Plastics entering the ocean face a fate which is still relatively unknown: how much of it will stay afloat, how quickly will it degrade, and how much of it will end up on the beach? Estimates of plastic inputs are orders of magnitude larger than the quantities found in the surface waters. In order to get a better understanding of the fate of these plastics, an inverse modelling methodology is presented here, where parameters in a Lagrangian ocean model are calibrated by comparing with field measurements of plastic concentrations. A case study is presented for the Mediterranean. Parameters for beaching, sinking, and for various sources of microplastics are estimated using surface water measurements. Results suggest that coastal population accounts for most plastic waste, about twice as much as river emissions. It is estimated that 49—63% of plastic waste ends up on coastlines, and 37—51% sinks down. The estimated input for 2015 of 2,100—3,400 metric tonnes per year is much less than previous estimates for the Mediterranean. This work is part of ongoing investigations into the marine plastic mass budget. The methodology is coupled to a fragmentation model, estimating size-classes of plastics in the environment. This enables us to estimate the magnitude of fragmentation as a sink, and to account for size-dependent transport processes. Adding more types of measurements, such as samples from beaches, should allow us to constrain the different parameters even more accurately in the future.