Critical Density Calculator
Compute the critical density of the universe rho_crit = 3 H0^2 / (8 pi G), the density needed for a flat geometry.
Critical Density
0.000000000000000000000000009216 kg/m³
Critical Density vs Hubble Constant (H0)
Formula
## Critical Density of the Universe The critical density is the dividing line between a universe that expands forever and one that eventually re-collapses. ### Formula **rho_crit = 3 H0² / (8 pi G)** - *H0* must be in SI units of 1/s (about 2.27 x 10⁻¹⁸ s⁻¹ for 70 km/s/Mpc) - *G* = 6.674 x 10⁻¹¹ N m² kg⁻² The observed value is roughly 9.5 x 10⁻²⁷ kg/m³, equivalent to about 5.7 hydrogen atoms per cubic metre.
Esempio Risolto
Using H0 = 2.27e-18 s⁻¹ (≈ 70 km/s/Mpc).
- 01rho_crit = 3 H0² / (8 pi G)
- 02H0² = (2.27e-18)² = 5.153e-36
- 038 pi G = 1.676e-9
- 04rho_crit = 3 * 5.153e-36 / 1.676e-9
- 05rho_crit ≈ 9.22e-27 kg/m³
Domande Frequenti
Why is it called the critical density?
It is the precise density at which the universe is geometrically flat. Below it, the universe is open and expands forever (even without dark energy). Above it, the universe is closed.
How do I convert H0 from km/s/Mpc to 1/s?
Divide by 3.086e19 (the number of km in a Mpc). So 70 km/s/Mpc becomes 70 / 3.086e19 ≈ 2.27e-18 s⁻¹.
Is the observed density close to critical?
Yes. Observations indicate the total density is within about 0.4% of the critical value, meaning the universe is very nearly flat.