We determine the uncertainty on the strong coupling S due to the experimental errors on the data fitted in global analysis of hard-scattering data, within the standard framework of leading-twist fixed-order collinear factorisation in the MS scheme, finding that S(M2Z) = 0.1202+0.0012-0.0015 at next-to-leading order (NLO) and S(M2Z) = 0.1171+0.0014−0.0014 at next-to-next-to-leading order (NNLO). We do not address in detail the issue of the additional theory uncertainty on S(M2Z), but an estimate is ±0.003 at NLO and at most ±0.002 at NNLO. We investigate the interplay between uncertainties on S and uncertainties on parton distribution functions (PDFs). We show, for the first time, how both these sources of uncertainty can be accounted for simultaneously in calculations of cross sections, and we provide eigenvector PDF sets with different fixed S values to allow further studies by the general user. We illustrate the application of these PDF sets by calculating cross sections for W, Z, Higgs boson and inclusive jet production at the Tevatron and LHC.