Soft magnetic sensors provide considerable merits for tactile perception, such as high precision, simple wiring, and easy expansion to large sensing areas. However, current magnetic sensors basically rely on data-driven methods, difficult to establish the relationship for the two-stage conversion (i.e., from magnetic signals to spatial displacements, then to force signals). In this study, a spherical magnet array is designed with magnetic powder and hyper-elastic rubber for multi-dimensional tactile perception. Besides, a highly interpretable and calculable method is proposed to analyze the two-stage conversion according to magnetic dipole model and dynamic Young's modulus. A nine-spherical-magnet array is constructed, and extensive analysis in terms of different magnet numbers are conducted in COMSOL environments. The results demonstrate the proposed method's high accuracy with mean square errors of 0.02 mT and 9.90 mN for the two stages, respectively. This fact also indicates the great potential of our method to various applications of tactile perception.