In this study, the effects of hydrostatic pressure ranges from 0 Gpa to 20 Gpa on detailed pressure induced computations of Barium Zirconate BaZrO3, including initial geometry optimization, energy minimization calculations, total energy values, lattice parameters, energy band gaps (Eg), optical and elastic constants are reported. All subjected computational results are collected by applying Local Density Approximation functional proposed by Ceperley-Alder and reformulated by Perdew-Zunger (LDA-CAPZ) using Cambridge Serial Total Energy Package (CASTEP) module under the formulation of Density Function Theory (DFT). The reduced nature of cell volume as well as lattice constants confirm the structural compressibility of BaZrO3 under the application of applied pressure. Increasing bulk modulus values indicate maximum structural stiffness of BaZrO3 under applied pressure. The collected values are compared with available theoretical and experimental parameters. The investigated band structures predict direct bandgap of BaZrO3, that increase under the influence of applied pressure which tend to increase all optoelectronic behavior. So, the current investigation signifies, that these calculations provide a baseline for new researchers to establish further pressure investigations and could be helpful for the uses of BaZrO3 in optoelectronic applications.