In this work, we present new methods for calculating the mean, standard deviation, median, and modal locations of the boundaries of volcanic hazards. These calculations are based on a new, mathematically rigorous definition of probabilistic hazard maps – a way to map the probabilities of inundation by a given hazard. We apply this analysis to several models of volcanic flows: simple models of viscous flows, complex models of a tabletop granular flow, and a complex model of a volcanic mud flow.