In gear skiving, tool wear is one of the primary issues owing to the large thermomechanical cutting load. However, the effective rake angle and depth-of-cut can vary continuously throughout a single cut, leading to a complex uncut chip geometry that significantly hinders the understanding of the cutting characteristics and adds further difficulty to the prediction of tool wear. This study proposes a parametric modeling method for calculating the uncut chip geometry for each cutting pass. Developments in the rake angle and depth-of-cut (as subjected to an uncut chip) were comprehensively investigated with an aim to advance the understanding of the cutting characteristics during a single cut. Based on the uncut chip geometry, the crater wear was successfully predicted using the derived stress and temperature data, followed by a single-tooth skiving wear test verification. By comparing numerical and experimental results for crater wear, an error of less than 5 % was obtained in both depth and area. The proposed method provides a non-CAD/CAM-engine-software/environment-based alternative for calculating the process of an uncut chip geometry, clearly advancing the flexibility in further potential applications such as cutting parameter optimization and cutter design.