We are developing a model called CLEO, a type of “Superdroplet Model” (SDM) for cloud microphysics, to try to overcome some of the issues faced by climate models which are caused by errors in cloud modelling. Here we describe the equations for cloud microphysics CLEO uses and how we solve them, such as to see how water-droplets move around and grow/shrink in the atmosphere. We also provide some demonstrations of the microphysical processes we model to show that CLEO works as intended.