The in-plane and out-of-plane piezoelectric properties of (001) strontium titanate (SrTiO3, STO) epitaxial thin films on pseudo-cubic (001) substrates are computed as a function of in-plane misfit strain. A nonlinear thermodynamic model is employed, which takes into account the appropriate mechanical boundary conditions, the electromechanical coupling between the polarization and the in-plane lattice mismatch, and the self-strains of the ferroelastic and ferroelectric phase transformations. The piezoelectric behavior of epitaxial STO films is described in various strain-induced ferroelectric phase fields in a temperature range from -50 to 50 A degrees C. The calculations show that by carefully tailoring in-plane misfit strains in both tensile and compressive ranges, piezoelectric coefficients that are of the order of prototypical lead zirconate titanate and other lead-based piezoceramics can be realized. These results indicate that strain engineered STO films may be employed in a variety of sensor and actuator applications as well as surface acoustic wave devices and thin-film bulk acoustic resonators.