We have constructed empirical formulae for the fusion and interaction barriers using a large number of experimental values chosen randomly from the literature available till date. The obtained fusion barriers have been compared with different model predictions based on the proximity, Woods–Saxon and double folding potentials along with several empirical formulas, time-dependent Hartree–Fock theories and experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for the reactions meant for the synthesis of super heavy elements also. Furthermore, it is seen that substitution of the predicted fusion barrier and radius in classic Wong formula (Wong,Phys. Rev. Lett. $31$:766 (1973) for the total fusion cross-sections agrees very well with the experiments. Similarly, current interaction barrier predictions have also been compared well with a few experimental results available and Bass potential model meant for the interaction barrier predictions. Importantly, the present formulae for the fusion as well as interaction barrier will have practical implications incarrying out physics research near the Coulomb barrier energies. Furthermore, the present fusion barrier and radius provide us with a good nucleus–nucleus potential which is useful for numerous theoretical applications.