Wien's Law Calculator

Wien's Displacement Law states that the peak wavelength of radiation emitted by a blackbody is inversely proportional to its absolute temperature. The formula is λmax = b / T, where b is Wien's displacement constant (2.897771955 × 10⁻³ m·K) and T is the temperature in Kelvin. As temperature rises, the peak emission shifts to shorter (higher-energy) wavelengths. See also our Specific Heat Calculator (Chemistry).

Rearrange the formula to T = b / λmax. Divide Wien's displacement constant (2.897771955 × 10⁻³ m·K) by the peak wavelength in metres. For example, if the peak wavelength is 502 nm (5.02 × 10⁻⁷ m), the temperature is approximately 5772 K.

The Sun's peak emission wavelength is approximately 502 nm (visible green light). Plugging this into T = b / λmax gives roughly 5778 K, which closely matches the accepted value for the Sun's photosphere temperature. This demonstrates how astronomers measure stellar surface temperatures from spectral observations.

Wien's law allows astronomers to estimate a star's surface temperature by measuring the wavelength at which it emits the most light. Hot blue stars (e.g. type O and B) have peak wavelengths in the ultraviolet, while cooler red stars (type M) peak in the infrared. The colour of a star is therefore a direct indicator of its surface temperature. You might also find our use the Coffee Cup Calorimeter Calculator useful.

Wien's law applies to any body that behaves as an ideal blackbody — meaning it absorbs and emits all radiation perfectly. Real objects are only approximate blackbodies, but the law gives excellent estimates for stars, lava, incandescent bulbs, the cosmic microwave background (~2.7 K), and other thermal radiators.

Temperature must be in Kelvin (K) and wavelength in metres for the raw formula, since Wien's constant b = 2.897771955 × 10⁻³ m·K. This calculator converts the result to nanometres (nm) and also shows the corresponding peak frequency in terahertz (THz) for convenience.

The Wien's displacement constant b has an exact value of 2.897771955 × 10⁻³ m·K (approximately 2898 μm·K). This is a fundamental physical constant defined precisely within the SI system of units.

Peak frequency and peak wavelength are related by the speed of light: f = c / λ, where c ≈ 2.998 × 10⁸ m/s. However, because the Planck distribution is not symmetric on a linear scale, the frequency at which radiance is maximum does not correspond exactly to the same photon energy as the wavelength maximum — a subtlety worth noting in advanced applications.