The transient, convective-diffusion equation for a single reactant consumed at a mass-transfer-limited rate on a rotating disk electrode (RDE) and a membrane-covered RDE is solved via a perturbation method in the Laplace domain for predicting the coulombs discharged following a potential step from open-circuit conditions. A formula is derived in each case for relating the rotation rate omega to the excess transient coulombs Q(t) passed during the time required to establish a steady-state current where Q(t) = integral(o)(x)[I(t) - I-ss]d ($) over cap t. For an uncoated RDE, a plot of Q(t) vs. omega(-1/2) is predicted to be linear through the origin with a slope proportional to the reactant diffusivity to the one-third power. For the membrane-covered RDE, a similar plot is predicted in the high-rotation rate limit to be a straight line with a nonzero intercept. The slope and intercept can be used with the formula provided for determining the diffusivity and partition coefficient of the reactant in the membrane. Experimental results are presented which validate the theoretical development.