Reef fishes are a treasured part of marine biodiversity, and also provide needed protein for many millions of people. Although most reef fishes might survive projected increases in ocean temperatures, corals are less tolerant. A few fish species strictly depend on corals for food and shelter, suggesting that coral extinctions could lead to some secondary fish extinctions. However, secondary extinctions could extend far beyond those few coral-dependent species. Furthermore, it is yet unknown how such fish declines might vary around the world. Current coral mass mortalities led us to ask how fish communities would respond to coral loss within and across oceans. We mapped 6964 coral-reef-fish species and 119 coral genera, and then regressed reef-fish species richness against coral generic richness at the 1° scale (after controlling for biogeographic factors that drive species diversification). Consistent with small-scale studies, statistical extrapolations suggested that local fish richness across the globe would be around half its current value in a hypothetical world without coral, leading to more areas with low or intermediate fish species richness and fewer fish diversity hotspots.