We developed a global X-ray data analysis method to determine the intrinsic curvatures of lipids hosted in inverted hexagonal phases. In particular, we combined compositional modelling with molecular shape-based arguments to account for non-linear mixing effects of guest-in-host lipids on intrinsic curvature. The technique was verified by all-atom molecular dynamics simulations and applied to sphingomyelin and a series of phosphatidylcholines and ceramides with differing composition of the hydrocarbon chains. We report positive lipid curvatures for sphingomyelin and all phosphatidylcholines with disaturated and monounsaturated hydrocarbons. Phosphatidylcholines with diunsaturated hydrocarbons in turn yielded intrinsic lipid curvatures with negative values. All ceramides, with chain lengths varying between C2:0 and C24:0, displayed significant negative lipid curvature values. Moreover, we report non-additive mixing for C2:0 ceramide and sphingomyelin. This suggests for sphingolipids that in addition to lipid headgroup and hydrocarbon chain volumes also lipid-specific interactions are important contributors to membrane curvature stress.