Abstract: The equations of conjugate depths for the channels with a parabolic cross section are implicit functions too complicated to solve directly. This study adopted identical transforms to simplify the equations of hydraulic jump in semi-cubic, square, and cubic parabola-shaped channels. Then for all these shapes, we derived dimensionless conjugate depths x and y as well as their relationship, using the fact that critical depth is between these two depths. We adopted the 1stopt software and its genetic algorithm to optimize and fit the parameters of established nonlinear models, and finally obtained direct calculation formulae of conjugate depths for all the channel shapes. Error analysis and example calculations show that the relative errors of x and y calculated by these formulae are in the ranges of 0.05% and -0.06%, 0.07% and -0.10%, and -0.0858% and 0.0985% for the semi-cubic, square, and cubic parabola-shapes respectively. The formulae are clear in physical concepts, convenient in calculation, and applicable to a wide range, and thus they would provide a theoretical basis and practical tool for design and operation management of parabola-shaped channels.