Many volcanic hazard factors--such as the likelihood and duration of an eruption, the eruption style, and the probability of its triggering large landslides or caldera collapses--relate to the depth of the magma source. Yet, the magma source depths are commonly poorly known, even in frequently erupting volcanoes such as Hekla in Iceland and Etna in Italy. Here we show how the length-thickness ratios of feeder dykes can be used to estimate the depth to the source magma chamber. Using this method, accurately measured volcanic fissures/feeder-dykes in El Hierro (Canary Islands) indicate a source depth of 11-15 km, which coincides with the main cloud of earthquake foci surrounding the magma chamber associated with the 2011-2012 eruption of El Hierro. The method can be used on widely available GPS and InSAR data to calculate the depths to the source magma chambers of active volcanoes worldwide.