Flexural deformations of atomically thin membranes are governed by bending rigidity and the Gaussian modulus. In one-atom-thick graphene membranes, these two parameters need to be determined via bending-induced changes in topology and interaction between electron orbitals, going beyond existing studies on flat graphene. Herein, we employ atomic force microscopy to demonstrate that the configurational (strain) energy can successfully be evaluated based on changes in the surface geometry with subatomic resolution via three-dimensional analyses of attractive interatomic forces. A quadratic relation of adhesion energy with monolayer curvatures of rolled and unrolled graphene led to the finding that the probe tip can detect spatially varying surface potentials owing to the rehybridization effects and the change in the next-neighbor hopping caused by bending. The tip-induced local strain inside graphene was found to generate topological defects, independently of in-plane stretch. Their energetic analysis and relationship with local curvatures reveal the applicability of the Helfrich Hamiltonian and determine the bending rigidity and Gaussian modulus. Those evaluated at the hollow sites of the honeycomb lattice are consistent with the isotropic elastic attributes. The remarkably large negative Gaussian modulus, observed at a pyramidalized carbon atom located at the topmost center of the tip-induced bump, provides evidence for attractive interactions between the charge inhomogeneity owing to the topological defects and geometric potentials of the Gaussian curvature.