Age of Universe Calculator

Calculator inputs

Choose a preset or enter custom cosmological density parameters. Results appear above this form after submission.

Model preset

Hubble constant H₀ (km/s/Mpc)

Matter density Ωm

Dark energy density ΩΛ

Radiation density Ωr

Curvature density Ωk

Graph maximum redshift

Integration steps

Auto-calculate Ωk = 1 − Ωm − ΩΛ − Ωr

Formula used

The calculator evaluates the Friedmann age integral for a universe with matter, radiation, curvature, and dark energy.

H(a) = H₀ E(a)

E(a) = √(Ωr/a⁴ + Ωm/a³ + Ωk/a² + ΩΛ)

t₀ = (1/H₀) ∫ da / (aE(a)), integrated from a very small scale factor to 1.

Simpson’s rule performs the numerical integration, which makes the page flexible for custom cosmological models rather than only one closed-form approximation.

How to use this calculator

Pick a preset for a quick benchmark or choose the custom model.
Enter H₀ and the density parameters for matter, dark energy, radiation, and curvature.
Keep auto-curvature checked if you want the total density to sum to one.
Choose graph range and integration steps for the detail level you want.
Click Calculate Age and review the result cards, summary table, and chart above the form.
Use the export buttons to save the current summary as CSV or PDF.

Example data table

Model	H₀	Ωm	ΩΛ	Ωr	Ωk	Typical age
Planck 2018	67.4	0.3150	0.6849	0.0001	0.0000	≈ 13.8 Gyr
WMAP9	69.3	0.2860	0.7139	0.0001	0.0000	≈ 13.7 Gyr
Einstein-de Sitter	70.0	1.0000	0.0000	0.0000	0.0000	≈ 9.3 Gyr
Milne / Empty	70.0	0.0000	0.0000	0.0000	1.0000	≈ 14.0 Gyr

FAQs

1) What does this calculator estimate?

It estimates the universe age implied by your chosen Hubble constant and density parameters. It uses a numerical cosmology integral, so the answer changes with the model you enter.

2) Why does a larger H₀ usually reduce the age?

A larger Hubble constant means faster present expansion. When everything else stays similar, the expansion timescale becomes shorter, so the inferred age usually becomes smaller.

3) What do Ωm, ΩΛ, Ωr, and Ωk mean?

They are present-day density fractions for matter, dark energy, radiation, and curvature. Together they shape the expansion history and therefore the computed age of the universe.

4) Should the density values add to one?

In the standard normalized form, yes. If you enable auto-curvature, the page forces Ωk so the total becomes one. Manual curvature lets you test alternate combinations directly.

5) Why is radiation usually tiny today?

Radiation energy density drops faster than matter as the universe expands. That makes its present-day fraction small, although it mattered much more in the early universe.

6) Why does dark energy often increase the estimated age?

Dark energy can produce late-time accelerated expansion. For similar present H₀ values, that history can allow an older universe than a matter-only model.

7) What does the chart show?

The chart plots age remaining after each redshift and the corresponding lookback time. It helps you see how cosmic time changes across your selected expansion history.

8) Is this suitable for classroom and research checks?

Yes, for quick exploration and comparison. It is excellent for teaching, sanity checks, and model intuition, though precision research should still confirm assumptions and observational inputs.