An increase in brain size is a hallmark of human evolution. Questions regarding the evolution of brain development and obstetric constraints in the human lineage can be addressed with accurate estimates of the size of the brain at birth in hominins. Previous estimates of brain size at birth in fossil hominins have been calculated from regressions of neonatal body or brain mass to adult body mass, but this approach is problematic for two reasons: modern humans are outliers for these regressions, and hominin adult body masses are difficult to estimate. To accurately estimate the brain size at birth in extinct human ancestors, an equation is needed for which modern humans fit the anthropoid regression and one in which the hominin variable entered into the regression equation has limited error. Using phylogenetically sensitive statistics, a resampling approach, and brain-mass data from the literature and from National Primate Research Centers on 362 neonates and 2802 adults from eight different anthropoid species, we found that the size of the adult brain can strongly predict the size of the neonatal brain (r2=0.97). This regression predicts human brain size, indicating that humans have precisely the brain size expected as an adult given the size of the brain at birth. We estimated the size of the neonatal brain in fossil hominins from a reduced major axis regression equation using published cranial capacities of 89 adult fossil crania. We suggest that australopiths gave birth to infants with cranial capacities that were on average 180cc (95% CI: 158-205cc), slightly larger than the average neonatal brain size of chimpanzees. Neonatal brain size increased in early Homo to 225cc (95% CI: 198-257cc) and in Homo erectus to approximately 270cc (95% CI: 237-310cc). These results have implications for interpreting the evolution of the birth process and brain development in all hominins from the australopiths and early Homo, through H. erectus, to Homo sapiens.