We study the determination of supersymmetric parameters at the LHC from a global fit including cross sections and edges of kinematic distributions. For illustration, we focus on a minimal supergravity scenario and discuss how well it can be constrained at the LHC operating at collision energies of 7 and 14TeV. We find that the inclusion of cross sections greatly improves the accuracy of the SUSY parameter determination, and allows the reliable extraction of model parameters even in the initial phase of LHC data taking with 7TeV collision energy and 1 fb −1 integrated luminosity. Moreover, cross section information may be essential to study more general scenarios, such as those with non-universal gaugino masses, and distinguish them from minimal, universal, models.