Wien's Displacement Law Calculator

What is Wien's Displacement Law: Why Hot Things Change Color?

Every object above absolute zero emits thermal radiation. Wien's displacement law tells you the peak wavelength of that emission. Hotter objects peak at shorter wavelengths: a red-hot iron bar (~1000 K) peaks in the infrared, our Sun (~5778 K) peaks in visible yellow-green, and a blue-white star (~25000 K) peaks in the ultraviolet. This single equation connects temperature to color across the entire electromagnetic spectrum.

Mathematical Foundation

Wien's Displacement Law

\lambda_{\text{max}} = \frac{b}{T}

\lambda_{\text{max}}

= Peak emission wavelength — the wavelength at which the blackbody emits the most radiation (meters or nanometers).

b

= Wien's displacement constant = 2.8977729 * 10^-3 m*K.

T

= Absolute temperature of the blackbody (Kelvin).

Laws & Principles

The constant b = 2.8977729 * 10^-3 m*K is derived from Planck's radiation law by finding the wavelength that maximizes the spectral radiance function. It is one of the most precisely known physical constants.
The peak wavelength is inversely proportional to temperature. Doubling the temperature halves the peak wavelength. This means the Sun (5778 K) peaks at 502 nm (green), while a light bulb filament (3000 K) peaks at 966 nm (infrared — which is why incandescent bulbs are inefficient as light sources).
Wien's law applies only to ideal blackbodies. Real objects have emissivity less than 1 and may not follow the blackbody spectrum exactly. However, stars, molten metals, and heated ceramics approximate blackbodies closely enough for Wien's law to give accurate peak wavelength estimates.

Step-by-Step Example Walkthrough

" Determine the peak emission wavelength of the Sun (surface temperature 5778 K). "

1. Apply Wien's law: lambda_max = b / T = 2.8977729 * 10^-3 / 5778.
2. Calculate: lambda_max = 5.016 * 10^-7 m = 501.6 nm.
3. Check the spectrum: 501.6 nm falls in the green portion of visible light (495-570 nm).

Final Result: The Sun's peak emission is at 502 nm (green). Despite this, the Sun appears white because it emits strongly across the entire visible spectrum. Our eyes perceive the combined output as white.

Object	Temperature (K)	Peak Wavelength	Spectral Band
Human Body	310 K	9,350 nm	Mid-infrared
Incandescent Bulb	3,000 K	966 nm	Near-infrared
The Sun	5,778 K	502 nm	Visible (green)
Sirius (A-type Star)	9,940 K	292 nm	Ultraviolet
O-type Star	40,000 K	72 nm	Extreme UV

Object

Temperature (K)

Peak Wavelength

Spectral Band

Human Body

310 K

9,350 nm

Mid-infrared

Incandescent Bulb

3,000 K

966 nm

Near-infrared

The Sun

5,778 K

502 nm

Visible (green)

Sirius (A-type Star)

9,940 K

292 nm

Ultraviolet

O-type Star

40,000 K

72 nm

Extreme UV

Applications

Stellar Classification

Astronomers measure a star's color (peak wavelength) to determine its surface temperature without visiting it. Red stars are cool (~3000 K), yellow stars are medium (~6000 K), and blue stars are extremely hot (~30000+ K). This is the basis of the Hertzsprung-Russell diagram.

Thermal Imaging

Thermal cameras detect infrared radiation from objects at everyday temperatures (250-350 K). At 310 K (body temperature), peak emission is at 9.35 micrometers. FLIR cameras use detectors optimized for the 8-14 micrometer atmospheric window to image this radiation.

Pro Tips

Do This

✓Always use Kelvin for temperature. Wien's law requires absolute temperature. To convert: K = C + 273.15. Room temperature (20C) is 293.15 K. Using Celsius or Fahrenheit will give completely wrong peak wavelengths.
✓Cross-reference with the electromagnetic spectrum. After calculating the peak wavelength, check which band it falls in: radio (> 1mm), infrared (700nm-1mm), visible (380-700nm), ultraviolet (10-380nm), X-ray (< 10nm).

Avoid This

✗Do not confuse peak wavelength with perceived color. The Sun peaks at green (502 nm) but appears white because it emits strongly across the entire visible spectrum. Peak wavelength tells you where the most energy is, not what color you will see.
✗Do not apply Wien's law to non-thermal emitters. Lasers, LEDs, and fluorescent lights do not follow the blackbody spectrum. Their emission wavelengths are determined by quantum transitions, not temperature.

Frequently Asked Questions

Why does the Sun appear white if it peaks in green?

The Sun emits across the entire visible spectrum — not just at the peak. While green gets slightly more energy, the difference between red, green, and blue output is small. Our eyes integrate all these wavelengths together and perceive the result as white. If the Sun only emitted at its peak wavelength, it would indeed appear green.

Why are incandescent bulbs inefficient?

A typical incandescent filament operates at about 3000 K, which gives a peak wavelength of 966 nm — in the near-infrared, invisible to human eyes. Only about 5% of the total radiated energy falls in the visible spectrum. The other 95% is wasted as invisible infrared heat. This is why LEDs (which emit only visible light) are far more efficient.

How do astronomers use Wien's law?

By measuring the peak wavelength of a star's spectrum, astronomers calculate its surface temperature using Wien's law in reverse: T = b / lambda_max. This is how stellar spectral classes (O, B, A, F, G, K, M — from hottest to coolest) are determined. Our Sun is a G-type star at 5778 K.

What is the cosmic microwave background radiation?

The CMB is thermal radiation left over from the Big Bang, now cooled to 2.725 K. Applying Wien's law: lambda_max = 2898 / 2.725 = 1063 micrometers = 1.06 mm (microwave band). This is why it is called "microwave" background radiation. It is the most perfect blackbody spectrum ever measured, matching the Planck curve to better than 1 part in 100,000.

Wien's Displacement Law Calculator — Peak Emission Wavelength

Blackbody Temperature

Electromagnetic Band

Peak Wavelength (λ max)

Peak Wavelength (m)