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# Planck density

The Planck density is the unit of density, denoted by ρP, in the system of natural units known as Planck units.

$rho_P = frac\left\{m_P\right\}\left\{l_P^3\right\} = frac\left\{c^5\right\}\left\{hbar G^2\right\}$ ≈ 5.1 × 1096 kg/m3

where:

mP is the Planck mass
lP is the Planck length
c is the speed of light in a vacuum
$hbar$ is Dirac's constant
G is the gravitational constant

This is a unit which is very large, about equivalent to 1023 solar masses squeezed into the space of a single atomic nucleus. At one unit of Planck time after the Big Bang, the mass density of the universe is thought to have been approximately one unit of Planck density.

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