Although several models exist for calculating the loss in a fiber optic butt-joint resulting from angular misalignment between the fiber ends, these models generally assume an even energy distribution both across the face of the emitting fiber and throughout the emission angle. We present a numerical method that allows for arbitrary and physically realizable energy distributions. This approach also takes into account the physical size of the cladding on joint geometry, a previously neglected factor that becomes important for large tilt angles. Our results show loss curves that are appreciably different from those predicted by simpler models.