In this brief paper we will propose a new equation for the proton charge radius. We will base our new equation on the Trinhammer-Bohr formula which states that the proton charge radius is directly proportional to the proton Compton wavelength. We will then propose a new equation for the proton Compton wavelength which is inversely proportional to the Rydberg constant and directly proportional to the running value of the fine structure constant on the protonic scale. This will define the proton charge radius only by the effective value of the fine structure constant and the Rydberg constant. This new equation also disproves the old value of the proton charge radius 0.877(50) which was measured by using electron-proton scattering and further solidifies the newer and smaller values 0.8414(19) provided by NIST.