iCosmos › Age of the universe calculator
Age of the universe calculator
The cosmic time since the Big Bang, today and when the light from redshift z was emitted.
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
The age of the universe is the time since the Big Bang, found by integrating the expansion history backwards. It depends mostly on H0 (the age scales as 1/H0) and on the mix of matter and dark energy: dark energy makes the universe older for the same H0.
Some universes you can build here have no Big Bang at all (they “bounce”); the calculator explains when the age is not defined.
Formula
- t(z) = (1 / H0) ∫z∞ dz′ / [(1 + z′) E(z′)]
- 1 / H0 = 977.79 / H0 Gyr (H0 in km s−1 Mpc−1)
Worked example
In the classic model (Ωm = 0.3, ΩΛ = 0.7, H0 = 70 km s−1 Mpc−1), the universe is 13.467 billion years old today and was 5.752 billion years old at z = 1.
With the Planck 2018 parameters (H0 = 67.66, Ωm = 0.3111) the age today is 13.79 Gyr. A matter-only universe with H0 = 70 would be only 9.31 Gyr old, younger than the oldest stars: one of the early clues that dark energy exists.
Common questions
How old is the universe?
About 13.8 billion years for the Planck 2018 cosmology. The exact value depends on the cosmological parameters, which you can change above.
Why does the age depend on the Hubble constant?
H0 sets the current expansion rate: a faster expansion means less time was needed to reach today’s size, so the age is proportional to 1/H0 for a fixed mix of matter and dark energy.
Why does dark energy make the universe older?
For the same expansion rate today, a matter-only universe has always been decelerating, so it was expanding much faster in the past and reached its present size quickly. With dark energy the expansion has sped up recently, so in the past it was expanding more slowly than a matter-only universe would have been, and it took longer to get here.
Related calculators
- Lookback time calculator
- Hubble parameter H(z) calculator
- Redshift to distance calculator
- Linear growth factor 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.