A mathematical model of the magnetospheric electric field imposed upon the ionosphere is presented. The model provides an interplanetary magnetic field (IMF) dependent description of the magnetospheric electric field at ionospheric altitudes for global ionospheric and thermospheric modelers. Although many theoretical and empirical ionospheric convection models have been published, none give both a quantitative and a general Kp, IMF (Bx, By, Bz) dependent description. The need for such a model is particularly pressing with the success of the Dynamic Explorer (DE) mission. As a result of this mission, extensive data sets of thermospheric and ionospheric parameters for well-defined IMF orientations have been acquired. These data sets, especially for northward IMF orientations, are so complex that global models of both the thermosphere and ionosphere are required to help unravel the physics. Our convection model is an empirical model based upon a synthesis of published observations and current understanding. It describes the convection electric field by a set of simple functions which are dependent on Kp and IMF (Bx, By, Bz). These simple functions create a framework by which current and future empirical data can be used to adjust the model. Since no recent major statistical surveys have been made of ionospheric electric fields, these functions (based upon a few published case studies) are exceedingly simple.