Planck density

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

$\rho_P = \frac{m_P}{l_P^3} = \frac{c^5}{\hbar G^2}$ ≈ 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

$\hbar$ 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.

v • d • e Planck's natural units

Base Planck units	Planck time · Planck length · Planck mass · Planck charge · Planck temperature

Derived Planck units	Planck energy · Planck force · Planck power · Planck density · Planck angular frequency · Planck pressure · Planck current · Planck voltage · Planck impedance · Planck momentum