AbstractCoral reef ecosystems are expected to undergo significant declines over the coming decades as oceans become warmer and more acidic. We investigate the environmental tolerances of over 650 Scleractinian coral species based on the conditions found within their present‐day ranges and in areas where they are currently absent but could potentially reach via larval dispersal. These “environmental envelopes” and connectivity constraints are then used to develop global forecasts for potential coral species richness under two emission scenarios, representing the Paris Agreement target (“SSP1‐2.6”) and high levels of emissions (“SSP5‐8.5”). Although we do not directly predict coral mortality or adaptation, the projected changes to environmental suitability suggest considerable declines in coral species richness for the majority of the world's tropical coral reefs, with a net loss in average local richness of 73% (Paris Agreement) to 91% (High Emissions) by 2080–2090 and particularly large declines across sites in the Great Barrier Reef, Coral Sea, Western Indian Ocean, and Caribbean. However, at the regional scale, we find that environmental suitability for the majority of coral species can be largely maintained under the Paris Agreement target, with 0%–30% potential net species lost in most regions (increasing to 50% for the Great Barrier Reef) as opposed to 80%–90% losses under High Emissions. Projections for subtropical areas suggest that range expansion will give rise to coral reefs with low species richness (typically 10–20 coral species per region) and will not meaningfully offset declines in the tropics. This work represents the first global projection of coral species richness under oceanic warming and acidification. Our results highlight the critical importance of mitigating climate change to avoid potentially massive extinctions of coral species.