In today’s world, the hemispherical-shaped component’s fine finishing with high wear resistance and dimensional accuracy is required in different applications such as shells, molds, and implants. The magnetorheological finishing (MRF) method using a novel hemispherical tip-based tool is used to finish the hemispherical cups. The study aims to develop a novel theoretical mathematical model to predict the surface roughness reduction of the hemispherical cups using the present MRF process. Because the magnetic field regulates forces in the MRF process, the effect of the magnetic flux density (MFD) in the fine finishing of the hemispherical acetabular cup workpiece has been examined theoretically and experimentally. The mathematical model for reducing surface roughness is next tested experimentally on a hemispherical acetabular cup workpiece surface. The results of the predicted roughness match well with the experimental values with the error ranging from 1.17% to 6.15%. Further, surface morphology, microhardness, and dimensional accuracy tests are done on the workpiece using scanning electron microscopy, a microhardness tester, and coordinate measuring equipment to evaluate the efficacy of the present process. The present mathematical model for the MRF process predicts fine finishing along with the overall enhancement in the surface quality of the hemispherical acetabular cup surface.