A laboratory study of state-to-state rate coefficients (STS rates) for H2:H2 inelastic collisions in the v = 0 state is reported. The study, which spans the 295–20 K thermal range, is based on the use of a kinetic master equation. It describes the time-space evolution of populations of H2 rotational levels as induced by inelastic collisions. It is applied here to a supersonic jet of natural H2. This medium bears a large amount of relevant data that allows for the establishment of best values and confidence margins for the dominant STS rates of H2:H2 inelastic collisions on an experimental basis. The primary experimental data derived from the supersonic jet are the local number density, the populations of the H2 rotational levels, and their gradients along the jet by means of high-sensitivity Raman spectroscopy with superb space resolution. First, two sets of theoretical STS rates from the literature have been tested against the experiment. The set that shows a better agreement with the experiment has then been scaled to derive an improved set of experiment-scaled STS rates (ES rates). They allow the reproduction of more than 50 experimental population gradient data within a standard deviation <1.4% along the 295–20 K thermal range. The estimated uncertainty for the ES rates ranges from ≈3% near 300 K to ≈6% near 20 K. ES rates and uncertainties for H2:H2 ground-state inelastic collisions between 300 and 20 K are presented in machine-readable format. Other (incomplete) sets of theoretical rates from the literature are discussed.