# Planck density

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

$\rho_\text{P} = \frac{m_\text{P}}{l_\text{P}^3} = \frac{c^5}{\hbar G^2}$ ≈ 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 the reduced Planck 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.