Black Body Peak Calculator Formula

Understand the math behind the black body peak calculator. Each variable explained with a worked example.

Use the Black Body Peak Calculator

Formulas Used

Peak Wavelength

peak_wavelength = 2.8978e-3 / temperature

Peak Wavelength (nm)

peak_wavelength_nm = 2.8978e-3 / temperature * 1e9

Variables

VariableDescriptionDefault
temperatureTemperature(K)5778

How It Works

Wien's Displacement Law

Wien's law states that the peak emission wavelength of a black body is inversely proportional to its temperature.

Formula

lambda_max = b / T

where b = 2.8978 x 10^-3 m·K is Wien's displacement constant. Hotter objects peak at shorter wavelengths (bluer light).

Worked Example

The Sun's surface temperature (~5778 K).

temperature = 5778
  1. 01lambda_max = b / T
  2. 02lambda_max = 2.8978e-3 / 5778
  3. 03lambda_max = 5.015e-7 m
  4. 04lambda_max = 501.5 nm (green-yellow visible light)

Ready to run the numbers?

Open Black Body Peak Calculator