Planck mass

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Prerequisites
Square root	<math>\sqrt x</math>
h-bar	<math>\hbar</math>
Speed of light	<math>c</math>
Gravitational constant	<math>G</math>

The Planck mass is the natural unit of mass, denoted by m_P. It is the mass for which the Schwarzschild radius is equal to the Compton length and the Planck length.

<math>m_P = \sqrt{\frac{\hbar{}c}{G}}</math> ≈ 2.176 × 10^-8 kg = 21.76 µ g

The 2002 CODATA-recommended value for the Planck mass is 2.176 45(16) × 10^-8 kg, where the part in parentheses indicates the uncertainty in the last digits shown — that is, a value of 21.7645 µg ± 0.0016 µg.

Particle physicists and cosmologists often use the reduced Planck mass, which is

<math>\sqrt{\frac{\hbar{}c}{8\pi G}}</math> ≈ 4.340 µg.

Adding the additional factor of 8π simplifies several equations in gravity.

It is interesting to note that unlike most of the other Planck units, the Planck mass is on a scale more or less conceivable to humans, as it is roughly the mass of some fleas.