Abstract: This paper analyzes multistage energy dissipation using the theory of hydraulics, mathematical derivation, and numerical analysis with Matlab to simplify repeated calculations in the design of multistage dissipators of water drops or practical weirs and lay a basis for optimal design of such dissipators. First, we derive analytical formulae for calculating contracted flow depth, depth after the hydraulic jump, and jump length, among other hydraulic parameters, by applying the Cartesian solution theory of cubic equations. And for the given flow coefficient φ = 0.80, 0.85, 0.90, 0.95 and 1.0, we work out high-accuracy lookup tables and curves for calculating relative flow depth hc'/T0 and relative hydraulic jump length Lj/T0 in engineering application. Then, an analytical formula for the depth of the last stage pool is obtained using the extreme value theory of stilling pool depth. Finally, two examples are used for comparative calculation and analysis, demonstrating the accuracy and convenience of applying our formulae. This study indicates that the design scheme of a multistage dissipator adopting equal head drops may not be optimal if considering the topography, geological conditions and excavation costs of the project. Thus, a variety of head drop alternatives should be compared and optimized to save project cost.