In all areas of engineering, testing full-scale models can be both costly and risky and often not necessary. The scaling laws can be implemented in electromagnetic launchers (EMLs). The objective is to obtain similar temperatures, magnetic induction, and stress fields (T, B, and S) compared to the full-size geometry. A few EML dimensions, such as its cross-section, rail separation, and length, must be scaled appropriately to obtain accurate results. Pulsed power supply (PPS) parameters require adjustments as well. However, designing a new PPS prototype requires considerable engineering time and budget. Therefore, in this study, scaling rules are studied utilizing an existing PPS. EMFY-4, a recently developed EML with a 50 x 60 mm concave bore and 6-m length, is scaled to be used with a 250 kJ capacitive PPS. A multi-objective optimization study is conducted to get the best design. The first objective is to get a minimum rail length to seek higher energy density. The second objective is to minimize the muzzle current to the peak rail current ratio for higher efficiency. The effect of armature mass, capacitor charging voltage, and the required number of PPS modules on the objective functions are discussed. The study showed that when the existing PPS is used, the scaling with the higher scaling factor, denoted as (λ), gives better results.