  The coupling constant of the strong force is determined from the
transverse-momentum distribution of $Z$ bosons produced in 8 TeV proton-proton
collisions at the LHC and recorded by the ATLAS experiment. The $Z$-boson cross
sections are measured in the full phase space of the decay leptons using 15.3
million electron and muon pairs, in a dataset collected in 2012 and
corresponding to an integrated luminosity of 20.2 fb$^{-1}$. The analysis is
based on predictions evaluated at third order in perturbative QCD, supplemented
by the resummation of logarithmically enhanced contributions in the low
transverse-momentum region of the lepton pairs. The determined value of the
strong coupling at the reference scale corresponding to the $Z$-boson mass is
$\alpha_\text{s}(m_Z) = 0.1183 \pm 0.0009$. This is the most precise
experimental determination of $\alpha_\text{s}(m_Z)$ achieved so far.
