Relativistic Doppler Calculator

About this calculator

This calculator applies the relativistic Doppler effect for light: f_obs = f_source·√((1+β)/(1−β)), where β = v/c is the source's speed as a fraction of the speed of light. Unlike the classical Doppler formula for sound, this version accounts for time dilation as well as the light-travel-time change, so it holds even when the source moves directly toward or away from the observer at relativistic speeds — a regime where the ordinary approximation breaks down.

Astronomers use this exact relation to convert the observed redshift or blueshift of spectral lines from stars, quasars, and receding galaxies into recession velocities, while particle physicists apply it to radiation from relativistic beams and accelerator experiments. It also appears in special relativity coursework as the standard example of how motion changes the frequency — and hence the color and energy — of light.