Use of block copolymer thin films in lithographic applications requires orientation of domains perpendicular to a substrate. Algebraic models were used to predict conditions that are favorable for perpendicular versus parallel domain orientation in films confined between two interfaces. The free energy of each orientation was evaluated, yielding response surface plots as a function of film thickness and the preferential interaction strength at each interface. The model predicts that perpendicular orientation is generally favored for thinner films and at thicknesses incommensurate with the bulk periodicity, L-0. If either the top or bottom interfaces are preferential for one block, the favorable thickness windows shift depending on the interface wetting behavior. An extensive body of thin film experimental work corroborated the analytical predictions. The algebraic model has predictive value, and it demonstrates the complexity of the dependence of block copolymer orientation on the wetting behavior of the interfaces and the film thickness.