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Strength research is always one of the study focuses of face gear drives. However, a strength calculation solution, in which bending stresses, contact stresses, and bulk temperatures are included, combined with gear design standards for face gear drives, is still not constructed due to complex face gear teeth. Thus, in this study, an equivalent face gear tooth is proposed by assessment of geometric characteristics of face gear teeth and tooth contact analysis, and a strength calculation solution of face gear drives, which is based on ISO 6336 standard associated with the proposed equivalent face gear teeth, is constructed. The fidelity of the proposed strength calculation solution of face gear drives is verified by comparing its results with the benchmark of results by finite element methods. Furthermore, the impact of geometric parameters on the strength of face gear drives is investigated, and some design suggestions are extracted. These contributions would benefit the improvement of engineering applications of face gear drives.