Circular treemaps provide an efficient approach for visualization of hierarchical data. This article presents variational circular treemaps with a layout algorithm by solving disk packing as a continuous optimization problem. Compared with the traditional circular treemaps, variational circular treemaps can achieve a higher space utilization ratio, and support natural interactions for data navigation, including focus+context distortions and drill-down and roll-up operations. Experimental results show the effectiveness of the presented method for visualization and interaction.