The GTPase dynamin polymerizes into a helical coat that constricts membrane necks of endocytic pits to promote their fission. However, the dynamin mechanism is still debated because constriction is necessary but not sufficient for fission. Here, we show that fission occurs at the interface between the dynamin coat and the uncoated membrane. At this location, the considerable change in membrane curvature increases the local membrane elastic energy, reducing the energy barrier for fission. Fission kinetics depends on tension, bending rigidity, and the dynamin constriction torque. Indeed, we experimentally find that the fission rate depends on membrane tension in vitro and during endocytosis in vivo. By estimating the energy barrier from the increased elastic energy at the edge of dynamin and measuring the dynamin torque, we show that the mechanical energy spent on dynamin constriction can reduce the energy barrier for fission sufficiently to promote spontaneous fission.