  We present a determination of the strong coupling constant $\alpha_s(m_Z)$
using inclusive top-quark pair production cross section measurements performed
at the LHC and at the Tevatron. Following a procedure first applied by the CMS
collaboration, we extract individual values of $\alpha_s(m_Z)$ from
measurements by different experiments at several centre-of-mass energies, using
QCD predictions complete in NNLO perturbation theory, supplemented with NNLL
approximations to all orders, and suitable sets of parton distribution
functions. The determinations are then combined using a likelihood-based
approach, where special emphasis is put on a consistent treatment of
theoretical uncertainties and of correlations between various sources of
systematic uncertainties. Our final combined result is $\alpha_s(m_Z) =
0.1177^{+0.0034}_{-0.0036}$.
