# The third dimension of cities - relating building height, urban area, and population

## TL;DR

This study analyzes the relationship between building height, urban area, and population using a global dataset, revealing that horizontal extent primarily drives population accommodation rather than vertical development.

## Contribution

It introduces a Cobb-Douglas model to quantify the impact of building height and urban area on population, challenging assumptions about the benefits of vertical growth.

## Key findings

- Population mainly driven by horizontal urban extent
- Vertical development has limited impact on population capacity
- Findings are consistent across all building types

## Abstract

For decades, urban development was studied on two-dimensional maps, largely ignoring the third dimension. However, building height is crucial because it dramatically potentiates the interior space of cities. Here, using a newly released global building height dataset of 2903 cities across 42 countries in 2015, we develop a Cobb-Douglas model to simultaneously examine the relationship between urban population size and both horizontal and vertical urban extents. We find that, contrary to expectations, the residents of most urban systems do not significantly benefit from vertical dimension, with population accommodation being primarily driven by horizontal extent. The associations with country-level external indicators demonstrate that the benefits of horizontal extent are more pronounced in urban systems with more extreme size distribution (most population concentrated in few cities). Moreover, building classification tests confirm the robustness of our findings across all building types. Our findings challenge the intuition that building height and high-rise development significantly contributes to urban population accommodation, calling for targeted policies to improve its efficiency.