Redshift to Velocity Calculator

About this calculator

When light from a distant galaxy is stretched to longer, redder wavelengths, astronomers measure that shift as redshift z. At low z, the recession velocity is simply v = c·z, where c is the speed of light — a good approximation for nearby galaxies. But as z approaches or exceeds 1, this simple relation breaks down and can even suggest speeds faster than light, so astronomers switch to the relativistic Doppler formula, v = c·[(1+z)² − 1] / [(1+z)² + 1], which stays correctly bounded below c.

This conversion underlies Hubble's law and the expansion of the universe: since Edwin Hubble's 1929 observations, redshift-to-velocity calculations have let cosmologists estimate how fast galaxies are receding and, combined with distance measurements, how fast the universe is expanding.