Wien's Displacement Calculator
Wien's displacement law, derived by Wilhelm Wien in 1893, relates the peak wavelength of blackbody radiation to its temperature: lambda_max = b / T, where b = 2.897771955 x 10^-3 m K. As temperature increases, the peak shifts to shorter wavelengths (higher energy photons). This explains why a heated metal first glows red (peak in the red/near-IR), then orange, then yellow-white as temperature rises. The Sun at about 5,778 K peaks at about 502 nm (green), while the cosmic microwave background at 2.725 K peaks at about 1.06 mm (microwave). This calculator works in both directions: temperature to peak wavelength, or peak wavelength to temperature.
Wien's displacement law formula
lambda_max = b / T
b = 2.897771955e-3 m K (Wien's displacement constant)
T = b / lambda_max
T is in kelvin, lambda_max is in meters. The constant b follows from Planck's radiation law: at the peak, d/dlambda [Planck function] = 0, which yields b = hc / (k * x0) where x0 = 4.965114... is the root of the transcendental equation (5 - x) e^x = 5.
Peak wavelengths for common temperatures
- Cosmic microwave background (2.725 K): lambda_max = 1.063 mm (microwave).
- Human body (310 K): lambda_max = 9.35 micrometers (mid-infrared, thermal cameras).
- Incandescent bulb filament (~2,700 K): lambda_max = 1,074 nm (near-IR, most energy wasted as heat).
- Sun surface (5,778 K): lambda_max = 502 nm (green, near center of visible spectrum).
- Blue supergiant (30,000 K): lambda_max = 97 nm (UV).
Wien's displacement law: frequently asked questions
What is Wien's displacement law?
Wien's displacement law states that the peak wavelength of blackbody radiation is inversely proportional to the absolute temperature: lambda_max = b / T, where b = 2.897771955 x 10^-3 m K (Wien's displacement constant) and T is temperature in kelvin. Hotter objects emit at shorter (bluer) wavelengths; cooler objects emit at longer (redder) wavelengths.
What is the Wien's displacement constant?
The Wien's displacement constant b = 2.897771955 x 10^-3 m K (exact in the 2019 SI, derived from Planck's constant, Boltzmann constant, and speed of light). It gives the wavelength of peak emission for a perfect blackbody at temperature T.
How does Wien's law relate to stellar colors?
Stars approximate blackbodies. The Sun's surface temperature is about 5,778 K, giving a peak wavelength of about 502 nm (green light), but the Sun appears yellowish-white because it emits substantially across the full visible spectrum. Red stars like Betelgeuse (3,500 K) peak near 828 nm (near-IR). Blue stars like Rigel (12,000 K) peak near 241 nm (UV).
What is the difference between Wien's law and the Stefan-Boltzmann law?
Wien's displacement law gives the peak wavelength (color) of emission. The Stefan-Boltzmann law gives the total radiated power: P = sigma T^4 A, where sigma = 5.67 x 10^-8 W m^-2 K^-4. Wien's law describes where the radiation peaks; Stefan-Boltzmann describes how much total radiation is emitted.
Can Wien's law be used for temperature measurement?
Yes. Optical pyrometers measure the peak wavelength or color of emitted light to determine temperature without contact. This is used in steelmaking (where temperatures exceed 1,000 degrees Celsius), semiconductor processing, and astrophysics to infer stellar surface temperatures.
Official sources
- NIST CODATA 2018: Wien Wavelength Displacement Law Constant.
- OpenStax University Physics Vol. 3: Blackbody Radiation.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.