Critical Density of the Universe Calculator
The critical density of the universe for a given Hubble constant — the mean density at which space is flat — in kilograms per cubic metre, hydrogen atoms per cubic metre and solar masses per cubic megaparsec, with the density parameter for any density you enter.
Friedmann’s equation says the universe is spatially flat when its mean density equals 3H² ÷ 8πG: about 9 × 10⁻²⁷ kg/m³ for a Hubble constant of 70 km/s/Mpc — five hydrogen atoms per cubic metre.
How the critical density of the universe calculator works
Friedmann’s equation says the universe is spatially flat when its mean density equals 3H² ÷ 8πG: about 9 × 10⁻²⁷ kg/m³ for a Hubble constant of 70 km/s/Mpc — five hydrogen atoms per cubic metre. Observations find the total density within a percent of critical, with ordinary matter about 5%, dark matter 26% and dark energy 69% of it. The density parameter Ω is a density divided by the critical value.
Formula: ρ_c = 3 H₀² ÷ (8π G); Ω = ρ ÷ ρ_c
Worked examples
| Inputs | Critical density (kg/m³) | Note |
|---|---|---|
| H₀ = 70 | 9.204e-27 | 9.2 × 10⁻²⁷ kg/m³; the entered density is Ω 0.049 (baryons) |
| H₀ = 67.4 (Planck) | 8.533e-27 | 8.53 × 10⁻²⁷ |
| H₀ = 73 (local measurements) | 1.001e-26 | 1.0 × 10⁻²⁶ |
FAQFrequently asked questions
Why does the critical density matter?
It decides the geometry: above it space curves like a sphere and (without dark energy) recollapses; below it space is open; at it space is flat. The cosmic microwave background shows the total is flat to within about 0.4%.
Why so empty?
Five atoms per cubic metre is a far better vacuum than any laboratory achieves; the universe is mostly void with matter clumped into galaxies. Averaged over the largest scales, that is all the density there is — and 95% of it is not atoms.
Does the critical density change with time?
Yes — it scales with H², and H was larger in the past. The density parameter Ω of matter falls as the universe expands while dark energy’s rises; today they are 0.31 and 0.69.
What is the Hubble time?
1 ÷ H₀, about 14 billion years at 70 km/s/Mpc — the age the universe would have if it had always expanded at today’s rate. The real age (13.8 billion years) is close because early deceleration and later acceleration roughly cancel.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- Royal Observatory Greenwich — the historic home of the prime meridian
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).