  The precise values of the running quark and lepton masses $m^{}_f(\mu)$,
which are defined in the modified minimal subtraction scheme ($\overline{\rm
MS}$) with $\mu$ being the renormalization scale and the subscript $f$
referring to all the charged fermions in the Standard Model (SM), are very
useful for the model building of fermion masses and flavor mixing and for the
precision calculations in the SM or its new-physics extensions. In this paper,
we calculate the running fermion masses by taking account of the up-to-date
experimental results collected by Particle Data Group and the latest
theoretical higher-order calculations of relevant renormalization-group
equations and matching conditions in the literature. The emphasis is placed on
the quantitative estimation of current uncertainties on the running fermion
masses, and the linear error propagation method is adopted to quantify the
uncertainties, which has been justified by the Monte-Carlo simulations. We
identify two main sources of uncertainties, i.e., one from the experimental
inputs and the other from the truncations at finite-order loops. The
correlations among the uncertainties of running parameters can be remarkable in
some cases. The final results of running fermion masses at several
representative energy scales are tabulated for further applications.
