There are provided an angle detection apparatus configured to correct an error included in angle information output from a multipolar angle detector, a motor having the angle detection apparatus, a torque sensor, an electric power steering apparatus, and a vehicle. A multiplication circuit (12) generates digital electrical angle information (θed) from analog angle information output from a multipolar optical encoder (11), a first differentiator 30 differentiates the electrical angle information (θed) to operate an electrical angular velocity (ωed), a first discontinuity correction circuit (31) carries out processing of correcting a discontinuity of an angular velocity in a temporal change for the electrical angular velocity (ωed), and a digital filter (32) carries out correction processing of reducing a high-frequency noise component for an electrical angular velocity (ωedc) corrected by the first discontinuity correction circuit (31).