Spatial variations of the local electric field in current-carrying thin gold films were studied with a scanning tunneling microscope on a nanometer scale. With a refined scanning tunneling potentiometry technique, it was possible to determine the local electric fields within single grains. At grain boundaries, we observe potential drops on length scales of less than 1 nm which exceed the potential difference within a grain greatly. We interpret our findings by applying a theory that models grain boundaries as barriers with a reflectivity R for the conduction electrons. With the assumption of isotropic background scattering within each grain, we determine the local current-density j(x,y) that passes a grain boundary. From that, we obtain the reflectivity of individual grain boundaries and find values ofR = 0.7toR = 0.9 which is much higher than expected from macroscopic experiments.