Lead-free piezoelectric ($Na_{1/2}K_{1/2}$)$NbO_3$ ceramics doped with CuO and $MnO_2$ were fabricated using the conventional oxide-mixing technique. With increasing content of CuO and $MnO_2$, the dielectric constant(${varepsilon}_{33}$) and mechanical quality factor($Q_m$) value increased, while electromechanical coupling factor($K_p$) and piezoelectric constant($d_{33}$) decreased. The piezoelectric and dielectric properties ($Na_{1/2}K_{1/2}$)$NbO_3$ ceramics doped with CuO 2.461 wt% and $MnO_2$ 0.538 wt% at sintered temperature $1050;^{circ}C$ were attained ${varepsilon}_{33}$ = 403, $K_p$ = 15, $Q_m$ = 122 and $d_{33}$ = 36 pC/N. Based on response surface methodology results using design of experiment, it was concluded that ($Na_{1/2}K_{1/2}$)$NbO_3$ doped with CuO 0.477 wt% and $MnO_2$ 0.269 wt% has possibility composition of being used for piezoelectric transformer.