Free 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.
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Critical Density
0.000000000000000000000000009216 kg/m³
Critical Density vs Hubble Constant (H0)
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)
The observed value is roughly 9.5 x 10⁻²⁷ kg/m³, equivalent to about 5.7 hydrogen atoms per cubic metre.
Example Calculation
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