Abstract: A forging die and a forging die manufacturing method for extruding externally or internally splined helical gears wherein the lead end face of each die tooth includes a compound angle such that the end face will have two end surfaces. One end surface will project from the crown to the lead edge of the drive side of the die tooth and the other end surface will project from the crown to the coast side of the die tooth. Each end surface projects or is formed or defined by an included angle, A or B, as the case may be, as seen in FIGS. 6 and 7, taken relative to a section through the die teeth at the plane y parallel with the vertical axis of the die which is computed to ensure that the average directional flow of the material will produce a resultant vector in a direction parallel to the die teeth at any angle upon which the helical die teeth are formed.