The plan-form structure of the world's river basins contains extensive information regarding tectonic, paleo-geographic and paleo-climate conditions, but interpretation of this structure is complicated by the need to disentangle these processes from the autogenic behavior of fluvial processes. One method of interpreting this structure is by integrating channel length and drainage area as characterized by the scaling relationship between slope and area, resulting in a characteristic length parameter, referred to in recent studies as χ. In this paper, we apply this methodology at a continental scale by calculating χ for the world's river networks. Mapping of χ', a modified version of χ including the influence of precipitation distribution on river discharge and correction of base level for χ' in closed basins, illustrates the geometric structure of global river networks, thus highlighting where tectonics or changing climate have resulted in an apparent disequilibrium of the river channel geometry. Our global χ maps quantify a dynamic view of Earth's river networks and help to identify past and ongoing evolution of Earth's landscape.