Developmental processes in different mammals are thought to share fundamental cellular mechanisms. We report a dramatic increase in cell size during postnatal pancreas development in rodents, accounting for much of the increase in organ size after birth. Hypertrophy of pancreatic acinar cells involves both higher ploidy and increased biosynthesis per genome copy; is maximal adjacent to islets, suggesting endocrine to exocrine communication; and is partly driven by weaning-related processes. In contrast to the situation in rodents, pancreas cell size in humans remains stable postnatally, indicating organ growth by pure hyperplasia. Pancreatic acinar cell volume varies 9-fold among 24 mammalian species analyzed, and shows a striking inverse correlation with organismal lifespan. We hypothesize that cellular hypertrophy is a strategy for rapid postnatal tissue growth, entailing life-long detrimental effects.