To facilitate the motion control of ironless planar motors with stationary circular coils, in this paper, a real-time model is proposed to predict the force and torque exerted on a magnet array. The force and torque are calculated with Lorentz force law, which can be essentially expressed as the calculation of the volume integral. Due to the symmetry of the circle, the force and torque generated by the coil will not change when the circular coil rotates around its z-axis. This characteristic is then significantly utilized in the calculation of the volume integral, and the integral in the real-time model calculation is independent of the position and the rotation angle of the moving magnet array. The calculation result of the numerical integrals can be considered as constants, and thus the real-time model in this paper can be computed quickly. Finally, experiments are carried out to provide verification of the proposed real-time model. The computation time of the model on a digital signal processor system is <15 mu s, and the force and torque predicted by the model are rigidly consistent with the measurement data.