The rapid progress in the performance of today's sophisticated transmission electron microscopes also demands computational and educational tools capable of simulating the intricacy of electron image formation. The tools ideally should be widely accessible to the microscopy community and capable of covering both the breadth and depth demanded by modern materials science. Here, a cloud-based microscopy simulation platform, called cloudEMAPS and powered by cloud computing and modern server-client web programming architecture, is described. Compared to the current desktop solutions for electron microscopy simulations, cloud computing offers the unique advantages of on-demand, data sharing, high-performance computation and internet easy access using the state-of-the-art web infrastructure. This article will demonstrate these advantages using examples of interactive simulations of electron diffraction patterns and aberration-corrected electron optics.