A direct measurement of the potential energy surface that characterizes individual chemical bonds in complex materials has fundamental significance for many disciplines. Here, we demonstrate that the energy profile for metallic single-atom contacts and single-molecule junctions can be mapped by fitting ambient atomic force microscope measurements carried out in the near-equilibrium regime to a physical, but simple, functional form. We extract bond energies for junctions formed through metallic bonds as well as metal-molecule link bonds from atomic force microscope data and find that our results are in excellent quantitative agreement with density functional theory based calculations for exemplary junction structures. Furthermore, measurements from a large number of junctions can be collapsed to a single, universal force-extension curve, thus revealing a surprising degree of similarity in the overall shape of the potential surface that governs these chemical bonds. Compared to previous studies under ambient conditions where analysis was confined to trends in rupture force, our approach significantly expands the quantitative information extracted from these measurements, particularly allowing analysis of the trends in bond energy directly.