An extensive study of pairing effects in the Sn isotopes is carried out. The pairing Hamiltonian is treated by the chain-calculation method which provides practically exact solutions while involving less computational work than a complete-basis diagonalization. The coupling strength is fixed by reproducing the energy of the 9\ state in Sn, while the single-particle energies have been determined by an analysis of the experimental low-energy spectra of the odd-A isotopes. A detailed comparison of the calculated results with experimental data evidences the importance of neutron pairing correlations in the 50-82 shell. The results of this paper complement those of our previous study of the N"82 isotones. It turns out that the role of pairing correlations is similar to a large extent in both cases.