Quantification of the interactions between nanoparticles is important in understanding their dynamic behaviors and many related phenomena. In this study, molecular dynamics simulation is used to calculate the interaction potentials (i.e., van der Waals attraction, Born repulsion, and electrostatic interaction) between two silica nanospheres of equal radius in the range of 0.975 to 5.137 nm. The results are compared with those obtained from the conventional Hamaker approach, leading to the development of modified formulas to calculate the van der Waals attraction and Born repulsion between nanospheres, respectively. Moreover, Coulomb's law is found to be valid for calculating the electrostatic potential between nanospheres. The developed formulas should be useful in the study of the dynamic behaviors of nanoparticle systems under different conditions.