Redshift Velocity Calculator
Convert a galaxy's cosmological redshift (z) into a recession velocity using Hubble's law. Useful for cosmology students and researchers estimating how fast distant objects are moving away.
About this calculator
Hubble's law states that in an expanding universe, the recession velocity of a galaxy is proportional to its distance: v = H₀ × d. For small redshifts (z ≪ 1), the redshift is directly proportional to velocity: z ≈ v / c, so the recession velocity is v = z × H₀ × d. However, this calculator uses the simpler linear Hubble approximation v = z × H₀, where H₀ is the Hubble constant in km/s/Mpc and the result is the recession velocity in km/s per megaparsec of distance. The Hubble constant is currently measured at approximately 67–73 km/s/Mpc (the exact value is debated in the 'Hubble tension'). This approximation is valid for z ≲ 0.1; at higher redshifts, special and general relativistic corrections are required. The formula captures the core insight that redshift arises from the stretching of space itself, not from a classical Doppler effect.
How to use
Suppose a galaxy has a measured redshift of z = 0.05 and you use H₀ = 70 km/s/Mpc. Step 1 – Enter z = 0.05 and H₀ = 70. Step 2 – Apply the formula: v = 0.05 × 70 = 3.5 km/s per Mpc. Step 3 – Interpret: the galaxy is receding at 3,500 km/s for every megaparsec of separation. Since z = 0.05 corresponds to a comoving distance of roughly 210 Mpc, the total recession velocity is approximately 3.5 × 210 ≈ 735 km/s — a comfortable margin where the linear approximation is valid.
Frequently asked questions
What is cosmological redshift and how is it different from Doppler redshift?
Cosmological redshift occurs because space itself expands while light travels through it, stretching the wavelength of photons. Doppler redshift arises from the relative motion of source and observer through static space. For nearby galaxies the two effects look identical, but at high redshifts (z > 0.1) they diverge significantly. Hubble's law recession velocities can even exceed the speed of light because they reflect the expansion rate of space, not motion through space — something that does not violate special relativity.
What value should I use for the Hubble constant in the redshift velocity calculator?
The Hubble constant H₀ is observationally measured but its precise value is actively debated. The Planck satellite's CMB measurements give H₀ ≈ 67.4 km/s/Mpc, while local distance ladder measurements (Cepheids, Type Ia supernovae) consistently yield H₀ ≈ 73 km/s/Mpc. For general coursework, 70 km/s/Mpc is a common round-number compromise. The calculator lets you enter any value so you can explore how the Hubble tension affects recession velocity estimates.
When does the linear redshift velocity approximation break down?
The simple formula v = z × H₀ is a good approximation only for small redshifts, typically z ≲ 0.1, where the universe's expansion has not changed significantly over the light travel time. At higher redshifts the expansion rate itself varies with cosmic time, and relativistic effects become important. Accurate distances and velocities for z > 0.1 require integrating the Friedmann equations with cosmological parameters (matter density, dark energy density, curvature). For quasars at z = 2 or the cosmic microwave background at z ≈ 1100, the linear formula is wildly inaccurate.