This paper presents a design procedure for a face gear and pinion used in a handpiece with a $160^{circ}acute{y}$ contra angle and 1:2 gear ratio. Based on the geometric theory of gearing, the tooth profile of the face gear and pinion is developed. To analyze the contact pressure, the gear profile should be determined before calculating the stress between the two gears. The concept of calculating the face gear profile is that it can be generated by the coordinate transformation of the shaper profiles, which have involute curves, using a simulation method from the gear manufacturing process.