CELL and lipid membranes are able to bend, as manifested during membrane fusion and the formation of non-lamellar lyotropic mesophases in water. But there is an energy cost to bending of lipid layers, called the curvature elastic energy. Although the functional form of this energy is known(1), a complete quantitative knowledge of the curvature elastic energy, which is central to predicting the relative stability of the large number of phases that lipid membranes can adopt, has been lacking. Here we use X-ray synchrotron diffraction measurements of the variation of lattice parameter with pressure and temperature for the periodic Ia3d (Q(230)) cubic phase of hydrated monoolein to calculate the complete curvature elastic-energy function for the lipid cubic mesophase. This allows us to predict the stabilities of different cubic and lamellar phases for this system as a function of composition.