Compute the Universe's age using H0 and density terms in seconds instantly. Choose presets or custom values, then compare Hubble time, fractions, units easily.
| Scenario | H0 | Ωm | ΩΛ | Ωr | Ωk | Age (approx.) |
|---|---|---|---|---|---|---|
| Planck-like ΛCDM | 67.4 | 0.315 | 0.685 | 0.00009 | ~0 | ~13.8 Gyr |
| WMAP-like ΛCDM | 69.3 | 0.286 | 0.714 | 0.00009 | ~0 | ~13.7 Gyr |
| Einstein–de Sitter | 70.0 | 1.0 | 0 | 0 | 0 | ~9.3 Gyr |
| Milne (empty) | 70.0 | 0 | 0 | 0 | 1.0 | ~14.0 Gyr |
Example ages are approximate and depend on numerical settings.
The cosmic age today is computed from the expansion history:
The calculator integrates in x = ln(a), which turns the integral into ∫ dx / E(ex) for better numerical stability at early times.
This calculator estimates cosmic age from H0 and the density parameters that control the Friedmann expansion. Results are shown in gigayears, years, and seconds, alongside helpful context metrics. Start with a preset to match a commonly cited cosmology, then adjust one parameter at a time to understand sensitivity and model assumptions.
The age t0 is the elapsed time from the early hot, dense phase to today (a=1). It is determined by the entire expansion history, so two models with the same current rate can still have different ages.
H0 scales the time unit: larger H0 generally shortens the age when densities are fixed. The tool also reports the Hubble time (1/H0) and the ratio Age/Hubble time to show how the density mix modifies simple scaling.
Ωm drives deceleration through gravity, especially at intermediate epochs. Increasing Ωm (with the same H0) usually decreases t0 because the Universe spends more time expanding slowly.
ΩΛ becomes dominant at late times and reduces deceleration, often increasing the computed age for a given H0. This is why ΛCDM-like models can be older than matter-only models even with similar present-day expansion rates.
Ωr scales as a−4, so it is most relevant at very small scale factor. Typical values are tiny (around 10−4), yet they help keep the early-time integral physically consistent when you choose very small amin.
Ωk contributes as a−2 and can change the age noticeably in open or closed models. With “Auto-compute Ωk” enabled, Ωk is set so Ωm+ΩΛ+Ωr+Ωk=1; disable it to explore curved scenarios and watch Ω total and Δ in the results.
For general mixtures of components, t0 requires evaluating an integral rather than a single closed-form formula. This tool uses Simpson’s rule in ln(a), which samples the early Universe efficiently across many orders of magnitude in a.
For ΛCDM-like inputs (H0≈67–70, Ωm≈0.3, ΩΛ≈0.7), ages commonly fall near 13–14 Gyr, matching the example table. Use the precision selector to verify stability, then export CSV or PDF to document inputs and reproduce the result later.
H0 scales the time unit. With the same density mix, a faster present expansion implies a shorter characteristic timescale, so the integral produces fewer gigayears once divided by H0.
Enable it to enforce Ω total = 1, which matches many standard models. Disable it only if you want to explore curved Universes and you understand how Ωk changes the expansion history.
For late-time age estimates, Ωr is small. Many users set Ωr around 0.00009 as a practical default. Changing Ωr mainly affects the earliest part of the integral.
It normalizes the age to the natural timescale 1/H0. This highlights how matter, dark energy, radiation, and curvature modify the expansion beyond simple scaling.
It adjusts the integration step count and the minimum scale factor amin. Higher precision samples early times more finely, reducing numerical error for extreme parameter choices.
Yes. Published ages depend on the adopted parameter set and data combination. If your H0 or density parameters differ, the computed age will shift accordingly.
It is a focused estimator for t0 given standard components. It does not include evolving dark energy, massive neutrino modeling, or detailed recombination physics. Use specialized solvers for high-precision research workflows.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.