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.
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