We investigate the phase stability of Na 1/2Bi 1/2TiO 3, a prototype lead-free relaxor material, under pressure. By means of total energy calculations within density functional theory, we study the pressure stability of several structures with polar and antipolar distortions, in-phase and out-of-phase tilts, and different chemically ordered configurations. Under positive (compressive) pressure an orthorhombic Pbnm-like phase is stabilized above 3GPa. At negative (tensile) pressure a non-tilted polar P4mm-like phase is stable. At zero pressure two phases are coexisting. The local chemical configuration determines whether the high-pressure Pbnm-like or another tilted and polar R3c-like structure is favored. Thus, two different variants of pressure phase diagrams depending on the cation arrangement are obtained, which raises the question of the existence of a mixed phase ground state in the disordered system. We discuss the stability of the mixed phase state in terms of lattice and tilt misfits and possible shapes and ferroic properties of the coexisting regions with different average structures. Our results clearly support the view that there are chemically ordered nanoregions with their own local ferroic properties embedded in a chemically disordered ferroelectric matrix representing the ground state. © 2012 American Physical Society.