Inelastic collisions in natural H2 are studied from the experimental and theoretical points of view between 10 and 140 K. Rotational populations and number densities measured by Raman spectroscopy along supersonic expansions of H2 provide the link between experimental and theoretical rotranslational state-to-state rate coefficients of H2 in the vibrational ground state. These rates are calculated in the close-scattering approach with the MOLSCAT code employing a recent ab initio H2-H2 potential. The calculated rates are assessed by means of a master equation describing the time evolution of the experimental rotational populations. The feasibility for obtaining the rates on the sole basis of the experiment is discussed. The dominant processes j(1)j(2)-->j'(1)j'(2) in the investigated thermal range are found to be 21-->01 >30-->12 >31-->11, proving the importance of double processes such as 30-->12. Good agreement is found between theory and experiment, as well as with earlier ultrasonic measurements of relaxation times. A spectral representation is proposed in order to visualize quantitatively the collisional contributions in any nonequilibrium time evolving process.