to find the corresponding temperature.

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Temperature

Enter temperature in Kelvin, Celsius, or Fahrenheit.

Quick Presets

Enter a value and click Calculate to see results.

Summary

Wien's displacement law states that the peak wavelength of blackbody radiation is inversely proportional to its absolute temperature: λ_max = b / T, where b = 2.897771955 × 10⁻³ m·K. This calculator lets you solve for either variable given the other. It is widely used in astrophysics, thermal imaging, and materials science to estimate surface temperatures from spectral data.

How it works

Select whether you want to solve for peak wavelength (given temperature) or temperature (given wavelength).
Enter the known value in the input field.
Click Calculate to apply the formula λ_max = b / T.
The result is displayed in multiple units (nm, μm, m for wavelength; K, °C, °F for temperature).
Use the preset buttons to quickly load common examples like the Sun or a human body.

Use cases

Estimate a star's surface temperature from its color or peak emission wavelength.
Determine the peak emission wavelength of an infrared heat lamp or furnace.
Understand why the Sun appears yellow-white (peak ~502 nm).
Calculate at what wavelength a blackbody at room temperature emits most strongly.
Thermal camera design: find the detector wavelength range needed for a target temperature.
Astrophysics coursework and physics lab reports.
Cross-check spectroscopic measurements against theoretical blackbody predictions.
Explore how peak wavelength shifts as a star cools from blue-white to red.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu

Wien's Law Calculator

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