It is possible to provide a rotary electric machine having a built-in permanent magnet and capable of reducing vibration and noise generated by the electromagnetic force while maintaining a small device size and high output. In the rotary electric machine, a rotor is arranged with an air gap inside an annular stator. The stator includes a stator iron core having a plurality of slots at an interval in the circumferential direction and a coil contained in each of the slots. The rotor includes a rotor iron core; permanent magnets embedded in a plurality of magnetic pole formation positions set along the external circumference of the rotor iron core; an iron core unit having magnetic pole forming positions which are magnetized by the permanent magnets to form magnetic poles on the surface opposing to the air gap; and concaves arranged at the center of the circumferential direction on the surface opposing to each iron core air gap, and extending in the axial direction.