The processes that give rise to arc magmas at convergent plate margins have long been a subject of scientific research and debate. A consensus has developed that the mantle wedge overlying the subducting slab and fluids and/or melts from the subducting slab itself are involved in the melting process. However, the role of kinematic variables such as slab dip and convergence rate in the formation of arc magmas is still unclear. The depth to the top of the subducting slab beneath volcanic arcs, usually approximately 110 +/- 20 km, was previously thought to be constant among arcs. Recent studies revealed that the depth of intermediate-depth earthquakes underneath volcanic arcs, presumably marking the slab-wedge interface, varies systematically between approximately 60 and 173 km and correlates with slab dip and convergence rate. Water-rich magmas (over 4-6 wt% H(2)O) are found in subduction zones with very different subduction parameters, including those with a shallow-dipping slab (north Japan), or steeply dipping slab (Marianas). Here we propose a simple model to address how kinematic parameters of plate subduction relate to the location of mantle melting at subduction zones. We demonstrate that the location of arc volcanoes is controlled by a combination of conditions: melting in the wedge is induced at the overlap of regions in the wedge that are hotter than the melting curve (solidus) of vapour-saturated peridotite and regions where hydrous minerals both in the wedge and in the subducting slab break down. These two limits for melt generation, when combined with the kinematic parameters of slab dip and convergence rate, provide independent constraints on the thermal structure of the wedge and accurately predict the location of mantle wedge melting and the position of arc volcanoes.