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Wien's Displacement Law Calculator

Find the colour a hot object glows from its temperature.

Result

502.04 nm
0.5020 µm
339.33 THz

How it is calculated

The only input is the absolute temperature T in kelvin, which must be above zero. The peak wavelength comes from Wien's displacement law, λmax = b / T, with b = 2.897771955 × 10−3 m·K. The tool shows it in nanometres (2 decimals) and micrometres (4 decimals). It also gives a frequency, f = 5.8789257 × 1010 Hz/K × T, in THz. That is the peak of the spectrum plotted per unit frequency, so it is not the same as c / λmax: the peak of a spectrum depends on whether it is plotted by wavelength or by frequency. Celsius or Fahrenheit values must be converted first, because only kelvin is accepted and zero or negative values return nothing.

Worked example

An object at 5,772 K, close to the Sun's effective surface temperature. The wavelength is 2.897771955 × 10−3 / 5,772 = 5.0204 × 10−7 m. That is 502.04 nm, or 0.5020 µm, in the green part of the visible range. The frequency figure is 5.8789257 × 1010 × 5,772 = 3.3933 × 1014 Hz, shown as 339.33 THz. The tool gives 502.04 nm, 0.5020 µm and 339.33 THz.

Try this example →

Common mistakes

  • Typing the temperature in degrees Celsius. 5,500 °C is about 5,773 K; entering 5,500 as if it were kelvin shifts the answer by a few per cent, and at low temperatures the error is huge.
  • Converting the 339.33 THz value with c / f and expecting 502 nm. The frequency shown is the peak of the per-frequency spectrum, which sits at a different place than the wavelength peak.
  • Expecting a wavelength field. This tool goes from temperature to wavelength only; to find a temperature from a measured peak, divide b by the wavelength yourself, in metres.
  • Treating a real object's colour as exactly the peak colour. A star or a lamp emits across a wide range, and the peak is only where the curve is highest.
  • Reading the 9,659.24 nm result for 300 K as visible light. It lies in the infrared, which is why room-temperature objects do not glow.

Sources

About this calculator

This calculator finds the peak emission wavelength of a blackbody radiator from its temperature using Wien's displacement law: λmax = b / T, where b is Wien's displacement constant (≈2.898 × 10⁻³ m·K) and T is the absolute temperature in kelvin. As an object gets hotter, its peak wavelength shifts to shorter (bluer) wavelengths.

Astronomers use it to estimate a star's surface temperature from its color (or vice versa), and physics students use it to connect thermal radiation to the visible spectrum — explaining, for instance, why a heated metal glows red before white-hot. Enter a temperature in kelvin to get the peak wavelength (in nm and µm) and the matching peak frequency. To go the other way, divide b by the wavelength yourself: a peak at 500 nm (5 × 10⁻⁷ m) means roughly 5,800 K.

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Comments (1)

  • Editorial team

    Peak wavelength is not the same as perceived colour. At the Sun's temperature the peak falls in the green, yet the Sun looks white because it emits strongly across the whole visible range. A good sanity check at the other end is body temperature: enter 310 K and the peak is about 9.35 micrometres, in the mid infrared, which is why thermal cameras work in that band. Which object or star temperature are you checking?

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