Redshift Calculator
What a galaxy's redshift means — its recession velocity, the Hubble-law distance, the shift of a spectral line and the scale of the universe when the light left.
Light from a receding galaxy is stretched: redshift z is the fractional increase in wavelength.
How the redshift calculator works
Light from a receding galaxy is stretched: redshift z is the fractional increase in wavelength. At small z the velocity is simply cz and the distance is v over the Hubble constant. At larger z the relativistic formula keeps the velocity below light, and the Hubble law itself stops being adequate — beyond z of about 0.2 the distance needs a cosmological model.
The scale factor, 1 over 1 + z, is the cleanest statement: at z = 1 the universe was half its present size when the light set out.
Formula: λ_obs = λ_rest (1 + z); v = c ((1+z)² − 1) / ((1+z)² + 1); d ≈ cz / H₀
Worked examples
| Inputs | Recession velocity (km/s) | Note |
|---|---|---|
| A galaxy at z = 0.1 | 28,487.1 | about 430 Mpc |
| A quasar at z = 2 | 239,834 | a third of the present size |
| Andromeda, approaching | -299.9 | blueshifted |
FAQFrequently asked questions
What is redshift?
The fractional stretch of light's wavelength between emission and observation. For distant galaxies it comes from the expansion of space itself, not motion through it.
How does redshift give distance?
Through the Hubble law: velocity is proportional to distance, with the Hubble constant as the ratio. It works well to about z = 0.2; beyond that a cosmological model is needed.
Why is there a relativistic formula?
Because cz exceeds the speed of light at z above 1, which is nonsense for a Doppler shift. The relativistic form keeps it below c. For cosmological redshifts neither is quite the right concept — the scale factor is.
What is the scale factor?
One over 1 + z: how big the universe was, relative to now, when the light left. At z = 1 it was half the size; at z = 7 an eighth.
Which Hubble constant should I use?
About 67 from the cosmic microwave background, 73 from nearby supernovae — the unresolved Hubble tension. Seventy is the usual compromize; enter whichever you prefer.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- NASA — the US space agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).