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Animals require a certain amount of habitat to persist and thrive, and habitat loss is one of the most critical drivers of global biodiversity decline. While habitat requirements have been predicted by relationships between species traits and home-range size, little is known about constraints imposed by environmental conditions and human impacts on a global scale. Our meta-analysis of 395 vertebrate species shows that global climate gradients in temperature and precipitation exert indirect effects via primary productivity, generally reducing space requirements. Human pressure, however, reduces realised space use due to ensuing limitations in available habitat, particularly for large carnivores. We show that human pressure drives extinction risk by increasing the mismatch between space requirements and availability. We use large-scale climate gradients to predict current species extinction risk across global regions, which also offers an important tool for predicting future extinction risk due to ongoing space loss and climate change.