The geometry of rails and armature is one of the most important parameters considered while designing a railgun. Optimized designs reduce the unnecessary loss of energy in the railgun, thus imparting higher kinetic energy to the projectile. This article proposes a new filleted and tapered rail geometry for a railgun and analyzes the improvements obtained by the geometry change with the existing conventional railgun geometry. A pulse-forming network consisting of cable resistances is designed to input the same energy in to the conventional and new railgun geometries. An electromagnetic-mechanical coupled analysis is performed using LS-DYNA to determine the parameters of the railguns. Breech voltages and breech energy are calculated to determine the barrel efficiency and total system efficiency. Compared to conventional electromagnetic railgun (EMRG), the new railgun results in a 3% larger Lorentz force, 9.2% greater exit velocity, and an improved barrel efficiency and total system efficiency.