Compact torus injection (CTI) is a novel approach to fueling the core of a fusion reactor. In this paper, the force-free equilibrium based on the EAST-CTI is calculated. It is found that the , which is proportional to the ratio of the toroidal current to the toroidal magnetic field, plays a key role for the force-free equilibrium. When it is smaller than the eigenvalue, the open poloidal magnetic flux decreases while the magnetic field strength increases as its value increases. However, once equals the eigenvalue, the amplitude of the magnetic field tends to infinity and the boundary magnetic field is tangential to the wall. In addition, in this work we found that the eigenvalue is mainly determined by the width of the formation region, enlarging the width will significantly reduce the eigenvalue and further affecting the compact torus (CT) formation. Another interesting phenomenon in this work is that the poloidal magnetic field plays a hindering role in the formation of CT, and theoretically, CT is difficult to detach from the forming region when is less than the threshold . In experiments, we show that a discharge with leads to an increased delay between the onset of the current in the acceleration and formation regions. These findings provide some guidance for the carrying out of the experiments and future modifications of the device.