Rotor failure is a significant factor in unmanned aircraft system accidents. In particular, the rotor failure heavily affects a quadrotor because its controller depends on rotor torque and thrust. Then, the fault tolerance control (FTC) system is adapted to a quadrotor controller. On the other hand, the traditional FTC system focuses only on its effect or not for failure; it is difficult to compensate for the performance of a failed quadrotor. The degree of controllability (DOC) is proposed to represent how controllable a given system is. The DOC is defined as the norm between the outer boundary of the stability point and the recovery region. The Available Reduced Control Authority Index (ArCAI) uses the DOC to analyze the controllability of a multirotor under rotor failure. However, the DOC of the failed quadrotor cannot be calculated accurately by the ArCAI because the criterion does not consider the gyroscopic moment despite the gyroscopic moment helps stabilize its attitude. Therefore, we propose a new analysis method of controllability for quadrotors under rotor failure called modified ArCAI. The method modifies its dynamics to calculate accurate DOC by considering the gyroscopic moment. The results of numerical simulation show that the modified ArCAI can calculate the DOC of a failed quadrotor accurately.