Wien’s Law Calculator
Convert between a black body’s temperature and its peak wavelength with λ_peak = b ÷ T.
That is 0.5015 µm — Visible — green. A black body this hot appears yellow-white. b = 2.897771955×10⁻³ m·K.
Wien’s law gives a black body’s peak wavelength as λ_peak = b ÷ T, with b = 2.898×10⁻³ m·K. The Sun (T ≈ 5778 K) peaks near 500 nm — green light — yet looks white because it radiates across the whole visible range. Hotter bodies peak at shorter, bluer wavelengths; cooler ones peak in the red and infrared.
Blackbody radiation and Wien’s law
Any object above absolute zero glows with thermal (blackbody) radiation, emitting across a broad range of wavelengths. The spectrum has a single hump, and the wavelength of that hump — the peak wavelength — depends only on temperature. Wien’s displacement law pins it down: λ_peak = b ÷ T, where b = 2.897771955×10⁻³ m·K is Wien’s displacement constant, T is the absolute temperature in kelvin, and λ_peak is the peak wavelength in metres.
Hotter means bluer. Because temperature sits in the denominator, raising T pushes the peak to shorter wavelengths — toward blue, then ultraviolet and beyond. A cool 3000 K ember peaks in the near-infrared and glows dull red, while a 25,000 K star peaks in the ultraviolet and looks blue-white. This is why astronomers can read a star’s temperature straight from its colour.
b = 2.898×10⁻³ m·K (Wien’s displacement constant), T = temperature in kelvin, λ_peak = peak wavelength in metres
Worked example
At what wavelength does the Sun’s surface (T ≈ 5778 K) radiate most strongly?
- 1 Make sure the temperature is in kelvin. Wien’s law needs absolute temperature: here T = 5778 K.
- 2 Write the law. λ_peak = b ÷ T with b = 2.897771955×10⁻³ m·K.
- 3 Divide the constant by the temperature. λ_peak = 2.898×10⁻³ ÷ 5778 ≈ 5.01×10⁻⁷ m.
- 4 Convert to nanometres (× 1×10⁹). 5.01×10⁻⁷ m × 10⁹ ≈ 501 nm — green light, in the middle of the visible band.
Peak wavelength of some objects
Peak wavelengths from λ_peak = b ÷ T. A star’s perceived colour follows its temperature, not the single peak wavelength.
| Object | Temperature | Peak wavelength | Region / colour |
|---|---|---|---|
| The CMB | 2.725 K | 1.06 mm | Microwave |
| Cool red star | 3500 K | 828 nm | Near-infrared (looks red) |
| The Sun | 5778 K | 502 nm | Green peak (looks white) |
| A-type star (Sirius) | 9940 K | 292 nm | Ultraviolet (blue-white) |
| Hot blue star | 25,000 K | 116 nm | Ultraviolet (looks blue) |
Reading the result
The peak is not the whole story. Wien’s law finds where the spectrum peaks, but a black body emits at every wavelength. The Sun peaks in green yet appears white because our eyes blend its strong red, green, and blue output together — no single colour dominates.
A peak outside the visible band is normal. Many familiar emitters peak in the infrared or ultraviolet: a 3500 K star peaks at about 828 nm (near-infrared) but still looks red, because plenty of its light spills into the visible red. Only the visible tail of the spectrum reaches your eye.
Use kelvin. Temperature must be absolute. Feeding Celsius or Fahrenheit into λ_peak = b ÷ T gives a meaningless answer — convert first with K = °C + 273.15.