  The measurement of the eta_b mass, together with a QCD result for the
hyperfine splitting E_{HFS}=M_{Upsilon(1S)}-M_{eta_b}, allows us to determine
the strong coupling constant alpha_s at a low energy scale. The result
alpha_s(M_{Upsilon(1S)})=0.197\pm 0.002_{Delta E_{HFS}^{exp}} \pm
0.002_{scheme} \pm 0.002_{delta <G^2>} \pm 0.006_{delta m_b} \pm 0.005_{ho},
alpha_s(M_{Z^0})=0.124\pm 0.001_{Delta E_{HFS}^{exp}} \pm 0.001_{scheme} \pm
0.001_{delta <G^2>} \pm 0.003_{delta m_b} \pm 0.002_{ho}, is compatible with
the current world average of alpha_s reported by the Particle Data Group, and
shows that the experimental lowest-lying \bar b b hyperfine splitting can be
reproduced in terms of a perturbative and nonperturbative QCD contribution.
