  Models of street networks underlie research in urban travel behavior,
accessibility, design patterns, and morphology. These models are commonly
defined as planar, meaning they can be represented in two dimensions without
any underpasses or overpasses. However, real-world urban street networks exist
in three-dimensional space and frequently feature grade separation such as
bridges and tunnels: planar simplifications can be useful but they also impact
the results of real-world street network analysis. This study measures the
nonplanarity of drivable and walkable street networks in the centers of 50
cities worldwide, then examines the variation of nonplanarity across a single
city. It develops two new indicators - the Spatial Planarity Ratio and the Edge
Length Ratio - to measure planarity and describe infrastructure and
urbanization. While some street networks are approximately planar, we
empirically quantify how planar models can inconsistently but drastically
misrepresent intersection density, street lengths, routing, and connectivity.
