We construct an accurate estimate for the root mean square force error of the particle-particle-particle mesh ((PM)-M-3) 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 las a function of system specifications and (PM)-M-3 parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.