Here we demonstrate that there is a wide range of pressures at supercritical temperatures where there is essentially monolayer coverage (i.e., there is nearly a complete layer of molecules adsorbed adjacent to the surface, but very little excess density in the second and subsequent layers). In this regime, the dependence of the Gibbs adsorption on the density is linear, and coefficients of this linear function depend on the monolayer capacity and surface area. It is shown that measurements of the Gibbs adsorption in this regime can be used to determine surface area without knowledge of the area per molecule or a model for the adsorption isotherm. This new method has the potential to provide reliable values of specific surface area for macroporous, mesoporous, and microporous systems without the limitations of previous methods. Lattice-theory calculations suggest that the best conditions for surface area measurements are in the supercritical region with temperatures about twice the critical temperature and pressures well above the critical pressure. These conditions allow nearly complete monolayer coverage but there is not multilayer adsorption because the temperature is sufficiently above the critical temperature of the adsorbate.