A numerical controller for machine tools that has function of controlling the speed of arc operation calculates a first operable feedrate based on the arc radius of a machining path and the allowable frequency (or allowable angular speed) to which servo position control is capable of responding. The numerical controller also calculates a second operable feedrate based on the arc radius of the machining path and the allowable acceleration to which servo position control can respond, and selects the minimum feedrate from the commanded feedrate and the calculated first and second feedrate to perform speed control.