Waves and water level setup during storms can create overwashing flows across barrier islands. Overwashing flows can cause erosion, barrier breaching, and inlet formation, but their sediments can also be deposited and form washover fans. These widely different outcomes remain difficult to predict. Here we suggest that a breach develops when the sediment volume transported by overwashing flows exceeds the barrier subaerial volume. We form a simple analytical theory that estimates overwashing flows from storm characteristics, barrier morphology, and dune vegetation, and which can be used to assess washover deposition and breaching likelihood. Our theory suggests that barrier width and storm surge height are two important controls on barrier breaching. We test our theory with the hydrodynamic and morphodynamic model Delft3D as well as with field observations of 21 washover fans and 6 breaches that formed during hurricane Sandy. There is reasonable correspondence for natural but not for developed barrier coasts, where traditional sediment transport equations do not readily apply. Our analytical formulations for breach formation and overwash deposition can be used to improve long-term barrier island models.