unit:PlanckMass

Type
Description

In physics, the Planck mass, denoted by $$m_P$$, is the unit of mass in the system of natural units known as Planck units. It is defined so that $$\approx 1.2209 \times 10 GeV/c_0 = 2.17651(13) \times 10 kg$$, (or $$21.7651 \mu g$$), where $$c_0$$ is the speed of light in a vacuum, $$G$$ is the gravitational constant, and $$\hbar$$ is the reduced Planck constant. Particle physicists and cosmologists often use the reduced Planck mass, which is $$\approx 4.341 \times 10 kg = 2.435 \times 10 GeV/c$$. The added factor of $$1/{\sqrt{8\pi}}$$ simplifies a number of equations in general relativity. Quantum effects are typified by the magnitude of Planck's constant.

Properties
0.0000000217644
$$m_P = \sqrt{\frac{ \hbar c^3}{G}} \approx 1.2209 \times 10^{19} GeV/c^2 = 2.17651(13) \times 10^{-8}$$, where $$c$$ is the speed of light in a vacuum, $$\hbar$$ is the reduced Planck's constant, and $$G$$ is the gravitational constant. The two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.
$$m_P$$
planckmass
Annotations
In physics, the Planck mass, denoted by $$m_P$$, is the unit of mass in the system of natural units known as Planck units. It is defined so that $$\approx 1.2209 \times 10 GeV/c_0 = 2.17651(13) \times 10 kg$$, (or $$21.7651 \mu g$$), where $$c_0$$ is the speed of light in a vacuum, $$G$$ is the gravitational constant, and $$\hbar$$ is the reduced Planck constant. Particle physicists and cosmologists often use the reduced Planck mass, which is $$\approx 4.341 \times 10 kg = 2.435 \times 10 GeV/c$$. The added factor of $$1/{\sqrt{8\pi}}$$ simplifies a number of equations in general relativity. Quantum effects are typified by the magnitude of Planck's constant.
Planck Mass(en)

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