Redshift & Hubble Distance Calculator

The stretching of light to longer wavelengths, z = (λ_observed − λ_emitted)/λ_emitted, as a source moves away from us.

For small z, v ≈ c·z; at large z a relativistic formula is needed because v cannot exceed the speed of light.

v = H₀·d, so dividing recession velocity by the Hubble constant gives an approximate distance to the galaxy.

It depends on the assumed Hubble constant and ignores cosmological model details, so it is an order-of-magnitude estimate.

This tool returns the simple Hubble-law distance d = v/H₀, which is only meaningful at low redshift. Cosmologists use several distinct distances at high z: the comoving distance (the present-day separation, factoring out expansion), the luminosity distance (how faint a standard candle appears, larger by a factor of 1+z), and the angular-diameter distance (how large an object looks, smaller by a factor of 1+z). They all converge to d = cz/H₀ as z approaches zero but diverge sharply once z is a significant fraction of 1.

It is the persistent disagreement between two ways of measuring H₀. The cosmic distance ladder (Cepheids and Type Ia supernovae) gives roughly 73-74 km/s/Mpc, while the early-universe value inferred from the cosmic microwave background gives about 67 km/s/Mpc. The gap is several standard deviations and has not gone away with better data, which is why some physicists suspect it points to new physics rather than measurement error. Because your distance scales as 1/H₀, this ~9% spread directly sets the uncertainty on any redshift-derived distance.