Redshift Velocity Calculator

About this calculator

This calculator converts a galaxy's cosmological redshift (z) into its recession velocity, offering both the classical (non-relativistic) approximation v = cz — valid for small z — and the full relativistic Doppler formula, which is needed for high-redshift objects where v approaches or would otherwise exceed the speed of light under the simple formula. Redshift is measured as z = (λ_observed − λ_emitted) / λ_emitted, the fractional stretch in a spectral line's wavelength caused by the expansion of space.

Astronomers use redshift as their primary tool for measuring how fast distant galaxies are receding from us due to the expansion of the universe (per Hubble's law), and combined with distance measurements, it underpins our understanding of cosmic expansion and the age of the universe. Enter a redshift value to get the corresponding recession velocity.