Provided are a numerical controller, a numerical control method, and a numerical control program capable of suppressing reduction in machining surface quality while increasing machining efficiency. A numerical controller comprises: a program analysis unit that analyzes a machining program for controlling a machine tool and calculates a cumulative moving distance for each command block based on a designated coordinate; a control point generation unit that generates, based on the moving distance and a designated speed for each command block, a control point as a set of the moving distance and the speed at a start point and an end point in the command block; a commanded speed generation unit that generates a parametric curve defining a commanded speed for the moving distance based on the control points; and a commanded speed output unit that outputs the generated commanded speed per interpolation unit.