Electrophoresis is often used to measure the "average" zeta (zeta) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of zeta potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or I potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92 sigma(zeta)/root N, and the average magnitude of the quadrupole moment is 1.302 sigma(zeta)/root N, where sigma(zeta) is the standard deviation of zeta potential over the surface of individual spheres. This is true for any random distribution of zeta potential, and the results emphasize that "random" implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (sigma(zeta)) Of zeta potential. Monte Carlo simulations were done to confirm and extend the analytical results.