We present a new method to accurately calculate the electrostatic energy and forces on charges in a system with periodic boundary conditions in one of three spatial dimensions. We transform the Coulomb sum via a convergence factor into a series of fast decaying functions similar to the Lekner method. Rigorous error bounds for the energies and the forces are derived and numerically verified. The method has a computational complexity of O(N(2)), but is faster and easier to use than previously reported methods.