The complete matrix parameters of the elastic, dielectric, and piezoelectric constants of high-quality Fe-doped KTa1-xNbxO3 (KTN) single crystals poled along [001]PC were successfully confirmed. The piezoelectric coefficients d33 and k33, which are of interest for various applications, are 137 pC/N and 50.4 %, respectively. The orientation dependence of these properties for the single-domain Fe:KTN samples was calculated, and it was found that the [001]PC direction is the optimal orientation for the highest performance with a single-domain state, at which the sample exhibits good transparency. Further, the single-domain sample exhibits a large effective electro-optical coefficient (γc = 126.6 p.m./V), and the combined piezoelectric and electro-optical effects provide a 0.4 % electro-optical coefficient. This is beneficial for applying high-response speed modulators with an effective electro-optical working mode and a low contribution of the inverse piezoelectric effect, owing to slower frequency response characteristics.