How do cell number and size determine brain size? Here, we show that, in the order Rodentia, increased size of the cerebral cortex, cerebellum, and remaining areas across six species is achieved through greater numbers of neurons of larger size, and much greater numbers of nonneuronal cells of roughly invariant size, such that the ratio between total neuronal and nonneuronal mass remains constant across species. Although relative cerebellar size remains stable among rodents, the number of cerebellar neurons increases with brain size more rapidly than in the cortex, such that the cerebellar fraction of total brain neurons increases with brain size. In contrast, although the relative cortical size increases with total brain size, the cortical fraction of total brain neurons remains constant. We propose that the faster increase in average neuronal size in the cerebral cortex than in the cerebellum as these structures gain neurons and the rapidly increasing glial numbers that generate glial mass to match total neuronal mass at a fixed glia/neuron total mass ratio are fundamental cellular constraints that lead to the relative expansion of cerebral cortical volume across species.