**Choosing constants to normalize[edit]**
Out of the many

physical constants, the designer of a system of natural unit systems must choose a few of these constants to normalize (set equal to 1). It is not possible to normalize just

*any* set of constants. For example, the mass of a proton and the mass of an electron cannot both be normalized: if the mass of an electron is defined to be 1, then the mass of a proton has to be approximately 1836. In a less trivial example, the

fine-structure constant,

*α* ≈

1/137

, cannot be set to 1, at least not independently, because it is a dimensionless number defined in terms of other quantities, some of which one may want to set to unity as well. The fine-structure constant is related to other fundamental constants through

*α* =

*k**e**e*2/*ħc*

, where

*k**e* is the

Coulomb constant,

*e* is the

elementary charge,

*ħ* is the

reduced Planck constant, and

*c* is the

speed of light.