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, (m_t^{pole}), or the strong coupling constant, (\alpha_S). With the parton distribution function set NNPDF2.3, a pole mass of (176.7_{-3.4}{+3.8}) GeV is obtained when constraining (\alpha_S) at the scale of the Z boson mass, mZ, to the current world average. Alternatively, by constraining (m_t^{pole}) to the latest average from direct mass measurements, a value of (\alpha_S(m_z) = 0.1151_{-0.0032}^{+0.0033}) is extracted. This is the first determination of (\alpha_S) using events from top-quark production.