Electric fields and potentials of an equilibrated assembly of ions and water molecules adjacent to a charged metal surface are calculated as a function of perpendicular distance = from the surface from data derived from molecular dynamics trajectories. The spatial distributions of atoms or molecules along direction z are found by ensemble averaging of trajectories followed by averaging with a localized function with a well defined length scale. Two methods were used calculate dependent charge density distributions. In the first, to be called the atom method, the trajectories of charged atoms are averaged. In the second, called the molecule method, a Taylor expansion of charged atom positions relative to molecular centres is performed and the charge density separated into monopole, dipole, quadrupole, octopole, ...components. These distributions are used to calculate the electric potential and in one example to study the progressive loss of structure due to water as the length parameter is scanned through the dimension of a water molecule. This latter result provides a link between simulations with detailed atomic modelling of intermolecular interactions and electric potentials derived from Gouy-Chapman theory. Illustrative examples are chosen from simulations of aqueous solutions of simple alkali halide electrolytes next to charged and uncharged flat metal surfaces. The smallest system has one ion and 157 water molecules, the largest 60 ions and 1576 water molecules.