<p>Additive manufacturing and topology optimization enable the design and fabrication of highly complex components with potential for significant weight savings in the aerospace and automotive industries. Recent research has developed methodologies for combined topology and build orientation optimization to minimize or eliminate overhanging surfaces. However, support structure volume is more representative of additive manufacturing cost, and no methods in literature have derived support structure volume as a smooth and continuous function with respect to element density and build orientation design variables. This paper develops a topology and build orientation optimization approach for additive manufacturing, capable of simultaneously considering support structure volume and overhang area in a multi-objective problem statement to better reflect additive manufacturing cost. To accomplish this, a novel method is proposed for differentiable mapping of element densities from any rotated finite element mesh to a structured mesh aligned with the print direction. Support structure density is calculated layer-by layer based on a supporting region that is applicable for a range of self-supporting threshold angles by varying the aspect ratio of the structured mesh. The proposed method is verified with four numerical problems, including an airplane bearing bracket, demonstrating the approach can be applied to complex, real-world problems. The cost savings obtained through optimization are validated using slicer software, showing that minimizing support structure volume resulted in a 5–54% reduction in support material use with a change in print time between + 6 and − 15% compared to overhang area minimization.</p>