How this calculator works
Planck spectra have a peak whose location depends on the spectral coordinate. For energy per wavelength interval, peak wavelength times temperature is constant. For energy per frequency interval, peak frequency divided by temperature is a different constant. Converting one peak using c/lambda does not give the other maximum because the interval widths change. This page uses the energy spectrum, not photon-count spectrum. A wavelength-independent grey emissivity changes amplitude without moving the peak. Constants are derived from CODATA 2018 h, c and kB.
Formula
lambda_max T = b_lambda = hc/(4.965114231744276 kB); nu_max/T = b_nu = 2.821439372122079 kB/h. These maxima describe different spectral densities.
Worked example
At 300 K, the energy-per-wavelength peak is about 9659.239851 nm. The energy-per-frequency peak is about 1.763677727e13 Hz. Doubling temperature halves the first peak and doubles the second.
Advertisement
Frequently asked questions
Why is nu_max not c/lambda_max?
Changing coordinates changes the width of a spectral bin and therefore the location of the density maximum.
Can this give a star temperature?
It gives an approximate colour temperature for a near-blackbody spectrum. Absorption lines, dust and instrumental response affect observations.
Does emissivity move the peak?
Constant grey emissivity does not. Emissivity that varies with wavelength can shift the maximum.