This study presents a novel theoretical approach and model, along with an equation for diatomic homonuclear molecules that contains a new molecular constant connecting the number of shared electrons and their circumference to determine their covalent radii. All diatomic homonuclear molecules consist of two atoms of the same element with certain geometrical shape held together by covalent bond. It is found that the homogenous distribution of electrons in the diatomic homonuclear molecules for their numbers and radii give a molecular constant value to be (5.4 X 10⁹ m^-1) .  The covalent radii can be calculated by using the main physical parameters (number of sharing electrons & constant of molecules). The calculations and results of covalent radii are in good agreement (95 %) with known experimentally determined values and there are only 5 % from 118 elements are deviated.​