Local potentials that arise between the tip of an atomic force microscope (AFM) and a sample add to the free AFM cantilever potential and thereby affect the thermally driven motion of the cantilever. Here we present a general framework for isolating the tip-sample interaction potential from the total potential based on the analysis of the perturbations to the thermally driven motion of the cantilever. To establish appropriate experimental parameters, we first examine the behavior of the free cantilever in air and in water. We then measure the total and interaction potentials of an AFM cantilever in a low salt aqueous solution, a classical electrical double-layer interaction, and validate the approach by reconstructing the force curve (force law) from the force gradients derived from the potentials. We also present three-dimensional representations of the total cantilever potential and the tip-sample interaction potentials as a function of tip-sample separation.