Galaxy formation entails the hierarchical assembly of mass, along with the condensation of baryons and the ensuing, self-regulating star formation1,2. The stars form a collisionless system whose orbit distribution retains dynamical memory that can constrain a galaxy's formation history3. The orbits dominated by ordered rotation, with near-maximum circularity λz ≈ 1, are called kinematically cold, and the orbits dominated by random motion, with low circularity λz ≈ 0, are kinematically hot. The fraction of stars on `cold' orbits, compared with the fraction on `hot' orbits, speaks directly to the quiescence or violence of the galaxies' formation histories4,5. Here we present such orbit distributions, derived from stellar kinematic maps through orbit-based modelling for a well-defined, large sample of 300 nearby galaxies. The sample, drawn from the CALIFA survey6, includes the main morphological galaxy types and spans a total stellar mass range from 108.7 to 1011.9 solar masses. Our analysis derives the orbit-circularity distribution as a function of galaxy mass and its volume-averaged total distribution. We find that across most of the considered mass range and across morphological types, there are more stars on `warm' orbits defined as 0.25 ≤ λz ≤ 0.8 than on either `cold' or `hot' orbits. This orbit-based `Hubble diagram' provides a benchmark for galaxy formation simulations in a cosmological context.