This paper reports an optimization study to find the optimal gear ratio of a three-stage helical gearbox to achieve the minimum gearbox bottom area. In this study, a simulation experiment was built and performed. Also, six main design parameters including the surface width coefficient of the first and second stages, the allowable contact stresses of the first and second stages, and the output torque were selected for the investigation. The influence of these parameters on the optimal gear ratios of the gearbox has been shown. Moreover, the optimal gear ratio u1 of the first stage can be easily calculated by means of a regression formula in the form of an explicit function.