This article proposes a novel geometric method to investigate whether a multirotor unmanned aerial vehicle (UAV) can achieve static hovering, i.e., hoverability. Hoverability is indispensable for a multirotor UAV to conduct its tasks safely and should be satisfied even after its rotors fail to prevent accidents. The proposed geometric method reveals the relationship between the position of the center of mass (CoM) and the rotor placement of a multirotor UAV with upward-oriented rotors to satisfy hoverability. It can be applied to a multirotor UAV with any number and positioning of rotors. This article also demonstrates that our proposed method can be applied to the investigation of a robust structure against rotor failures. This investigation provides a geometric proof that a pentarotor UAV with robustness against an arbitrary rotor failure cannot be developed. Furthermore, a quantitative measure of hoverability is newly presented based on the analysis method. This enables us to design a multirotor UAV with an optimal structure by maximizing it. Finally, experimental validation is performed by using a hexrotor UAV whose CoM position is adjusted.