Iceberg calving accounts for around half of the ice lost annually from Antarctica, but realistic representation of fracture and calving in large-scale ice sheet models remains a major unsolved problem in glaciology. We present a new phase-field visco-elastic model for fracture. The model can capture both the long timescale visco-elastic deformation of ice, as well as the nucleation and evolution of fractures. By incorporating the effect of pore pressure into the degraded tensile energy, the model can also nucleate basal crevasses. We show that this approach is capable of simulating the physical process of calving. Numerical experiments suggest that, for a floating ice shelf with no variation across flow the calving rate for thin-end calving scales with the ice thickness to a power of around 5.5 to 9.5. The equations make no assumptions about the style of calving, and can therefore also simulate numerous more realistic settings in Antarctica for which material parameters and three-dimensional effects can be expected to influence the calving rate.