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Deforestation and habitat loss are widely expected to precipitate an extinction crisis among tropical forest species. Humans cause deforestation, and humans living in rural settings have the greatest impact on extant forest area in the tropics. Current human demographic trends, including slowing population growth and intense urbanization, give reason to hope that deforestation will slow, natural forest regeneration through secondary succession will accelerate, and the widely anticipated mass extinction of tropical forest species will be avoided. Here, we show that the proportion of potential forest cover remaining is closely correlated with human population density among countries, in both the tropics and the temperate zone. We use United Nations population projections and continent‐specific relationships between both total and rural population density and forest remaining today to project future tropical forest cover …