  In this paper, we derive mathematical formulas for the skin friction
coefficient in wall-bounded turbulence based on the Reynolds averaged
streamwise momentum equation and the total stress. Specially, with the
theoretical or empirical relation of the total stress, the skin friction
coefficient is expressed in terms of the mean velocity and the Reynolds shear
stress in an arbitrary wall-normal region $[h_0, h_1]$. The formulas are
validated using the direct numerical simulation data of turbulent channel and
boundary layer flows, and the results show that our formulas estimate the skin
friction coefficient very accurately with an error less than $2\%$. We believe
that the present integral formula can be used to determine the skin friction in
turbulent channel and boundary layer flows at high Reynolds numbers where the
near wall statistics are very difficult to measure accurately.
