Aims. We report on experimental and computational studies of hydrogenation of polycyclic aromatic hydrocarbon (PAH) cations, H n PAHs, which are relevant to the interstellar medium. Methods. The yield of the hydrogenated PAH cations produced in a plasma-ion source and by electrospray ionization was measured. DFT calculations at the B3LYP/6-311+G(d, p) and B3LYP/6-31+G(d, p) level of theory were performed to investigate the hydrogenation pattern. Results. A clear pattern in the yield and binding energies of hydrogen is revealed. Hydrogenated closed shell molecules with an even number of attached hydrogen atoms are significantly more stable than molecules with an odd number of hydrogen atoms and show as a consequence to be more abundant in mass spectra of H n PAHs. The binding energy of a hydrogen atom to H n−1 PAH with an even n is ∼2 eV higher than for odd n. The exact distribution in n observed in the experimental mass spectra remains to be solved due to the unknown internal ion source conditions. Conclusions. The H n PAH cations have been produced under very different conditions, and the measured yield indicates high stability and likely high abundance in the interstellar medium.