Universe Age at Redshift Calculator

Enter a redshift and see how old the universe was when that light set out, how long it has travelled to reach us (the lookback time), and how much smaller the universe was back then (the scale factor). The calculation uses the standard flat ΛCDM model; open Cosmological parameters to change H₀ and Ωm or pick a published model.

How much the universe has expanded since the light was emitted.
Scale factor a 0.5000 the universe was this fraction of its present size
Age of the universe then 5.841 Gyr time elapsed since the Big Bang at redshift z
Lookback time 7.950 Gyr how long the light has been travelling to us
Age today13.79 Gyr Fraction of current age42.4% ΩΛ0.6849

At z = 1, the universe was 5.841 Gyr old. The light we receive now left when the cosmos was that age — 7.950 Gyr ago.

Cosmological parameters

A spatially flat universe is assumed, so ΩΛ = 1 − Ωm − Ωr, and the radiation density Ωr (photons and neutrinos) is derived from H₀.

a = 1 / (1 + z)
t(z) = (1 / H₀) · ∫0a da′ / ( a′ · E(a′) )
E(a) = √( Ωr·a⁻⁴ + Ωm·a⁻³ + ΩΛ )  (flat: Ωk = 0)
lookback = t₀ − t(z)

The age integral is evaluated numerically (composite Simpson's rule). Values are approximate and depend on the chosen parameters; the defaults are the Planck 2018 results.

Reference values at Planck 2018 parameters (H₀ = 67.4, Ωm = 0.315)
Redshift z Scale factor a Age then Lookback time
0 (today) 1.0000 13.79 Gyr 0 yr
0.25 0.8000 10.74 Gyr 3.047 Gyr
0.5 0.6667 8.581 Gyr 5.210 Gyr
1 0.5000 5.841 Gyr 7.950 Gyr
2 0.3333 3.269 Gyr 10.52 Gyr
3 0.2500 2.138 Gyr 11.65 Gyr
5 0.1667 1.168 Gyr 12.62 Gyr
7 0.1250 758.5 Myr 13.03 Gyr
10 0.0909 470.1 Myr 13.32 Gyr
15 0.0625 267.5 Myr 13.52 Gyr
20 0.0476 177.6 Myr 13.61 Gyr
50 0.0196 46.4 Myr 13.74 Gyr
1100 9.08 × 10−4 365,530 yr 13.79 Gyr

See also: the Interactive Cosmic Timeline for a visual journey through these epochs.