Abstract: A transmission gear has a tooth surface formed of a free-form surface instead of an involute surface and a root area formed of a free-form surface instead of a trochoid surface. With such a transmission gear, the fatigue strength against contact pressure can be increased by reducing the Hertzian stress in the area around the meshing point of the tooth surface. The tooth surface is formed of a free-form surface in which the smallest radius of curvature in an area around a mating pitch point is maximized, and the fatigue strength against bending can be increased by reducing the bending stress at a tooth root portion of the bottom land. In addition, the gear noise can be reduced. The bottom land is formed of a free-form surface in which the smallest radius of curvature in an area around a tooth root is maximized.