Cosmological Distance Calculator

Because the universe expands, a single redshift maps to several different “distances.” Enter a redshift and cosmological parameters to get the comoving, luminosity and angular‑diameter distances together with the lookback time. Ωm and ΩΛ are independent inputs, so you can model a flat, open or closed universe.

Geometry flat · Ωk = -0.0001
Comoving distance 3,401 Mpc 11.09 Gly · present distance (line of sight)
Luminosity distance 6,802 Mpc 22.19 Gly · sets how bright it looks
Angular diameter distance 1,700 Mpc 5.546 Gly · sets its apparent size
Lookback time 7.950 Gyr how long the light has travelled
Hubble distance4,448 Mpc Transverse comoving3,401 Mpc Distance modulus μ44.16

E(z) = √( Ωr(1+z)⁴ + Ωm(1+z)³ + Ωk(1+z)² + ΩΛ )
DC = (c / H₀) · ∫0z dz′ / E(z′)  (comoving, line of sight)
DM = curvature transform of DC (sinh / sin when Ωk ≠ 0)
DA = DM / (1 + z)   DL = (1 + z) · DM

Ωk = 1 − Ωm − ΩΛ − Ωr is derived from your inputs, so the universe can be flat, open or closed. Radiation Ωr is included (it matters for the distance to the CMB). Integrals use composite Simpson's rule; distance modulus μ = 5·log₁₀(D_L / 10 pc). Defaults are the Planck 2018 results.

Reference values at Planck 2018 parameters (H₀ = 67.4, Ωm = 0.315, ΩΛ = 0.685)
z Comoving Luminosity Ang. diameter Lookback
0.1 434.1 Mpc 477.5 Mpc 394.6 Mpc 1.350 Gyr
0.25 1,044 Mpc 1,305 Mpc 835.3 Mpc 3.047 Gyr
0.5 1,951 Mpc 2,927 Mpc 1,301 Mpc 5.210 Gyr
1 3,401 Mpc 6,802 Mpc 1,700 Mpc 7.950 Gyr
1.5 4,482 Mpc 11,204 Mpc 1,793 Mpc 9.531 Gyr
2 5,311 Mpc 15,934 Mpc 1,770 Mpc 10.52 Gyr
3 6,505 Mpc 26,018 Mpc 1,626 Mpc 11.65 Gyr
5 7,944 Mpc 47,660 Mpc 1,324 Mpc 12.62 Gyr
7 8,807 Mpc 70,451 Mpc 1,101 Mpc 13.03 Gyr
10 9,630 Mpc 105,917 Mpc 875.4 Mpc 13.32 Gyr
20 10,946 Mpc 229,852 Mpc 521.2 Mpc 13.61 Gyr
1100 13,862 Mpc 15,260,323 Mpc 12.6 Mpc 13.82 Gyr

See also: Universe Age at Redshift · Interactive Cosmic Timeline.