There is provided a rotor for a rotary electrical machine for improving mechanical strength of the rotor against centrifugal force. The rotary electrical machine is provided with a stator, and a rotor disposed with a gap from the stator, which has a rotor core 252. The rotor includes a magnet insertion hole, and a permanent magnet 254 inserted into the magnet insertion hole. A clearance part 263 is formed at a position of the magnet insertion hole corresponding to a corner of the inserted permanent magnet 254, which has a facing surface 266 that is formed to face a surface of the permanent magnet 254 via a gap. The facing surface 266 of the clearance part 263 has inflection points 264a to 264d so that each of obtuse angles 267a, 267b is formed by the two facing surfaces contiguous with the inflection points 264b, 264c.