The proton densities for the nuclei with the nucleon number A ranging from 49 to 209 are used to determine the nuclear potentials by solving the nonlinear wave equation of a classical neutral scalar meson field. These proton densities were measured from the high energy electron scattering experiment by Hahn, Ravenhall and Hofstadter.The nuclear potentials determined are fitted to two types of approximate formula. When A is given, the potentials may be readily calculated from these formula. Next, a comparison is made between the conventionally used Woods-Saxon potential and the potential given by these formula.