The Yang equation of the excess-path-length distribution of fast charged particles due to multiple Coulomb scattering under general conditions is completely solved. The solution is an improvement of the Fermi solution, giving the joint distribution of only the angular and the lateral spreads, to include the excess-path-length distribution. The distributions are indicated in figures, and the mean values and the variances of them are tabulated. The influence of the excess-path-length distribution upon the width of other related distributions is found important; e.g., the distribution gives about four times more correction on the width of the energy-loss distribution than on the probable energy loss. The effect of a single scattering on the excess-path-length distribution is also investigated using the Moli\`ere theory.