New coupler Q switch rate equations were obtained by taking account that the intracavity photo density and the initial population-inversion density are both ellipse Gaussian distributed. The space dependent rate equations were solved numerically. The key parameters like maximum energy, optimized reflectivity, and optimized small signal transparency were determined under the ellipse Gaussian distribution approximation, and a group of general curves were generated for the first time. The optimal calculations for a diode laser near end pumped passively Nd:YVO4 laser was presented to demonstrate the use of the curves and related formulas, the maximal pulse energy of 1.5 ?滋J, peak power 81 W, and pulse width 18.4 ns can be obtained when small signal transparency T0 is 75% and reflectivity 91.8% after calculation. The pulse energy of 1.25 ?滋J, peak power 76.4 W and pulse width 16.3 ns was obtained by using a saturable absorber with 73.4% small signal transparency and a 87% reflector in experiments. Experiments agree with theoretical results well.