To provide an electromagnetic clutch and an electromagnetic brake capable of restricting displacement of a driving shaft and a driven shaft when transmitting the rotation torque of the driving shaft to the driven shaft.

In an electromagnetic clutch and an electromagnetic brake, the concentricity of a driving shaft and a driven shaft with each other can be secured by forming a conical projection in a friction surface of a rotor fixed to the driving shaft, forming a recess in a friction surface of an armature fixed to the driven shaft, and fitting the recess and the projection to each other when the friction surfaces of the rotor and the armature are brought in contact with each other.