  A numerical value for the running electromagnetic coupling constant in the MS
scheme is calculated at the low energy normalization scale equal to the
tau-lepton mass M_\tau. This low energy boundary value is used for running the
electromagnetic coupling constant to larger scales where high precision
experimental measurements can be performed. Particular scales of interest are
the b-quark mass for studying the \Upsilon-resonance physics and the Z-boson
mass M_Z for high precision tests of the standard model and for the Higgs mass
determination from radiative corrections. A numerical value for the running
electromagnetic coupling constant at M_Z in the on-shell renormalization scheme
is also given.
