# Planck mass

The Planck mass is the natural unit of mass, denoted by mP.

mP = (c [itex]\hbar[itex]/ G)1/2 ≈ 2.176 × 10-8 kg = 21.76 µg

where:

c is the speed of light

[itex]\hbar[itex] is Planck's constant

G is the gravitational constant

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. This is 21.7645 µg ± 0.0016 µg.

It is interesting to note that unlike most of the other Planck units, the Planck mass is on an approximately human scale, being roughly the mass of some fleas.

The Planck mass is the value for which the Schwarzschild radius and the Compton length are equal, and equal to the Planck length.

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