Wien's Law Calculator
Blackbody peak nm and band from Kelvin.
What it does
Hotter bodies glow bluer because their emission peaks shift shorter with temperature. The sun at 5,778 K peaks near 501.6 nm in green-yellow while a 3,000 K bulb peaks at 966 nm in the infrared and human skin at 310 K peaks near 9,348 nm. One division rules starlight to night vision.
The tool above runs Wien displacement with band and frequency attached. Enter Kelvin and it prints peak nanometers, the UV/visible/IR band with color, and terahertz frequency. Defaults show the sun; practice spans bulbs and bodies.
Metrology fixes the constant exactly. NIST CODATA lists 2.897771955e-3 m K as exact, HyperPhysics derives the peak from Planck's law with worked stellar examples, and the peak-derivation page shows the transcendental solution behind the law. Colors subdivide visible by measured bands.
Peaks describe ideal blackbodies first. Real stars, filaments, and skin ride emissivity curves that reshape heights while peaks hold near the law. Filters, atmospheres, and detectors then select what observers actually record.
How to use
- Enter the temperature in Kelvin.
- Read peak nm first.
- Read the UV/visible/IR band.
- Read the frequency.
- Compare bodies by peak shift.
- Add emissivity analysis separately.
Formula
- T
- Absolute temperature in Kelvin, 100 to 100,000.
NIST CODATA exact constant with HyperPhysics peak-derivation backing; colors subdivide visible by wavelength.
Worked example
Example: sun surface
Defaults: 5,778 K.
- Input: 5,778 K sun surface.
- Meters: 2.898e-3 / 5778 = 5.0156e-7 m.
- Nanometers: x1e9 = 501.6 nm.
- Band: 380-750 is visible (green-yellow).
- Frequency 598 THz. Tool shows 501.6 nm, visible green-yellow.
Reference table
| Temp | Peak | Band |
|---|---|---|
| 310 K (body) | 9348.4 nm | IR |
| 3000 K (bulb) | 966 nm | IR |
| 5778 K (sun) | 501.6 nm | Visible green |
| 6500 K (blue star) | 445.8 nm | Visible blue |
Limits
- Ideal blackbodies only. Emissivity shifts heights.
- Single temperature assumed; gradients differ.
- Bands simplified; edges blend.
- Relativistic sources excluded.
Common mistakes
- Entering Celsius as Kelvin.
- Reading frequency for wavelength.
- Expecting blue suns from yellow peaks.
- Ignoring emissivity on real bodies.
- Mixing nm with microns (1000x).
Try it yourself
Quick checks. Answers sit tucked under each question.
3,000 K bulb?
2.898e-3 / 3000 = 9.66e-7 m = 966 nm IR. f = 310 THz.
310 K human body?
2.898e-3 / 310 = 9.3484e-6 m = 9348.4 nm IR. f = 32 THz.
Questions
How is peak wavelength figured?
2.898e-3 over Kelvin, times 1e9 for nm. Here 501.6 nm.
How is the band figured?
Under 380 nm UV, 380-750 visible, over 750 IR. Here visible green-yellow.
How is frequency figured?
Light speed over wavelength: 598 THz here.
Do hotter bodies peak bluer?
Hotter peaks shorter: 6,500 K peaks 445.8 nm blue; 3,000 K peaks 966 nm IR.
Is the constant exact?
Yes, exactly 2.897771955e-3 m K per NIST 2022 CODATA; 2.898e-3 here.
Does everything follow it?
Yes. Stars, bulbs, and bodies all follow; emissivity shifts heights, not peaks.
Sources
- NIST CODATA: Wien Displacement Constant (exact)
- HyperPhysics: Wien's Displacement Law
- HyperPhysics: Blackbody Peak Derivation