This paper gives the results of a calculation of the characteristic size of the plasmasphere based on a specific formulation of the prevailing view that its size is determined by a dynamic equilibrium between two essentially independent processes: depletion by magnetospheric convection and refill by flux from the ionosphere. The first of these processes exhibits a time behavior best described as being stochastic. The characteristic size of the plasmasphere is therefore also stochastic. The formulation given here combines simple models of dayside magnetic merging, corotation and convection patterns, and the refill process. It predicts statistical characteristics of the plasmasphere size from measurements of the solar wind convection electric field. From Mariner 5 measurements the method predicts the median value of the characteristic size of the plasmasphere to be 4.8 RE with a 50% central range of 3.8--5.2 RE, values entirely compatible with observations. Although the method gives no information about the shape of the plasmapause, it has the advantage that it can be applied to geophysical situations different from those that exist at present. This is illustrated by applying it to a case in which the dipole strength is double the present value.