The problem of determining the shear rate in a non-Newtonian fluid sheared between rotating coaxial cylinders has eluded exact solution, although many approximations and solutions in infinite series form are available. The present paper shows that certain of the infinite series which appear in Krieger and Elrod’s solution [J. Appl. Phys., 24, 134 (1953)] can be summed in closed form, leading to an expression for the shear rate in which the dominant term is identical to the local power-law approximation, and the correction terms take account of deviation from power-law behavior. As a consequence, point-by-point application of the power law is shown to give an excellent approximation to the true shear rate in Couette flow, with a small and readily calculable error.