Halide perovskites are promising photovoltaic, solar cell, and semiconductor materials. Density-functional theory (DFT) models address compressive and tensile biaxial strain effects on APbCl3, where A = (K, Rb, and Cs). This research shows how A-cation impacts bandgap energy and band structure. The direct bandgap for KPbCl3, RbPbCl3, and CsPbCl3 is found 1.612, 1.756, and 2.046 eV, respectively; increases from A = K to Cs. When spin–orbital coupling (SOC) is introduced, bandgaps in KPbCl3, RbPbCl3, and CsPbCl3 perovskites are reduced to 0.356, 0.512, and 0.773 eV, respectively. More tensile strain widens the bandgap; compressive strain narrows it. Without SOC, the bandgaps of KPbCl3, RbPbCl3, and CsPbCl3 were tuned from 0.486 to 2.213 eV, 0.778 to 2.289 eV, and 1.168 to 2.432 eV, respectively. When the compressive strain is increased, the dielectric constant of APbCl3 decreases (redshift) and increases (blueshift) as the tensile strain is increased. Strain improves APbCl3 perovskite’s optical performance.