Redshift Calculator
Above z = 0.1, v = cz stops being true.
Work out Redshift. Above z = 0.1, v = cz stops being true. Free, with no account and nothing to install.
656.3 nm is the hydrogen-alpha line, the usual reference.
Recession velocity
29,979.2 km/s
10% of c · 428.3 Mpc away
Redshift is the fractional stretch in wavelength: z = (observed − rest)/rest. A z of 1 means the light arrived at twice the wavelength it left with, which puts it in the infrared if it started as visible. Converting z to a velocity needs care. The simple v = cz is a low-redshift approximation and it produces velocities above the speed of light beyond z = 1, so this switches to the relativistic Doppler form above z = 0.1 and says which one it used. Cosmological redshift is not really a Doppler shift at all — it is space itself expanding while the light is in transit, stretching the wave along with it. The distinction matters at high z, where recession velocities genuinely can exceed c without violating anything, because nothing is moving through space faster than light.
How the Redshift Calculator works
Recession velocity and Hubble distance from a redshift, using the relativistic Doppler form above z = 0.1. The simple v = cz approximation gives velocities above the speed of light beyond z = 1.
Also known as: z to recession velocity · hubble law distance · how far away is a galaxy · can galaxies move faster than light
Frequently asked questions
What is redshift?
The fractional stretch in wavelength: z = (observed − rest) / rest. A z of 1 means light arrived at twice the wavelength it left with.
Why does v = cz break down?
Because it is a low-redshift approximation. At z = 1 it gives exactly the speed of light and beyond that it exceeds it, which is why the relativistic Doppler form is used above z = 0.1.
What is Hubble's law?
Recession velocity is proportional to distance, with the Hubble constant as the proportionality. At around 70 km/s per megaparsec, it is the basis of every cosmological distance estimate.
Can galaxies recede faster than light?
Yes, and it violates nothing. Cosmological redshift is space itself expanding while light is in transit, not motion through space — so the usual speed limit does not apply to it.
Is cosmological redshift the same as Doppler shift?
Not really, though they look alike at low z. Doppler shift comes from motion through space; cosmological redshift comes from space stretching the wave along with it. The distinction matters at high redshift.
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