Grid cells in the medial entorhinal cortex (MEC) are part of an environment-independent spatial coordinate system. To determine how information about location, direction, and distance is integrated in the grid-cell network, we recorded from each principal cell layer of MEC in rats that explored two-dimensional environments. Whereas layer II was predominated by grid cells, grid cells colocalized with head-direction cells and conjunctive grid × head-direction cells in the deeper layers. All cell types were modulated by running speed. The conjunction of positional, directional, and translational information in a single MEC cell type may enable grid coordinates to be updated during self-motion-based navigation.