Planck density

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

<math> \rho_P = \frac{m_P}{l_P^3} = \frac{c^5}{\hbar G^2}</math> ≈ 5.1 × 10⁹⁶ kg/m³

where:

m_P is the Planck mass

l_P is the Planck length

c is the speed of light in a vacuum

<math>\hbar</math> 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.