Wien's Displacement Law Calculator

Wien's displacement law: λ_max·T = b

Wien's law says the wavelength where a black body radiates most strongly is inversely proportional to its absolute temperature: λ_max = b / T, where b = 2.898·10⁻³ m·K is Wien's displacement constant. Run the Sun through it: at T ≈ 5778 K the peak lands at λ_max ≈ 502 nm, a green-yellow, and that happens to be where human vision is most sensitive. A cooler red giant at 3000 K peaks near 967 nm in the infrared, while your own body at 310 K glows around 9.3 µm in the mid-infrared, which is exactly the band a thermal camera reads.

Applications

In astronomy a star's color reads out its surface temperature straight away, with blue stars running hot and red ones cool. Beyond that, the law shows up in infrared thermography of buildings and electronics, in tuning incandescent and LED lamps to a target color temperature, in remote sensing of planetary surfaces, and in calibrating pyrometers.

FAQ

Does T need to be in kelvin? Yes. Wien's law is built on absolute temperature, so plugging in Celsius or Fahrenheit gives a number with no physical meaning.

Why does the Sun look white if it peaks in green? Black-body emission spreads out widely. The Sun puts out plenty of light across the whole visible range, and the eye adds it all up as white. The green peak is genuine, it just sits in a mix that includes red and blue.

Is there a frequency version of Wien's law? There is. It reads f_max·T = constant, but with a different numerical factor (≈ 5.879·10¹⁰ Hz/K). Watch out for one thing: f_max is not the same as c/λ_max, because the two peaks fall in different parts of the spectrum.