🔴 Redshift Calculator
Enter a redshift or recession velocity to get the other, the stretched wavelength and a rough Hubble distance — relativistic or classical.
Redshift z
0.1
Recession velocity
28,487 km/s
0.095c
Observed wavelength
721.9 nm
Hubble distance
407 Mpc
Cosmological redshift z stretches light to longer (redder) wavelengths as the universe expands: λ_observed = λ_rest × (1 + z). At small z the recession velocity is v ≈ cz; near light speed the relativistic relation 1 + z = √((1+β)/(1−β)) applies — tick the box for z ≳ 0.1. The Hubble distance v ÷ H₀ is a rough estimate (H₀ ≈ 70 km/s/Mpc); precise cosmological distances need a full model. 🔒 In your browser.
How the redshift calculator works
As the universe expands, light from distant galaxies is stretched to longer wavelengths — cosmological redshift, z. The tool converts between z and recession velocity (v ≈ cz at small z, or the exact relativistic relation 1 + z = √((1+β)/(1−β)) for large z), gives the observed wavelength of a spectral line (λ_observed = λ_rest × (1+z)), and estimates the distance from Hubble's law, v ÷ H₀.
Use the relativistic option once z is more than about 0.1, where v ≈ cz noticeably overestimates the velocity. The Hubble-law distance is a first approximation with an adjustable H₀ (≈ 70 km/s/Mpc); true cosmological distances (comoving, luminosity) require integrating a full cosmological model. This is educational; professional work uses those models.
Frequently asked questions
What is redshift?
The stretching of light to longer, redder wavelengths. Cosmological redshift z comes from the expansion of the universe: λ_observed = λ_rest × (1 + z). The larger the z, the more distant and faster-receding the object.
How do I convert redshift to velocity?
For small z, v ≈ c × z. For large z you need the relativistic Doppler relation, 1 + z = √((1+β)/(1−β)) where β = v/c, because v ≈ cz would exceed the speed of light. The tool applies whichever you choose.
What is Hubble's law?
That a galaxy's recession velocity is proportional to its distance: v = H₀ × d, with H₀ ≈ 70 km/s/Mpc. Rearranged, d ≈ v ÷ H₀ gives a rough distance from the velocity — a first estimate, not a precise cosmological distance.
When do I need the relativistic formula?
Once z is more than roughly 0.1, the simple v = cz overestimates the velocity, and beyond z = 1 it would give faster than light. The relativistic relation keeps the velocity below c for any redshift.
What is the difference between redshift and the Doppler effect?
The everyday Doppler effect comes from motion through space (like a passing siren). Cosmological redshift comes from space itself expanding between us and a distant galaxy — the light is stretched in transit, not just shifted by relative motion.