Cloud computing allows for vast computational resources to be leveraged quickly and easily in bursts as and when required. Here we describe a technique that allows for Monte Carlo radiotherapy dose calculations to be performed using GEANT4 and executed in the cloud, with relative simulation cost and completion time evaluated as a function of machine count. As expected, simulation completion time decreases as 1/n for n parallel machines, and relative simulation cost is found to be optimal where n is a factor of the total simulation time in hours. Using the technique, we demonstrate the potential usefulness of cloud computing as a solution for rapid Monte Carlo simulation for radiotherapy dose calculation without the need for dedicated local computer hardware as a proof of principal.