# Planck energy

In physics, Planck energy, denoted by EP, is the unit of energy in the system of natural units known as Planck units.

$E_\text{P} = \sqrt{\frac{\hbar c^5}{G}} \approx$ 1.956 × 109 J $\approx$ 1.22 × 1028 eV $\approx$ 0.5433 MWh

where c is the speed of light in a vacuum, $\hbar$ is the reduced Planck's constant, and G is the gravitational constant. EP is a derived, as opposed to basic, Planck unit.

An equivalent definition is:

$E_\text{P} = {\frac{\hbar} {t_\text{P}}},$

where $\ t_\text{P}$ is the Planck time.

Also:

$E_\text{P} = {m_\text{P}} {c^2},$

where $\ m_\text{P}$ is the Planck mass.

The ultra-high-energy cosmic rays observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5×10−8 EP. Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena (or fantastically large, as in the case of Planck density). One EP, on the other hand, is definitely macroscopic, approximately equaling the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy).

Planck units are designed to normalize the physical constants $\hbar$, G, and c to 1. Hence given Planck units, the mass-energy equivalence E = mc² simplifies to E = m, so that the Planck energy and mass are numerically identical. In the equations of general relativity, G is often multiplied by 8π. Hence writings in particle physics and physical cosmology often normalize 8πG to 1. This normalization results in the reduced Planck energy, defined as:

$\sqrt{\frac{\hbar{}c^5}{8\pi G}}$ $\approx$ 0.390 × 109 J $\approx$ 2.43 × 1018 GeV.