iCosmos › Redshift to distance calculator
Redshift to distance calculator
Redshift does not give a single distance: here are all of them, and which one to use.
The interactive calculator loads here: change the redshift and the cosmological parameters (Ωm, ΩΛ, Ωr, w0, wa, H0) and the result and plot update instantly.
What it is
In an expanding universe “distance” has several meanings. Use the comoving distance DC for where an object is today, the angular diameter distance DA to convert angles into sizes, the luminosity distance DL to convert fluxes into luminosities, and the lookback time for how long ago the light left.
Distances are shown in megaparsecs (1 Mpc = 3.26 million light-years) and in billions of light-years. The Gly value is a unit conversion of each distance, not the light-travel time.
Formula
- DC = (c/H0) ∫0z dz′/E(z′)
- DA = DM/(1+z)
- DL = (1+z) DM
Worked example
In the classic model (Ωm = 0.3, ΩΛ = 0.7, H0 = 70 km s−1 Mpc−1), the table below gives the main distances at a few redshifts.
| z | DC (Mpc) | DC (Gly) | DA (Mpc) | DL (Mpc) | Lookback (Gyr) |
|---|---|---|---|---|---|
| 0.1 | 418.454 | 1.365 | 380.413 | 460.3 | 1.30 |
| 0.5 | 1,888.63 | 6.16 | 1,259.08 | 2,832.94 | 5.04 |
| 1 | 3,303.83 | 10.78 | 1,651.91 | 6,607.66 | 7.72 |
| 2 | 5,179.86 | 16.89 | 1,726.62 | 15,539.6 | 10.24 |
| 3 | 6,355.69 | 20.73 | 1,588.92 | 25,422.7 | 11.35 |
| 5 | 7,775.37 | 25.36 | 1,295.9 | 46,652.2 | 12.31 |
| 10 | 9,440.25 | 30.79 | 858.205 | 103,843 | 13.00 |
Common questions
How far away is redshift 1?
In the classic model, 3,304 Mpc (10.8 billion light-years) in comoving distance; the light took 7.7 billion years to reach us. The angular diameter and luminosity distances are 1,652 Mpc and 6,608 Mpc.
Which distance should I quote?
Quote the one that matches your measurement (DA for sizes, DL for brightness) and always state the cosmological parameters used. Every iCosmos export records them.
Related calculators
- Comoving distance calculator
- Angular diameter distance calculator
- Luminosity distance calculator
- Lookback time calculator
- The full iCosmos cosmology calculator
About iCosmos
iCosmos was created by Mihran Vardanyan. Mihran Vardanyan is a cosmologist who earned his DPhil in cosmology at the University of Oxford, supervised by Joseph Silk and Roberto Trotta. He developed iCosmos during his research years at Oxford Astrophysics, where his work applied Bayesian model selection to the curvature and size of the Universe.
How to cite: Vardanyan, Mihran. iCosmos V4: Cosmology Calculator. https://icosmos.co.uk/. Include your access date, model parameters and exported data when reporting calculations.