  Based on a simple but effective regularization-renormalization method (RRM),
the running coupling constants (RCC) of fermions with masses in quantum
electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by
renormalization group equation (RGE). Starting at Q=0 ($Q$ being the momentum
transfer), the RCC in QED increases with the increase of $Q$ whereas the RCCs
for different flavors of quarks with masses in QCD are different and they
increase with the decrease of $Q$ to reach a maximum at low $Q$ for each flavor
of quark and then decreases to zero at $Q\longrightarrow 0$. The physical
explanation is given.
