Hydro-fracturing is a routine industrial technique whose safety depends on fractures remaining confined within the target rock volume. Both observations and theoretical models show that pockets of fluid can propagate large distances in the Earth's crust, in a self-sustained, uncontrolled manner, providing that the fluid volume is large enough. Existing models that describe when self-sustaining ascent starts are difficult to use for predictions, as they are mostly twodimensional (2D) and depend on parameters (typically the fracture length) that are hard to assess, even a posteriori.Here we constrain, both analytically and numerically in three-dimensions (3D), scale-independent critical volumes as a function of only rock and fluid properties. We apply our model to laboratory, industrial and natural settings, showing that our critical volumes are consistent with observations and can be used as a conservative estimate in geological applications. We find typical injection volumes exceed the limit we define for the start of self-sustaining fracture ascent. We describe a number of other processes that may work to arrest fractures with volumes exceeding this limit.This appears to have resulted in a false sense of operational safety when working with large injection volumes. In Non-peer reviewed EarthArXiv preprint the context of our findings we outline the quantitative work that would be required to better elucidate the processes causing fracture arrest, which could help to assess more comprehensively the safety of such operations.