Redshift Calculator

This calculator applies the definition of cosmological redshift, z = (lambda_obs - lambda_rest) / lambda_rest, comparing the wavelength you actually observe against the same spectral line's rest-frame wavelength -- H-alpha, 656.3 nm, is the default because it is one of the most commonly measured lines in galaxy spectra. Because that formula only involves the two wavelengths, Redshift (z) and the derived Velocity from Redshift respond only to Observed Wavelength and Rest Wavelength -- Recessional Velocity has no effect on either, even though it sits on the same page. Recessional Velocity instead drives a separate branch of outputs entirely: Distance (in megaparsecs and gigalight-years) and Lookback Time come from Hubble's Law, distance = velocity / H0, using a fixed Hubble constant of 70 km/s/Mpc, and Relativistic Redshift comes from the special-relativistic Doppler formula sqrt((1+v/c)/(1-v/c)) - 1.

Neither wavelength input touches those three outputs. This split matters practically: at the velocities typical of nearby galaxies the simple velocity-from-redshift approximation (z times the speed of light) tracks the fully relativistic result closely, but the two diverge as Recessional Velocity climbs toward the speed of light, which is why both are shown separately rather than collapsed into one number. The calculator does not correct for cosmological effects beyond a flat Hubble's Law -- no dark energy, no time-varying expansion rate -- so treat Distance and Lookback Time beyond a few hundred megaparsecs as a first estimate, not a precision cosmological distance from a full Friedmann-model calculation.