Workpiece diameter measurement method and machine tool

A machine tool comprising:

• a main spindle that has a rotary axis;
• a sensor that is movable in a first direction and a second direction that are orthogonal to the rotary axis and orthogonal to each other, and calculates coordinates of a point P that is on an outer circumferential surface of a cylindrical workpiece that is supported such that the rotary axis and a central axis of the cylindrical workpiece coincide with each other, the coordinates having a maximum or minimum coordinate in the first direction, with respect to change of coordinate in the second direction, and coordinates of a reference point Q that is a point at which a distance D1 in the first direction from the rotary axis is known;
• and
• a computation unit that calculates a distance D2 in the first direction between the point P and the reference point Q based on the coordinates of the point P and the coordinates of the reference point Q, and also calculates a workpiece diameter of the cylindrical workpiece based on the distance D1 and the distance D2.