At the global scale, cities are hotspots of human activity, associated energy and resource consumption, and pollution. The distribution of their size, in terms of population, is very well documented (associated with Zipf’s law), and scaling laws have linked this size to different outputs.

However, comparatively much less is known about their internal spatial structure. Here we present two empirical studies of 1800+ world cities of more than 300,000 inhabitants each, studying at the same time the radial (center-periphery) component of their internal structure, and the effect of city size (scaling laws).

We focus on two variables of interest, closely associated with urban morphology, built-up land, and population density.

Using rescaling methods (data collapse) and very parsimonious non-linear regressions, we identify a general structure, at the global scale, for each of these two variables. Land use scales like a homothetic surface, with a scaling exponent of 1/2 in both horizontal dimensions. And population density scales like a homothetic volume (an exponential cone), with a scaling exponent of 1/3 in each of the 3 dimensions. Such results are unprecedented at the world scale, and very meaningful for the still-open problem of city delineation.

We provide scale-free parameters capturing fluctuations around these general tendencies, which show strong links to national measures of wealth (gross domestic product per capita and energy use per capita). This suggests a choice between economic development and sustainability.