AbstractConvective entrainment is a process that is poorly represented in existing convective parameterizations. By many estimates, convective entrainment is the leading source of error in global climate models. As a potential remedy, an Eulerian implementation of the Stochastic Parcel Model (SPM) is presented here as a convective parameterization that treats entrainment in a physically realistic and computationally efficient way. Drawing on evidence that convecting clouds comprise air parcels subject to Poisson‐process entrainment events, the SPM calculates the deterministic limit of an infinite number of such parcels. For computational efficiency, the SPM groups parcels at each height by their purity, which is a measure of their total entrainment up to that height. This reduces the calculation of convective fluxes to a sequence of matrix multiplications. The SPM is implemented in a single‐column model and compared with a large‐eddy simulation of deep convection.