The design of microstrip patch antenna (MPA) demands reliable electro-magnetic interactions (EmI) to meet the antenna design requirement. The antenna array faces problem with adjustment of design parameters such as elements dimensions, shape, spacing etc. Under this scenario, mathematical approach required to be essential to design the systematic design of array. But, the realistic models of arrays are computationally expensive in providing accuracy. Thus provide low cost computation, various approaches based on meta-heuristics like particle swarm optimization, genetic algorithms are proven effective against handling of such issues of pattern synthesis i.e., existence of side lobes. But, meta-heuristics requires thousands of function to evaluate the antenna design. In this paper, accurate mathematical modelling approach is presented to design Micro strip Patch Antenna with Optimal Performance. The mathematical model (using MATLAB) includes optimization of side lobes, optimization of radiation as well as reflection responses. The performance analysis of the approach is performed by considering the radiation, reflection coefficients, operating frequency and minimization of side lobes. The simulation outcomes of the antenna design give the reduced computational cost at 10GHz micro strip patch antenna.