The comparative analysis of animal growth still awaits full integration into life-history studies, partially due to the difficulty of defining a comparable measure of growth rate across species. Using growth data from 50 primate species, we introduce a modified "general growth model" and a dimensionless growth rate coefficient β that controls for size scaling and phylogenetic effects in the distribution of growth rates. Our results contradict the prevailing idea that slow growth characterizes primates as a group: the observed range of β values shows that not all primates grow slowly, with galago species exhibiting growth rates similar or above the mammalian average, while other strepsirrhines and most New World monkeys show limited reduction in growth rates. Low growth rate characterizes apes and some papionines. Phylogenetic regressions reveal associations between β and life-history variables, providing tests for theories of primate growth evolution. We also show that primate slow growth is an exclusively postnatal phenomenon. Our study exemplifies how the dimensionless approach promotes the integration of growth rate data into comparative life-history analysis, and demonstrates its potential applicability to other cases of adaptive diversification of animal growth patterns.