Did dinosaurs grow in a manner similar to extant reptiles, mammals or birds, or were they unique? Are rapid avian growth rates an innovation unique to birds, or were they inherited from dinosaurian precursors? We quantified growth rates for a group of dinosaurs spanning the phylogenetic and size diversity for the clade and used regression analysis to characterize the results. Here we show that dinosaurs exhibited sigmoidal growth curves similar to those of other vertebrates, but had unique growth rates with respect to body mass. All dinosaurs grew at accelerated rates relative to the primitive condition seen in extant reptiles. Small dinosaurs grew at moderately rapid rates, similar to those of marsupials, but large species attained rates comparable to those of eutherian mammals and precocial birds. Growth in giant sauropods was similar to that of whales of comparable size. Non-avian dinosaurs did not attain rates like those of altricial birds. Avian growth rates were attained in a stepwise fashion after birds diverged from theropod ancestors in the Jurassic period.