Cell division concludes with cytokinesis, the physical division of the parent cell into two daughter cells. In fungal and animal cells, the constriction of a tensile actomyosin ring features prominently in cytokinesis. This ring constriction is widely thought to drive cell cleavage. However, other processes also occur concurrently such as cortical flow, membrane addition at the furrow, and the inward growth of new cell wall (septum) in the wake of the constricting ring in cell-walled organisms such as fission yeast. Thus, the ultimate goal is a quantitative model of ring constriction coupled with these processes. Here I will describe our progress towards this goal using experimental measurements of cytokinetic ring tension and mathematical modeling To measure ring tension, we used a novel method that combines membrane tension measurements with images of the cytokinetic furrow in live fission yeast protoplasts, cells that lack a cell wall. We measured a ring tension of ~400 pN. We used this in a mathematical model of septum cell wall growth, mediated by the cell wall growing beta-glucan synthases (Bgs) which we hypothesized were mechanosensitive (Thiyagarajan et al., 2015). The stochastic growth produced by Bgs resulted in rough edges with growth defects. In simulations, ring tension modulated Bgs growth rates in a curvature-dependent fashion, suppressing defects and roughness so septum edges were nearly circular. Simulated edges had low roughnesses (~5%) and a roughness exponent ~0.5, consistent with septum edges we measured in live cells. Our model revealed a mechanosensitivity ~15% per pN per Bgs complex. Thus, ring tension regulates septum growth to ensure the septum closes as a shrinking circle (not a slit) and daughter cells are properly sealed by new cell wall. However, ring tension has little effect on the constriction rate which is set by the septum growth machinery.