Prior research on mastery learning has examined relationships between achievement and time on task, motivation variables, as well as the effects of prior learning. One can show that the results of prior research lead to certain requirements on a model for mastery learning. This article uses those requirements to develop a mathematical model for mastery learning. This model includes measures of a motivational factor and of the specific ability of a learner with respect to the content being learned. The model also contains a variable to reflect prior learning. The model has been developed to include a computer program which accepts student data and from which predictions can be made and tested. Assumptions and limitations of the model are discussed, and some research questions are raised. In most respects the model proposed in this article is susceptible to the same tests and refinements as an empirical law in the physical or life sciences.