The description of electrode-electrolyte interfaces is based on the concept of the formation of an electric double layer. This concept was derived from continuum theories extended by introducing point charge distributions. Based on molecular dynamics simulations, we analyze the electric double layer in an approach beyond the point charge scheme by instead assessing charge polarizations at electrochemical metal-water interfaces from first principles. We show that the atomic structure of water layers at room temperature leads to an oscillatory behavior of the averaged electrostatic potential. We address the relation between the polarization distribution at the interface and the extent of the electric double layer and subsequently derive the electrode potential from the charge polarization.