Redshift and Hubble's Law Distance Calculator
Distance of a galaxy from its redshift using Hubble's law, with the recession speed, the shifted wavelength of a spectral line and the Hubble time.
Results
The dashed line marks the value you entered.
What this tool does
Light from receding galaxies is stretched, so a spectral line arrives at (1 + z) times its laboratory wavelength, and Hubble's law turns the speed c·z into a distance d = c z ÷ H₀. The relation is a straight line only for small redshifts, up to roughly z = 0.1; beyond that the expansion history of the universe matters and the simple distance is no longer the true one. The value of H₀ itself is still debated — measurements cluster around 67 and 73 km/s/Mpc — so the chart shows how much the distance depends on it.
Formula
d = c z ÷ H₀ · 1 + z = λ_observed ÷ λ_rest · β = [(1+z)² − 1] ÷ [(1+z)² + 1]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
z | Redshift z | — |
h0 | Hubble constant | km/s/Mpc |
wl | Wavelength of the line in the lab (656.28 nm is hydrogen-alpha) | nm |
D | Distance by Hubble's law | Mpc |
DL | Distance in millions of light years | Mly |
V | Recession speed, c × z | km/s |
VR | Speed by the relativistic Doppler formula | km/s |
WO | Wavelength you would measure | nm |
HT | Hubble time, 1 ÷ H₀ | Gyr |
Worked example
- Redshift z0.01
- Hubble constant70 km/s/Mpc
- Wavelength of the line in the lab (656.28 nm is hydrogen-alpha)656.28 nm
- Distance by Hubble's law42.83 Mpc
- Distance in millions of light years139.7 Mly
- Recession speed, c × z2998 km/s
- Speed by the relativistic Doppler formula2983 km/s
- Wavelength you would measure662.84 nm
- Hubble time, 1 ÷ H₀13.97 Gyr
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.