A permanent magnet rotating electric machine includes: a stator including: a stator core having teeth, and an armature winding wound around each of the teeth to configure the multiple phases; and a rotor including a rotor core, and permanent magnets provided in order around the rotor core. The rotor is arranged to be spaced apart from the stator with an air gap therebetween. Each of the permanent magnets has a curved surface opposed to the stator and is configured to satisfy the following relationship: 0.65 ≤ Rm × h   1 W  ( h   1 + g ) ≤ 1.37 where Rm denotes a radius of curvature of the curved surface, h1 denotes a thickness of a central portion of the permanent magnet in the peripheral direction, W denotes a width of the permanent magnet in the peripheral direction, and g denotes an air gap length of the air gap.