The human cerebral cortex undergoes a protracted, regionally heterogeneous development well into young adulthood. Cortical areas that expand the most during human development correspond to those that differ most markedly when the brains of macaque monkeys and humans are compared. However, it remains unclear to what extent this relationship derives from allometric scaling laws that apply to primate brains in general, or represents unique evolutionary adaptations. Furthermore, it is unknown whether the relationship only applies to surface area (SA), or also holds for cortical thickness (CT). In 331 participants aged 4 to 30, we calculated age functions of SA and CT, and examined the correspondence of human cortical development with macaque to human expansion, and with expansion across nonhuman primates. CT followed a linear negative age function from 4 to 30 years, while SA showed positive age functions until 12 years with little further development. Differential cortical expansion across primates was related to regional maturation of SA and CT, with age trajectories differing between high- and low-expanding cortical regions. This relationship adhered to allometric scaling laws rather than representing uniquely macaque–human differences: regional correspondence with human development was as large for expansion across nonhuman primates as between humans and macaque.