As Cities Grow, They Spread Out Rather Than Rise
Cities and settlements are a global phenomenon, and their continued expansion is fundamentally transforming patterns of resource demand. This transformation is reflected in growing pressures on land, material use, and infrastructure. Thus, understanding how cities grow in space is essential for planning future urban development and determining all its consequences. Here, we characterize four geometrically related dimensions of urban growth: two horizontal dimensions describing the urban area, one vertical dimension represented by average building height, which together with the urban area defines building volume, and the population dimension. Analyzing a global dataset of growing cities, for the period 1975-2025 we identify three main patterns. First, urban growth is fundamentally anisotropic -- as cities gain population, they expand much more rapidly in the horizontal than in the vertical direction. Second, average building height decreases in the vast majority of cities as they grow, indicating that vertical development is not only slower than horizontal expansion but on average, can act in an effectively negative manner by giving greater weight to the horizontal dimensions. Third, despite their diverse growth trajectories, cities converge toward characteristic population densities, both with respect to urban area and building volume. We further explore alternative scenarios for future urban growth. These projections show that different assumptions about horizontal and vertical scaling can lead to substantially different demands for urban land and building volume. These findings reveal constraints on the long-term evolution of urban form and provide a quantitative assessment for understanding the spatial dynamics and development of cities.