Calculate peak wavelength from temperature (or vice versa) using Wien's displacement law. Includes spectral distribution, Stefan-Boltzmann power, and color visualization.
Wien's displacement law relates the temperature of a blackbody to the wavelength at which it emits most intensely: λ_max = b/T, where b = 2.898 × 10⁻³ m·K. Hotter objects peak at shorter wavelengths — this is why the Sun (5778 K) peaks in visible yellow-green light at 502 nm, while a room (293 K) peaks at 9.9 µm in the thermal infrared.
This simple inverse proportionality has profound consequences. Stars' colors reveal their surface temperatures: red giants (~3500 K) peak in the red, white dwarfs (~25000 K) peak in the ultraviolet. The cosmic microwave background (2.725 K) peaks at 1.06 mm in the microwave band — a relic of the Big Bang cooled by 13.8 billion years of cosmic expansion.
Combined with the Stefan-Boltzmann law (P = εσT⁴), Wien's law completely characterizes blackbody radiation. The total radiated power scales as the fourth power of temperature: doubling temperature increases radiation 16-fold. This calculator provides both the peak wavelength and total power, plus a spectral distribution showing the full Planck curve shape.
Use this calculator when you want a fast link between temperature and peak emission wavelength without running the full blackbody math separately.
It is useful for thermal-radiation intuition, star temperatures, infrared applications, and understanding why hotter emitters shift toward shorter wavelengths while also radiating much more total power. That makes it a good first-pass bridge between temperature and the part of the spectrum you expect to matter most.
Wien's Law: λ_max = b/T, b = 2.898×10⁻³ m·K. Stefan-Boltzmann: P = εσT⁴, σ = 5.670×10⁻⁸ W/m²K⁴. Planck: B(λ,T) = 2hc²/λ⁵ × 1/(e^(hc/λkT)−1).
Result: Peak: 501 nm (visible green), Power: 63.2 MW/m²
The Sun at 5778 K: λ_max = 2.898e-3/5778 = 501 nm (green, though the Sun appears white due to broad spectrum). Power = σ(5778)⁴ = 63.2 MW/m², consistent with the solar constant after accounting for the Sun's surface area and our distance.
Wien's law is best used for identifying the spectral neighborhood where an emitter is strongest. It gives a quick temperature-to-peak relationship and is especially useful when you want to know whether a source is mainly infrared, visible, or ultraviolet before moving into a fuller spectral model.
The most common mistake is treating the peak wavelength as the whole story. Real sources radiate across a broad spectrum, and apparent color comes from the overall visible distribution, not from a single wavelength. Emissivity changes total power, but for a grey body it does not shift the Wien peak itself.
It states that the peak emission wavelength of a blackbody is inversely proportional to temperature: λ_max = b/T. Higher temperature → shorter peak wavelength.
An idealized object that absorbs all incident radiation and re-emits it thermally. Stars, furnaces, and the CMB are excellent approximations. The spectrum depends only on temperature.
Higher kinetic energy means more energetic (shorter wavelength) photons dominate the emission. This shifts the peak from infrared → red → white → blue → UV as temperature increases.
The ratio of actual emission to blackbody emission at the same temperature. ε = 1 for a perfect blackbody. Polished metals can have ε = 0.05; most non-metals are 0.8-0.95.
A light source's color temperature is the blackbody temperature whose emission matches the source's apparent color. A candle (~1800K) appears warm/orange; daylight (~5500K) appears neutral.
Total radiated power per unit area: P = εσT⁴. The T⁴ dependence means even modest temperature increases dramatically boost radiation. Doubling T → 16× more power.