The surface energy of graphene and its chemical derivatives governs fundamental interfacial interactions like molecular assembly, wetting, and doping. However, quantifying the surface energy of supported two-dimensional (2D) materials, such as graphene, is difficult because (1) they are so thin that electrostatic interactions emanating from the underlying substrate are not completely screened, (2) the contribution from the monolayer is sensitive to its exact chemical state, and (3) the adsorption of airborne contaminants, as well as contaminants introduced during transfer processing, screens the electrostatic interactions from the monolayer and underlying substrate, changing the determined surface energy. Here, we determine the polar and dispersive surface energy of bare, fluorinated, and hydrogenated graphene through contact angle measurements with water and diiodomethane. We accounted for many contributing factors, including substrate surface energies and combating adsorption of airborne contaminants. Hydrogenating graphene raises its polar surface energy with little effect on its dispersive surface energy. Fluorinating graphene lowers its dispersive surface energy with a substrate-dependent effect on its polar surface energy. These results unravel how changing the chemical structure of graphene modifies its surface energy, with applications for hybrid nanomaterials, bioadhesion, biosensing, and thin-film assembly.