Despite extensive studies on size effects in ferroelectrics, how structures and properties evolve in antiferroelectrics with reduced dimensions still remains elusive. Given the enormous potential of utilizing antiferroelectrics for high-energy-density storage applications, understanding their size effects will provide key information for optimizing device performances at small scales. Here, the fundamental intrinsic size dependence of antiferroelectricity in lead-free NaNbO₃ membranes is investigated. Via a wide range of experimental and theoretical approaches, an intriguing antiferroelectric-to-ferroelectric transition upon reducing membrane thickness is probed. This size effect leads to a ferroelectric single-phase below 40 nm, as well as a mixed-phase state with ferroelectric and antiferroelectric orders coexisting above this critical thickness. Furthermore, it is shown that the antiferroelectric and ferroelectric orders are electrically switchable. First-principle calculations further reveal that the observed transition is driven by the structural distortion arising from the membrane surface. This work provides direct experimental evidence for intrinsic size-driven scaling in antiferroelectrics and demonstrates enormous potential of utilizing size effects to drive emergent properties in environmentally benign lead-free oxides with the membrane platform.