In this paper, the results of an optimization study to calculate the optimal partial gear ratios of three-stage bevel helical gearboxes are presented. The objective of the study was to achieve the minimum gearbox bottom area. To implement it, a simulation experiment was conducted. In the experiment, the influence of eight main design parameters including the total gearbox ratio, the coefficients of wheel face width of three stages, the allowable contact stresses of all stages, and the output torque to the optimal transmission ratios of the analyzed gearbox. In addition, regression formulas determining the optimal gear ratios of the second stage u2 and the third stage u3 components have been given.