A cutter for electrode graphite which has a shank at one end and a tool tip at the other end, and flutes extending from the shank to the tool tip, which space machining lands apart from each other in the circumferential direction. The tool tip is formed as a ball head section, in which the machining lands have a rounded contour, extending along a ball head radius. At least one of the machining lands is a rough-machining land and at least one other of the machining lands is a fine-machining land. Each machining land has a circumferential working area with a cylindrical surface-segment-shaped shell surface, the working area of each rough-machining land is a circumferential file with teeth which are worked into the shell surface of the working area, and the working area of each fine-machining land exterior grooves extends with a twist about the tool axis.