Horizontal and vertical patterns of built-up land are essential to analyse a range of environmental change impacts, such as exposure to natural hazards, urban heat islands, and trapping air pollution, as well as for decision making in this context. However, while data on horizontal patterns are abundant, they are relatively rare for vertical patterns. Here, we present global maps of 3D built-up patterns at a 1-km² resolution for the nominal year 2015. These data are estimated using random forest models, fed with a wide range of spatial data and trained on reference data from all continents except Antarctica. Independent testing indicates that R² values of the global models for built-up footprint, height, and volume equal 0.89, 0.73, and 0.84, respectively. Our results show that buildings worldwide are 6.16-m high on average, and total building volume is 1645 km³, which is the equivalent of a solid cube of 12 km on each side. Yet, we find large variations in 3D built-up patterns, both within and across world regions. In particular, floor space per person exceeds 200 m² in both Oceania and North America, while it is only 29 m² in South Asia and 38 m² in Sub-Saharan Africa. Our results provide novel insights into the global distribution of 3D built-up patterns and offer new opportunities for the assessments of urban environmental impacts. The global data for building footprint, height and volume can be downloaded from https://doi.org/10.34894/4QAGYL.