An electric power steering system includes steering a torque detector that detects steering torque, and a motor that provides assist torque based on the detected steering torque, wherein for the purpose of estimating, without detecting motor rotation angular information and rotation angular velocity information, the road reaction torque in which the influence of the motor inertia torque is eliminated, a value corresponding to rotation velocity of a steering shaft is calculated based on the steering torque and the assist torque, to calculate road reaction torque based on the value corresponding to the rotation velocity of the steering shaft.