See the Math Planck length and Planck mass

We can use dimensional analysis to construct a length and a mass scale using Planck's constant, , Newton's universal gravitational constant, G, and the speed of light, c.

Planck's constant has units of:   length2 mass time
Newton's constant has units of:  length3 (mass time2)
The speed of light has units of:   length/time

We can construct a new constant that has units of length as follows:

The above expression has units of:

If we instead combine , G, and c into a new constant with units of mass, we find:

When we plug in actual numbers, we find that the Planck length is 1.61 x 10-35 m, 1020 times smaller than the nucleus of an atom. The Planck mass (which, of course, also determines an energy scale) is around 10-5 g, which is equivalent to ~ 1019 GeV. These length and mass scales help physicists estimate when it's necessary to do a calculation using a quantum theory of gravity.