# Planck energy

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In physics, Planck energy, denoted by EP, is the unit of energy in the system of natural units known as Planck units.[1]

${\displaystyle E_{\mathrm {P} }={\sqrt {\frac {\hbar c^{5}}{G}}}\approx 1.956\times 10^{9}\ \mathrm {J} \approx 1.2209\times 10^{19}\ \mathrm {GeV} \approx 0.54336\ \mathrm {MWh} }$[2]

where c is the speed of light in a vacuum, ћ 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:

${\displaystyle E_{\mathrm {P} }={\frac {\hbar }{t_{\mathrm {P} }}},}$

where tP is the Planck time.

Also:

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

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.[3] Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena (or fantastically large, as in the case of Planck temperature). Energy of 1 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 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 8π. Hence writings in particle physics and physical cosmology often normalize G to 1. This normalization results in the reduced Planck energy, defined as:

${\displaystyle {\sqrt {\frac {\hbar {}c^{5}}{8\pi G}}}\approx 3.90\times 10^{8}\ \mathrm {J} \approx 2.43\times 10^{18}\ \mathrm {GeV} \approx 0.10814\mathrm {MWh} .}$

## References

1. ^ "Planck Energy". Cosmos, The SAO Encyclopedia, Swinburne University of Technology. Retrieved 18 September 2015.
2. ^ "CODATA Value: Planck mass energy equivalent in GeV". physics.nist.gov. Retrieved 2016-12-21.
3. ^ "HiRes - The High Resolution Fly's Eye Ultra High Energy Cosmic Ray Observatory". www.cosmic-ray.org. Retrieved 2016-12-21.