Piezoelectric materials exhibit a mechanical response to electrical inputs, as well as an electrical response to mechanical inputs, which makes them useful in sensors and actuators. Lead-based piezoelectrics demonstrate a large mechanical response, but they also pose a health risk. The ferroelectric BiFeO(3) is an attractive alternative because it is lead-free, and because strain can stabilize BiFeO(3) phases with a structure that resembles a morphotropic phase boundary. Here we report a reversible electric-field-induced strain of over 5% in BiFeO(3) films, together with a characterization of the origins of this effect. In situ transmission electron microscopy coupled with nanoscale electrical and mechanical probing shows that large strains result from moving the boundaries between tetragonal- and rhombohedral-like phases, which changes the phase stability of the mixture. These results demonstrate the potential of BiFeO(3) as a substitute for lead-based materials in future piezoelectric applications.