Piezoelectric properties of epitaxial (001) barium strontium titanate (BST) films are computed as functions of composition, misfit strain, and temperature using a non-linear thermodynamic model. Results show that through adjusting in-plane strains, a highly adaptive rhombohedral ferroelectric phase can be stabilized at room temperature with outstanding piezoelectric response exceeding those of lead based piezoceramics. Furthermore, by adjusting the composition and the in-plane misfit, an electrically tunable piezoelectric response can be obtained in the paraelectric state. These findings indicate that strain engineered BST films can be utilized in the development of electrically tunable and switchable surface and bulk acoustic wave resonators.