Black Body Peak Calculator Formula
Understand the math behind the black body peak calculator. Each variable explained with a worked example.
Formulas Used
Peak Wavelength
peak_wavelength = 2.8978e-3 / temperaturePeak Wavelength (nm)
peak_wavelength_nm = 2.8978e-3 / temperature * 1e9Variables
| Variable | Description | Default |
|---|---|---|
temperature | Temperature(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).
- 01lambda_max = b / T
- 02lambda_max = 2.8978e-3 / 5778
- 03lambda_max = 5.015e-7 m
- 04lambda_max = 501.5 nm (green-yellow visible light)
Frequently Asked Questions
Why does the Sun appear yellow-white if it peaks in green?
The Sun emits broadly across the visible spectrum. Our eyes and atmosphere combine to make it appear yellow-white rather than green.
What color are the hottest stars?
Blue. Very hot stars (>30,000 K) peak in the ultraviolet and appear blue-white. Cool stars (~3000 K) peak in infrared and appear red.
How is Wien's law used in astronomy?
By measuring the peak wavelength of a star's spectrum, astronomers can determine its surface temperature without visiting it.
Ready to run the numbers?
Open Black Body Peak Calculator