A workpiece measuring device, a collision preventing device, and a machine tool acquires 3D data of the shape of a workpiece used to prevent a collision between the workpiece and part of the machine tool. A measuring section measures the distance to the workpiece through scanning in a non-contact manner; and a shape recognition section generates a 3D mesh structure. The coordinates of a measurement point on the workpiece based on distance information about the measured distance to the workpiece, and that generates a measurement geometry map such that, when the ratio of the number of times the calculated measurement point is included in one unit of the 3D mesh structure to the number of times a position of the workpiece corresponding to the one unit is scanned is equal to or larger than a predetermined threshold, the one unit is regarded as part of the workpiece are included.