In metal additive manufacturing (AM) processes, parts are manufactured in layers by sintering or melting metal or metal alloy powder under the effect of a powerful laser or an electron beam. As the laser/electron beam scans the powder bed, it melts the powder in successive tracks which overlap each other. This overlap, called the hatch overlap, results in a continuous cycle of rapid melting and resolidification of the metal. The melting of the metal from powder to liquid and subsequent solidification causes anisotropic shrinkage in the layers. The thermal strains caused by the thermal gradients existing between the different layers and between the layers and the substrate leads to considerable thermal stresses in the part. As a result, stress gradients develop in the different directions of the part which lead to distortion and warpage in AM parts. The deformations due to shrinkage and thermal stresses have a significant effect on the dimensional inaccuracies of the final part. A three-dimensional thermomechanical finite element (FE) model has been developed in this paper which calculates the thermal deformation in AM parts based on slice thickness, part orientation, scanning speed, and material properties. The FE model has been validated and benchmarked with results already available in literature. The thermal deformation model is then superimposed with a geometric virtual manufacturing model of the AM process to calculate the form and runout errors in AM parts. Finally, the errors in the critical features of the AM parts calculated using the combined thermal deformation and geometric model are correlated with part orientation and slice thickness.