The quantitative application of micromagnetic theory to barium ferrite particulate media is reported. The theory includes magnetostatic, anisotropic crystalline, and exchange interactions. It is found that neither packing, stacking, thermal fluctuations, nor curling can account for the discrepancy between the predictions of noninteracting coherent rotation theory and experimental observations. Induced domain nucleation can reduce the coercivity sufficiently: however, ignorance of the nucleation mechanism prevents first principles predictions. Important practical consequences of the calculation include a demonstration that stacked particles switch together, which implies increased recording noise, and quantitative predictions for the effect of thermal fluctuations on barium ferrite coercivity.