  We construct an accurate estimate for the root mean square force error of the
particle-particle-particle-mesh (P3M) algorithm by extending a single particle
pair error measure which has been given by Hockney and Eastwood. We also derive
an easy-to-use analytic approximation to the error formula. This allows a
straightforward and precise determination of the optimal splitting parameter
(as a function of system specifications and P3M parameters) and hence knowledge
of the force accuracy prior to the actual simulation. The high quality of the
estimate is demonstrated in several examples.
