Determining whether magma fragments during eruption remains a seminal challenge in volcanology. There is a robust paradigm for fragmentation of high viscosity, silicic magmas, however little is known about the fragmentation behaviour of lower viscosity systems—the most abundant form of volcanism on Earth and on other planetary bodies and satellites. Here we provide a quantitative model, based on experiments, for the non-brittle, fluid dynamic induced fragmentation of low viscosity melts. We define the conditions under which extensional thinning or liquid break-up can be expected. We show that break-up, both in our experiments and natural eruptions, occurs by both viscous and capillary instabilities operating on contrasting timescales. These timescales are used to produce a universal break-up criterion valid for low viscosity melts such as basalt, kimberlite and carbonatite. Lastly, we relate these break-up instabilities to changes in eruptive behaviour, the associated natural hazard and ultimately the deposits formed.