Numerical control device

A numerical control device has: a program reading unit reading a machining program; an inclined-surface setting unit setting an inclined-surface coordinate system regarding an inclined surface; an indexing-angle generating unit calculating an indexing angle where a tool used for machining of the inclined surface is oriented perpendicular to the inclined surface, and generating a move command. The program reading unit outputs an inclined-surface setting command instructing setting of the inclined-surface coordinate system, an inclined-surface indexing command instructing calculation of the indexing angle, and a tool selection command instructing selection of any of tools respectively having different mounting angles. The inclined-surface setting unit sets the inclined-surface coordinate system according to the inclined-surface setting command. The indexing-angle generating unit calculates, according to the inclined-surface indexing command, the indexing angle regarding the tool that is selected according to the tool selection command.