The Shape Compactness of Urban Extents

The shape compactness of urban extents matters, just like urban density matters. Other things being equal, both metrics determine the average travel distances in cities, and hence their energy consumption and their greenhouse gas emissions. They also affect the length of infrastructure lines and the length of commutes, and hence also labor market integration and overall productivity. In principle, therefore, increasing either the shape compactness or the density of cities can contribute—in different yet equal measure—to mitigating climate change. There are strong forces that push urban extents to become more compact, circular or near circular in shape, and these forces have evolved over time. There are also key forces that have pushed urban extents to become less compact over time. We introduce these key forces and illustrate their effects on particular cities. We then define a set of metrics for measuring the shape compactness of cities. We use them to measure urban extents obtained from satellite imagery in a stratified global sample of 200 cities in three time periods: 1990, 2000, and 2014. We find that the shape compactness of cities the world over is independent of city size, area, density, and income and that, not surprisingly, it is strongly affected by topography. We also find that it has declined overall between 1990 and 2014 and explain some of the sources of this decline. We conclude the paper by assessing the ways in which the shape compactness of cities can be increased to make them more productive, more inclusive, more sustainable, and more climate-resilient in decades to come.