This Wien’s law calculator finds the wavelength at which a hot object glows brightest from its temperature — λmax = 2.898×10⁻³ ÷ T — the law that reads the colors of stars, furnace peep-holes and thermal cameras.

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The Color of Heat, as an Equation

Everything warm emits light — most of it invisible — and the spectrum's peak moves with temperature by an iron rule Wilhelm Wien found in 1893: λmax = b/T, b = 2.898×10⁻³ m·K. Hotter means shorter peak wavelength, in exact inverse proportion. The Sun's 5,778 K surface peaks at 501.5 nm — blue-green visible light, the heart of the spectrum our eyes evolved to catch. A 3,100 K incandescent filament peaks at 935 nm in the near-infrared (which is why bulbs waste most of their output as invisible heat and feel warm rather than merely bright). Your skin at ~310 K peaks at 9.35 μm, mid-infrared: you are glowing, constantly, in a band no human eye detects but every thermal camera does. At the extremes the law reads the universe: the cosmic microwave background, the cooled fireball of the Big Bang at 2.725 K, peaks at 1.06 mm in microwaves; a 10⁷ K stellar corona peaks in X-rays at 0.29 nm. One division spans them all, and it only needs the temperature.

Wien's law is one vertex of the blackbody triangle — with Planck's law (the full spectrum, of which Wien's is the peak-finding shortcut) and the Stefan-Boltzmann law (total power, σT⁴) completing the set. Its practical life is pyrometry: measuring temperatures too hot, distant or dangerous to touch. Steelworkers judge a furnace by color because the peak is marching through the visible as it heats — dull red ~800 K, orange ~1,200 K, yellow-white ~1,600 K — and optical pyrometers formalize the judgment by matching filament brightness at a known wavelength. Astronomers classify every star first by color (O blue, B blue-white, A white, F yellow-white, G yellow like the Sun, K orange, M red) — a spectral sequence that is simply Wien's law read off the sky, refined by absorption lines. Caveats: real objects are not perfect blackbodies (emissivity below 1 shifts measured brightness, though the PEAK position of a thermal emitter still tracks temperature well), and the law gives the peak of the spectrum per unit wavelength — per unit frequency peaks elsewhere, a classic technicality this page's wavelength form avoids.

Worked Examples (Verified)

  • The Sun: 5,778 K → 501.5 nm — visible, blue-green.
  • Human body: 310 K → 9.35 μm — mid-infrared; why thermal cameras see people in the dark.
  • Incandescent filament: 3,000 K → 966 nm — near-infrared peak, hence inefficient light.
  • Cool red star (M class): 3,200 K → 906 nm; its visible tail is the red part — hence "red dwarf."
  • Cosmic background: 2.725 K → 1.06 mm — microwave, the oldest light there is.

Wien's Law Discipline

  • Kelvin only. A Celsius input is the most common Wien error and moves the answer by hundreds of nanometres.
  • The peak is per-unit-wavelength; the per-unit-frequency peak sits at a different place (the spectrum's shape depends on the variable) — quote which one you mean.
  • Real surfaces: emissivity changes total brightness, and selective emitters (LEDs, lasers, fluorescent tubes) are NOT thermal spectra — Wien doesn't apply to their "color" at all.
  • Observed starlight is redshifted: a distant galaxy's peak is stretched by (1+z), so temperature estimates from raw peaks need the redshift correction.
  • Color temperature of a lamp is a blackbody EQUIVALENT (the T whose color matches), not necessarily the filament's true temperature — close for incandescents, metaphorical for LEDs.

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Frequently Asked Questions

How do you calculate Wien's law?

λmax = 2.898×10⁻³ m·K ÷ T, with T in kelvin. The Sun at 5,778 K: 2.898×10⁻³/5778 = 5.015×10⁻⁷ m = 501.5 nm. Halve the temperature and the peak doubles in wavelength; double the temperature and it halves. This calculator takes any temperature in kelvin and returns the peak wavelength in the friendliest unit plus the spectral band it falls in — from X-ray hot to microwave cold.

Why does the Sun peak in green but look white-yellow?

Because the peak is not the whole spectrum. The Sun's blackbody curve is broad: it pours out violet, blue, green, yellow and red in comparable (if not equal) amounts around the 501 nm peak, and the mixture of the full visible band registers as white — tinted yellow-ish from the ground because the atmosphere scatters away some blue (Rayleigh scattering, the same reason the sky is blue). "Green sun" is a statement about one mathematical point of the curve, not the integrated color your eye computes.

How do astronomers use Wien's law?

As the first thermometer for anything that shines. A star's color (measured precisely as the difference in brightness through blue and visual filters) locates its spectral peak, hence its surface temperature, hence its spectral class on the O-B-A-F-G-K-M sequence — all before any spectrum is taken. The same division prices exoplanet host stars, dates the cooling of white dwarfs and neutron stars (whose peaks march from X-ray toward infrared over billions of years), and reads the 2.725 K temperature of the cosmic background — cosmology's most important number, obtained by fitting the blackbody curve whose peak sits at 1.06 mm.

Why do objects change color as they heat up?

The peak marches across the spectrum toward shorter wavelengths as T rises, dragging the visible tail with it. At ~800 K the peak is deep infrared but the spectrum's short-wave tail just reaches dull red — the first visible glow. By 1,200 K the tail supplies orange; by 1,600 K yellow and white enter; forge-hot steel at 1,800 K+ looks near-white because all visible colors are now well supplied. Blacksmiths and glassblowers have read this scale by eye for millennia; Wien's law is its calibration into numbers.

What temperature peaks in the infrared humans can feel?

Everything near room temperature. A 300 K object peaks at 9.66 μm — deep in the thermal infrared your skin senses as radiant warmth but your eyes cannot see. The whole thermal-camera industry lives in the 8–14 μm atmospheric window precisely because 280–310 K objects (terrain, vehicles, people) peak there. Wien's law also sizes the design: a sensor for furnace monitoring (1,500 K) instead peaks around 1.9 μm and uses different detector materials — same equation, different band, different hardware.

Does Wien's law apply to LEDs and lasers?

No — they are not thermal emitters. An LED's color is set by its semiconductor bandgap, a laser's by its gain medium's transitions; neither spectrum is a blackbody curve, so dividing b by some "temperature" yields nothing meaningful. Lighting's "color temperature" for such sources is a correlated color temperature — the blackbody temperature whose color the light most resembles — a perceptual label, not Wien physics. Apply the law to things heated until they glow: stars, filaments, furnaces, planets, people.

What is the peak wavelength of the Earth?

Earth radiates to space as roughly a 255 K blackbody (its effective emission temperature, colder than the 288 K surface because the atmosphere radiates from altitude): 2.898×10⁻³/255 ≈ 11.4 μm. The surface alone at 288 K peaks at ~10.1 μm. This outgoing infrared is the planet's cooling exhaust — and the greenhouse effect is, in these terms, atmospheric gases absorbing in exactly this band and re-radiating, which is why the 8–12 μm "window" matters so much to climate physics.

Is this Wien's law calculator free?

Yes — free, instant, no sign-up. Enter a temperature in kelvin for the peak emission wavelength and its spectral band.