An apparatus for calculating a tool reference plane utilizes a machining plane model and an inversed tool model to create a collection of sphere regions having three dimensional grid points as their center, and identifies a nearest point on each of the model planes from the respective center point of the sphere regions. The positions within the tool reference plane can be accurately identified to the degree of the grid interval of the three dimensional grid points using the machining plane model and the inversed tool model consisting of the collection of sphere regions. By using the nearest point on each of the model planes, the position of the tool reference plane is identified using the accuracy created by the model planes. According to this apparatus, a tool reference plane can be created accurately irrespective of the shape of the machining plane model.