Despite being a fundamental aspect of biodiversity, little is known about what controls species range sizes. This is especially the case for hyperdiverse organisms such as plants. We use the largest botanical data set assembled to date to quantify geographical variation in range size for ~ 85 000 plant species across the New World. We assess prominent hypothesised range-size controls, finding that plant range sizes are codetermined by habitat area and long- and short-term climate stability. Strong short- and long-term climate instability in large parts of North America, including past glaciations, are associated with broad-ranged species. In contrast, small habitat areas and a stable climate characterise areas with high concentrations of small-ranged species in the Andes, Central America and the Brazilian Atlantic Rainforest region. The joint roles of area and climate stability strengthen concerns over the potential effects of future climate change and habitat loss on biodiversity.