The inclusive cross section for top-quark pair production measured by the CMS experiment in proton–proton collisions at a center-of-mass energy of 7 TeV is compared to the QCD prediction at next-to-next-to-leading order with various parton distribution functions to determine the top-quark pole mass, mtpole, or the strong coupling constant, αS. With the parton distribution function set NNPDF2.3, a pole mass of 176.7−3.4+3.8GeV is obtained when constraining αS at the scale of the Z boson mass, mZ, to the current world average. Alternatively, by constraining mtpole to the latest average from direct mass measurements, a value of αS(mZ)=0.1151−0.0032+0.0033 is extracted. This is the first determination of αS using events from top-quark production.