Redshift Velocity Calculator
When galaxies recede from us, the light they emit is stretched to longer, redder wavelengths. The dimensionless redshift z quantifies this stretching: z equals the fractional increase in wavelength. For small redshifts (z less than 0.1), the recession velocity is well approximated by v = c times z, where c is the speed of light. Hubble's law then gives the distance as d = v / H0. This calculator implements both the velocity from redshift and the Hubble distance estimate, and shows the lookback time approximation for low-z objects.
Redshift and Hubble's law formulas
v = c * z (non-relativistic, z < 0.1)
d = v / H0 (Hubble distance, Mpc)
Where c = 299,792 km/s, z is the observed redshift, H0 = 67.4 km/s/Mpc (Planck 2018), and 1 Mpc = 3.0857 x 10 to the 19th km. 1 Mpc = 3.2616 million light-years. For z greater than 0.1, a proper cosmological distance calculation is needed.
Notable redshifts
Andromeda (M31): z = -0.001 (blueshifted, approaching). Virgo Cluster: z = 0.0036. Great Wall: z = approximately 0.03. Sloan Great Wall: z = approximately 0.073. Most distant known galaxy (2023): z = approximately 13.2. CMB: z = 1,089.
Redshift velocity: frequently asked questions
What is redshift (z)?
Redshift z is the fractional change in wavelength of light from a distant object: z = (observed wavelength - emitted wavelength) / emitted wavelength. A z of 0 means no shift. A z of 1 means the wavelength has doubled. Positive z indicates recession from the observer.
What is Hubble's law?
Hubble's law states that distant galaxies recede at velocities proportional to their distance: v = H0 * d, where H0 is the Hubble constant. For small z (non-relativistic case), the recession velocity is approximately v = c * z, where c is the speed of light.
What value of the Hubble constant does this calculator use?
This calculator uses H0 = 67.4 km/s/Mpc, the Planck 2018 CMB-based measurement. Note that the Hubble constant is subject to ongoing debate; the local distance ladder yields approximately 73 km/s/Mpc. This is the so-called Hubble tension.
At what redshift does the simple v = cz formula break down?
The non-relativistic approximation v = cz is accurate to within a few percent for z less than about 0.1. For larger z, a relativistic formula should be used. For cosmological distances, the proper comoving distance calculation requires integration of the Friedmann equations.
What is the redshift of the cosmic microwave background?
The CMB was emitted when the universe was about 380,000 years old. Its redshift is approximately z = 1,089, corresponding to a time when the universe was about 1,100 times smaller than today.
Official sources
- Planck Collaboration 2018 (H0 = 67.4 km/s/Mpc): esa.int/Planck.
- NASA Hubble constant overview: hubblesite.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.