A programming device includes an information storage unit that stores, in association with identification information assigned to a tool, coordinate conversion information used to convert a coordinate value in a rotating coordinate system into a coordinate value in a reference coordinate system, an execution command generation unit that generates a coordinate conversion execution command based on the coordinate conversion information stored in association with the identification information, and a programming unit that creates a coordinate conversion program including the coordinate conversion execution command generated by the execution command generation unit.

In a numerical controller that controls a machine tool having a plurality of driving axes, coordinate system conversion processing for a machining program is performed in which the machining program is analyzed and then an instruction based on a right-handed coordinate system and an instruction based on a left-handed coordinate system are interchanged.