Redshift Calculator — Cosmic Expansion and Galaxy Recession Velocities
Calculate cosmological redshift, recession velocity, and lookback time for distant galaxies. Understand Hubble's law and what redshift tells us about the universe.
When Edwin Hubble noticed that distant galaxies had their light systematically shifted toward the red end of the spectrum, he was seeing direct evidence that the universe is expanding. Redshift is the cosmological equivalent of a Doppler shift — and it's one of astronomy's most powerful measurement tools.
Explore redshift calculations at CalcHub.
What Redshift Measures
Redshift (symbol z) is defined as:
z = (λ_observed - λ_emitted) / λ_emitted
Where λ is wavelength. A spectral line emitted at 656nm (hydrogen alpha) but observed at 700nm has z = (700 - 656)/656 = 0.067.
For nearby galaxies, z translates directly to recession velocity: v ≈ z × c (where c is the speed of light, ~300,000 km/s). For z = 0.067: v ≈ 0.067 × 300,000 = 20,000 km/s — this galaxy is receding at 20,000 km/s.
Hubble's Law
For small redshifts (nearby galaxies), recession velocity relates to distance through the Hubble constant H₀:
v = H₀ × d
Where H₀ ≈ 70 km/s/Mpc (current best estimate). A galaxy 100 Mpc away recedes at ~7000 km/s and has z ≈ 0.023.
Redshift Reference Table
| Object | Redshift z | Recession Velocity | Lookback Time |
|---|---|---|---|
| Andromeda Galaxy | -0.001 (blueshifted) | Approaching at 110 km/s | ~2.5 Myr |
| Virgo Cluster | 0.0036 | ~1080 km/s | ~54 Myr |
| Coma Cluster | 0.023 | ~6900 km/s | ~340 Myr |
| Quasar 3C 273 | 0.158 | ~47,400 km/s | ~2 Gyr |
| Typical distant quasar | 2.0 | Apparent >2c* | ~10.5 Gyr |
| Farthest confirmed galaxy | ~13 | Expansion dominated | ~13.4 Gyr |
| CMB (Big Bang afterglow) | ~1100 | — | 13.8 Gyr |
How to Use the Calculator
- Enter redshift value (z) to get recession velocity and distance
- Or enter distance in Mpc to get expected z and recession velocity
- See lookback time — how far back in the universe's history you're observing
If galaxies are receding faster than light at high redshift, how do we still see them?
At the time the light was emitted, those galaxies were much closer and within our observable horizon. The light started its journey when the universe was much younger and more compact, and has been traveling ever since — even as the galaxy that emitted it has moved beyond where we could currently "reach" information-theoretically. It's a subtle point in cosmology that confuses even physics students.
What causes redshift besides cosmic expansion?
Three types: cosmological redshift from universal expansion (discussed here), Doppler redshift from objects moving away in a static space (like a receding source of any wave), and gravitational redshift from light climbing out of a gravity well (photons lose energy escaping strong gravity). Measuring stellar spectra requires accounting for all three to get accurate velocities.
What is blueshift?
Blueshift is the opposite — wavelengths shortened, objects approaching. Andromeda has a slight blueshift because it's on a collision course with the Milky Way (in about 4.5 billion years). Within the Local Group of galaxies, peculiar velocities dominate over Hubble expansion, which is why some local galaxies show blueshift.
Related Calculators
- Light Year Converter — distances to the objects you're measuring
- Parsec Calculator — the distance unit used in Hubble's law
- Schwarzschild Radius Calculator — gravitational redshift at black holes