Error estimates for algorithms based on truncations for evaluating ele
ctrostatic interactions in molecular dynamics applications are very im
portant for several reasons. For example, the estimates are necessary
to establish the validity of the simulations and can be used to estima
te various simulation parameters. Very precise estimates have been fou
nd for the Ewald method and the related particle mesh Ewald method. Ho
wever, for the very popular fast multipole method such a precise estim
ate is not available. In this paper, we illustrate the rather complica
ted error behavior of the fast multipole method and we use statistical
methods to derive an estimate for the root mean square error on the f
orces. Furthermore, the expected maximum error on the force acting on
a single particle is studied. The estimates are tested against errors
obtained from simulations and are found to be very precise.