# Planck energy

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

EP is a derived, as opposed to basic, Planck unit. It is defined by:

$E_{\mathrm {P} }={\sqrt {\frac {\hbar c^{5}}{G}}},$ where c is the speed of light in a vacuum, ћ is the reduced Planck's constant, and G is the gravitational constant.

Substituting values for the various components in this definition gives the approximate equivalent value of this unit in terms of other units of energy:

$1\ E_{\mathrm {P} }\approx 1.956\times 10^{9}\ \mathrm {J} \approx 1.2209\times 10^{19}\ \mathrm {GeV} \approx 543.36\ \mathrm {kWh}$ An equivalent definition is:

$E_{\mathrm {P} }={\frac {\hbar }{t_{\mathrm {P} }}},$ where tP is the Planck time.

Also:

$E_{\mathrm {P} }={m_{\mathrm {P} }}{c^{2}},$ where mP is the Planck mass.

The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5×10−8 EP. Theoretically, the highest energy photon carries precisely 1 EP of energy (see Ultra-high-energy gamma ray). Most Planck units are extremely small or extremely large, as in the case of Planck temperature and Planck acceleration. For comparison, the Planck energy is approximately equal to 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 G, ћ 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 4π. Hence writings in particle physics and physical cosmology often normalize G to 1. This normalization results in the reduced Planck energy, defined as:

${\sqrt {\frac {\hbar {}c^{5}}{4\pi G}}}\approx 7.80\times 10^{8}\ \mathrm {J} \approx 4.86\times 10^{18}\ \mathrm {GeV} \approx 216.28\ \mathrm {kWh} .$ 