Climate’s effect on global biodiversity is typically viewed through the lens of temperature, humidity and resulting ecosystem productivity. However, it is not known whether biodiversity depends solely on these climate conditions, or whether the size and fragmentation of these climates are also crucial. Here we shift the common perspective in global biodiversity studies, transitioning from geographic space to a climate-defined multidimensional space. Our findings suggest that larger and more isolated climate conditions tend to harbour higher diversity and species turnover among terrestrial tetrapods, encompassing more than 30,000 species. By considering both the characteristics of climate itself and its geographic attributes, we can explain almost 90% of the variation in global species richness. Half of the explanatory power (45%) may be attributed either to climate itself or to the geography of climate, suggesting a nuanced interplay between them. Our work evolves the conventional idea that larger climate regions, such as the tropics, host more species primarily because of their size. Instead, we underscore the integral roles of both the geographic extent and degree of isolation of climates. This refined understanding presents a more intricate picture of biodiversity distribution, which can guide our approach to biodiversity conservation in an ever-changing world.