Blackbody Peak Wavelength Calculator Formula

Understand the math behind the blackbody peak wavelength calculator. Each variable explained with a worked example.

Use the Blackbody Peak Wavelength Calculator

Formulas Used

Peak Wavelength

peak_wavelength = 2.898e-3 / temperature

Peak Wavelength (nm)

peak_nm = 2.898e-3 / temperature * 1e9

Peak Frequency

peak_frequency = 2.998e8 / (2.898e-3 / temperature)

Variables

VariableDescriptionDefault
temperatureTemperature(K)5778

How It Works

Wien's Displacement Law

The wavelength at which a blackbody emits most intensely is inversely proportional to its temperature.

Formula

lambda_max = b / T

  • *b* = 2.898 x 10^-3 m K (Wien displacement constant)
  • *T* = temperature in kelvin

    • Hotter objects peak at shorter (bluer) wavelengths; cooler objects peak at longer (redder) wavelengths.

    Worked Example

    The Sun's surface at 5778 K.

    temperature = 5778
    1. 01lambda_max = b / T
    2. 02lambda_max = 2.898e-3 / 5778
    3. 03lambda_max = 5.015e-7 m = 501.5 nm
    4. 04This falls in the green part of the visible spectrum.

    Frequently Asked Questions

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

    The Sun emits across the entire visible spectrum. Our eyes perceive the broad combination as white or slightly yellow, not green.

    What does a room-temperature object emit?

    At 300 K, the peak is at about 9.66 micrometres, in the mid-infrared. This is why thermal cameras work in the infrared.

    Is this law exact?

    Wien's law gives the peak of the Planck spectrum as a function of wavelength. The peak in frequency differs slightly because the Planck function has different shapes in wavelength vs. frequency space.

    Ready to run the numbers?

    Open Blackbody Peak Wavelength Calculator