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It is shown that laminar vortex rings can be generated by impulsive body forces having particular spatial and temporal characteristics. The method produces vortex rings in a fluid initially at rest, and once generated, the flow field automatically satisfies the boundary conditions and is divergence-free. Numerical simulations and analytical models show that the strength of these rings can be accurately predicted by considering diffusion alone, despite the nonlinear nature of the generation process. A particularly simple model, which approximates the source of vorticity within vertical slabs, is proposed. This model predicts the ring circulation almost as accurately as a model that uses the exact geometry of the source of vorticity. It is found that when the duration of the force is less than a timescale based on the force radius and fluid viscosity, the ring circulation can be predicted accurately using an inviscid model.