Recent measurements of ratios of quarkonium annihilation rates are used to evaluate the strong fine-structure constant ${\ensuremath{\alpha}}_{s}$. Expressions are presented for QCD radiative corrections with ${\ensuremath{\alpha}}_{s}$ referred to the quark-mass scale. We find ${\mathrm{\ensuremath{\alpha}}}_{\mathit{s}}$(${\mathit{m}}_{\mathit{b}}$)=0.${179}_{\mathrm{\ensuremath{-}}0.008}^{+0.009}$ from the ratio \ensuremath{\Gamma}(\ensuremath{\Upsilon}\ensuremath{\rightarrow}\ensuremath{\gamma}gg)/ \ensuremath{\Gamma}(\ensuremath{\Upsilon}\ensuremath{\rightarrow}ggg). The corresponding range of ${\ensuremath{\Lambda}}_{\mathrm{MS}{\ifmmode\bar\else\textasciimacron\fi{}}^{(4)}}$ (the QCD scale factor for four light-quark flavors) is 146--210 MeV, where MS\ifmmode\bar\else\textasciimacron\fi{} denotes the modified-minimal-subtraction scheme. The experimentally more precise but theoretically more questionable ratio of the gluonic and muonic widths of J/\ensuremath{\psi} and \ensuremath{\Upsilon} yields ${\ensuremath{\alpha}}_{s}$(${m}_{c}$)=0.29\ifmmode\pm\else\textpm\fi{}0.02, ${\ensuremath{\alpha}}_{s}$(${m}_{b}$)=0.189\ifmmode\pm\else\textpm\fi{}0.008 when ${v}^{2}$/${c}^{2}$ corrections to these ratios for J/\ensuremath{\psi} and \ensuremath{\Upsilon} are parametrized linearly. Further predictions are made for ratios of rates.