Redshift and Recession Velocity Calculator
Calculate galaxy recession velocity from redshift z, or find z from rest and observed wavelengths.
Includes relativistic formula and Hubble distance.
Redshift (z) measures how much a galaxy’s light has been stretched to longer (redder) wavelengths as the universe expands.
Calculating z from wavelengths:
z = (λ_observed - λ_rest) / λ_rest
For small redshifts (z « 1) — nearby galaxies:
v = z × c
For large redshifts — relativistic formula:
v/c = ((z + 1)² - 1) / ((z + 1)² + 1)
This gives the recession velocity without exceeding c. Note: cosmological recession velocities can exceed c — this does not violate special relativity, because the recession is due to the expansion of space itself, not motion through space.
Hubble distance:
d = v / H₀
Using H₀ = 70 km/s/Mpc (standard value).
Famous redshifts:
- Andromeda Galaxy (M31): z ≈ −0.001 (blueshifted — approaching!)
- Virgo Cluster: z ≈ 0.004
- Quasar 3C 273: z ≈ 0.158
- Most distant galaxies observed: z ≈ 10–14
- Cosmic Microwave Background: z ≈ 1100
Cosmological vs Doppler redshift: At low z, the two are indistinguishable. At high z, the cosmological interpretation (space expansion) is more appropriate. The speed of light c = 299,792.458 km/s.