Hubble's Law Calculator

This calculator turns a galaxy's measured redshift into a recession velocity and distance using Hubble's Law. Two velocity figures are computed side by side: the classical version, v = cz, which is simple and accurate only for small redshifts, and a relativistic version using the relativistic Doppler formula, v = c×((1+z)² − 1)/((1+z)² + 1), which stays valid as redshift grows large and velocities approach the speed of light (where the classical formula would nonsensically exceed c). Distance in megaparsecs comes from dividing the classical recession velocity by your entered Hubble constant, then the calculator converts that into million and billion light-years for more familiar units. Lookback time — how far into the past you're actually observing, since light from distant objects took time to arrive — is approximated from redshift and the Hubble constant converted into inverse seconds, then expressed in billions of years (Gyr).

The Hubble time (1/H₀) represents a rough age-of-the-universe estimate under the simplifying assumption of constant expansion since the Big Bang. Scale factor (1/(1+z)) describes how much smaller the universe was when the light was emitted, and wavelength stretch (1+z) is literally what redshift measures — light stretched to longer wavelengths by cosmic expansion during its journey. Because the Hubble constant itself is contested (the Planck collaboration's 2018 cosmic-microwave-background analysis gives H₀ = 67.4 ± 0.5 km/s/Mpc, while the SH0ES team's 2022 local Cepheid-supernova distance ladder gives H₀ = 73.04 ± 1.04 km/s/Mpc), your chosen value meaningfully shifts every distance and time result here — this reflects a live area of unresolved astrophysics known as the "Hubble tension," not settled science.