How this instrument works
A blackbody at any temperature above absolute zero radiates across a continuous spectrum, but that spectrum has a single peak — the wavelength carrying more power per unit wavelength than any of its neighbours. Wien's displacement law says that peak, λ_max, is inversely proportional to absolute temperature: λ_max = b ⁄ T, where b is Wien's displacement constant, 2.897771955×10⁻³ m·K. Hotter objects push their peak toward shorter wavelengths, which is why the law carries the name 'displacement.'
The relationship falls directly out of Planck's radiation law. Differentiate the Planck spectral radiance with respect to wavelength, set that derivative to zero, and solve for the wavelength at the maximum; every temperature-dependent term collapses into the single constant b. An entire spectral curve, described by Planck's full equation, reduces to one division — that compression is the whole payoff of doing the calculus once and keeping only the result.
The law describes an idealized blackbody, not any particular real surface, so it works best for stars, incandescent filaments, and glowing metal — objects close to thermal equilibrium radiators. It also names only the peak, not the shape of the curve or the total power radiated; a foundry worker judging steel temperature by its color, or an astronomer classifying a star from its color index, is really reading this displacement, whether or not they ever write the formula down.
- Enter the object's Absolute temperature, K — use the actual surface or filament temperature in kelvin, not Celsius or Fahrenheit.
- The instrument divides Wien's displacement constant by that temperature automatically; there is nothing else to configure.
- Read Peak emission wavelength, the wavelength at which the object radiates most strongly for its temperature.
- Toggle the unit menu between nanometres and micrometres to match the scale of your source.
- For visible-light checks such as stars or filaments, keep nanometres; for furnaces and other infrared sources, switch to micrometres.
Worked example — the Sun's photosphere
The Sun's visible surface, the photosphere, sits at an effective temperature of about 5,778 K. Divide Wien's constant by that figure: λ_max = 0.002897771955 ⁄ 5778 = 5.0151816459×10⁻⁷ m, or 501.5 nanometres.
That wavelength lands squarely in the green band of the visible spectrum, close to the 555 nm peak of human daytime vision. It is very likely not a coincidence — eyes evolved under exactly this light, tuned by natural selection to the part of the solar spectrum carrying the most power. A cooler source radiates further into the red or infrared instead; a hotter one shifts toward blue and ultraviolet.
Questions
What is Wien's displacement constant?
It is b = 2.897771955×10⁻³ m·K, a fixed value that falls out of Planck's radiation law once you combine Planck's constant, the speed of light, and Boltzmann's constant and solve for the spectral maximum. CODATA fixes it to that precision, and dividing it by a temperature in kelvin always returns a length in metres.
Why does hotter mean a shorter wavelength?
Because λ_max = b ⁄ T is an inverse relationship: as temperature climbs, the peak wavelength must fall to keep the product λ_max·T fixed at b. Human skin at 310 K (37°C) peaks near 9,347 nm, deep infrared — exactly the band a thermal camera detects. Heat something to star temperatures instead and the same law pushes the peak into visible light.
Does Wien's law give the total radiated power?
No. It only locates the peak of the spectral curve, not the area beneath it. Total radiated power per unit area comes from the Stefan-Boltzmann law, P = σT⁴, a separate relation with its own constant. The two are often used together — one finds the color, the other finds the brightness — but neither substitutes for the other.
Does this only apply to stars?
No, it applies to anything close to a thermal blackbody radiator: a tungsten filament, molten steel, a ceramic kiln, even the cosmic microwave background at 2.725 K, which peaks near 1.06 millimetres. It grows less accurate for selective emitters like LEDs or gas-discharge lamps, whose spectra come from specific atomic transitions rather than thermal equilibrium.
What temperature scale does the formula need?
Absolute temperature in kelvin, always positive and measured from absolute zero. Celsius or Fahrenheit readings must be converted first — 20°C is 293.15 K, not 20 K — because Wien's law only holds when temperature is counted from true zero, the point where thermal radiation itself would vanish.
Is the peak wavelength the only color a hot object emits?
No. A blackbody radiates across every wavelength at once; Wien's law just marks where the curve is tallest. A 5,778 K surface peaking at 501.5 nm still emits plenty of red, blue, and ultraviolet light too, which is why the Sun looks white, not pure green, to the eye: perceived color blends the whole curve, not just its peak.