Wien's Displacement Law Calculator
Enter absolute temperature T to get the blackbody peak wavelength λ_max=b/T (b=2.89777e-3 m·K) and peak frequency. T=5778 K (Sun) → λ_max=502 nm (green, visible); T=300 K → 9.66 µm (IR).
Input Data
Results
At a glance:Wien's displacement law (Wilhelm Wien, 1893, German physicist) states that a blackbody's spectral radiance peaks at a wavelength inversely proportional to its absolute temperature: λ_max=b/T, where b=2.897771955×10⁻³ m·K is Wien's displacement constant (derived from Planck's law). T is the absolute temperature (K). The peak frequency is f_max=c/λ_max ≈ 5.879×10¹⁰·T Hz (the frequency-domain peak differs from the wavelength peak by a factor of ~1.76 because of the variable change). Physical meaning: hotter objects radiate at shorter wavelengths — the colour shifts from red to orange to white to blue. This is why an incandescent bulb's filament glows red/dull at low temperature and white-hot at high. History: Wien derived it empirically in 1893 before Planck's law (1900); it was a key step toward quantum theory. Example: the Sun's surface T≈5778 K → λ_max=2.898e-3/5778≈5.02e-7 m=502 nm (green, but the Sun looks white because it emits broadly); the human body T≈310 K → λ_max≈9.34 µm (infrared, invisible); a star at 3000 K (red) peaks at ~966 nm (near IR); a 12000 K blue star peaks at ~242 nm (UV). Applications: (1) incandescent colour — predict filament colour from temperature; (2) stellar temperature — measure a star's λ_max to infer its surface T (e.g. red supergiant Betelgeuse ~3500 K, blue Rigel ~11000 K); (3) infrared thermometry — measure the peak/colour to get temperature without contact; (4) thermal cameras and radiation-cooling design. Notes: (1) T must be absolute K; (2) this gives the peak of the Planck curve — the actual colour is a broad mix; (3) the wavelength and frequency peaks are not simply related by c because of the Jacobian; (4) keep SI units.
Formula
Wien's law: λ_max = b/T, b=2.897771955×10⁻³ m·K
Peak frequency: f_max = c/λ_max
Hotter ⇒ shorter peak wavelength (colour shifts to blue)
T must be absolute (K)
$$\lambda_{max} = \frac{b}{T}, \quad b = 2.897771955\times 10^{-3}\ \mathrm{m\cdot K}$$How to Use
- Enter absolute temperature T (K; °C + 273.15 = K).
- The tool gives peak wavelength λ_max (m, nm) and peak frequency f_max.
- Hotter objects peak at shorter (bluer) wavelengths.
Case Studies
Sun peak and incandescent colour
Sun T=5778 K → λ_max=2.898e-3/5778≈502 nm (green).
The Sun looks white because it radiates across the visible band.
A 3000 K red star peaks at ~966 nm (near IR); the body at 310 K peaks at 9.34 µm (thermal-IR).
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.