We present a determination of the strong coupling constant α s (m Z ) based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the Zp T distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology – th e correlated replica method – which allows for a simultaneous determination of α s and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find α s (m Z ) = 0.1185 ± 0. 0005 (exp) ± 0. 0001 (meth) , showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N 3 LO and beyond) from half the shift between the NLO and NNLO α s values, finding Δαsth=0.0011.E. S. and J. R. are supported by an European Research Council Starting Grant “PDF4BSM”. J. R. is also supposed by the Netherlands Organization for Scientific Research (NWO). The work of Z.K. is supported by the European Research Council Consolidator Grant “NNLOforLHC2” and by the Executive Research Agency (REA) of the European Commission under the Grant Agreement PITN-GA-2012-316704 (HiggsTools). S. C. is supported by the HICCUP ERC Consolidator Grant (614577). S. C. and S. F. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement no 740006). R. D. B and L. D. D. are supported by UK STFC Grants ST/L000458/1 and ST/P0000630/1
