The extinction of dinosaurs at the Cretaceous/Paleogene (K/Pg) boundary was the seminal event that opened the door for the subsequent diversification of terrestrial mammals. Our compilation of maximum body size at the ordinal level by sub-epoch shows a near-exponential increase after the K/Pg. On each continent, the maximum size of mammals leveled off after 40 million years ago and thereafter remained approximately constant. There was remarkable congruence in the rate, trajectory, and upper limit across continents, orders, and trophic guilds, despite differences in geological and climatic history, turnover of lineages, and ecological variation. Our analysis suggests that although the primary driver for the evolution of giant mammals was diversification to fill ecological niches, environmental temperature and land area may have ultimately constrained the maximum size achieved.