The measurement of the eta(b) mass, together with a QCD result for the hyperfine splitting E-HFS = M-Gamma(1S) - M-eta b, allows us to determine the strong coupling constant alpha(s) at a low energy scale. The result alpha(s)(M-Gamma(1S)) = 0.197 +/- 0.002 vertical bar(Delta EHFSexp) +/- 0.002 vertical bar(scheme) +/- 0.002 vertical bar delta < G(2)> +/- 0.006 vertical bar(delta mb) +/- 0.005 vertical bar(ho), alpha(s)(M-Z0) = 0.124 +/- 0.001 vertical bar(Delta EHFSexp) +/- 0.001 vertical bar(scheme) +/- 0.001 vertical bar(delta < G2 >) +/- 0.003 vertical bar(delta mb) +/- 0.002 vertical bar(ho) is compatible with the current world average of alpha(s) reported by the Particle Data Group, and shows that the experimental lowest-lying (b) over barb hyperfine splitting can be reproduced in terms of a perturbative and nonperturbative QCD contribution.