Traditional trial calculation method for the sill height and depth of stilling pool for energy dissipation is burdensome, and in particular, the calculation of submergence coefficient requires repeated check. In view of this, in the light of dimensionless principle, a simple analytical solution to submergence coefficient is given through mathematical deduction and numerical analysis in MatLab. The solution is of high precision with the maximum relative error only 0.405%, favorable for engineering application. Moreover, the analytical formula of conjugate water depth after jump with dimensionless unit width discharge parameter λ is given, and a concise analytical formula of dimensionless sill height is also presented. In addition, the two-dimensional surface diagram of dimensionless sill height with dimensionless unit width discharge, downstream water depth, and stilling pool’s depth are obtained. The calculation formula for the extreme value of sill height under the most unfavorable energy dissipation condition is also given. The depth of stilling pool and sill height displays an approximate negative linear relation, which is affected by submergence coefficient and dimensionless parameter K. Two engineering calculation examples verify that the formulas proposed in this paper are highly precise and convenient.