In this study, we demonstrated the relationship between the phase diagrams and the electrical properties of (Bi1/2Na1/2)TiO3 (BNT)-based solid solutions. In this study, (1-x)(Bi1/2Na1/2)TiO3-xNaNbO(3) and (1-x)(Bi1/2Na1/2)TiO3-xKNbO(3) (abbreviated to BNT-NN100x and BNT-KN100x) ceramics were prepared by a conventional ceramic fabrication process, and (1-x)(Bi1/2Na1/2)TiO3-x(Bi1/2K1/2)TiO3 (abbreviated to BNKT100x) ceramic was prepared for comparison. We revealed the phase transition temperatures, such as the depolarization temperature T-d, rhombohedral-tetragonal phase transition temperature TR-T, and the temperature T-m of the maximum dielectric constant, from the temperature dependence of dielectric properties using poled and unpoled specimens. As a result, it was shown that the BNT-based solid solutions form three types of phase diagrams. In addition, we clarified the relationship between the phase diagrams and the electrical properties of BNT-NN100x, BNT-KN100x, and BNKT100x. The piezoelectric properties were markedly enhanced when TR-T shifted to a lower temperature, and a large piezoelectric constant d(33) of 168 pC/N was obtained at the morphotropic phase boundary (MPB) between the ferroelectric rhombohedral and ferroelectric tetragonal phases for BNKT100x. Although the piezoelectric properties almost disappeared when T-d shifted to room temperature, the field-induced strain S and the normalized strain d(33)(*) (=S-max/E-max) abruptly increased to 0.22% and 259 pm/V, respectively, for BNT-NN100x. In particular, a very large reversible strain of S=0.40 with d(33)(*)=498 pm/V was obtained at the MPB between the ferroelectric rhombohedral and ferroelectric relaxor with pseudocubic (tetragonal) phases for BNT-KN100x. This very large reversible strain was clarified to be due to non-180 degrees (71 degrees and 109 degrees) domain switching of the field-induced ferroelectric rhombohedral phase.