The fission yeast cell is shaped as a very regular cylinder ending by hemi-spheres at both cell ends. Its conserved phenotypes are often used as read-outs for classifying interacting genes and protein networks. Using Pascal and Young-Laplace laws, we proposed a framework where scaling arguments predicted shapes. Here we probed quantitatively one of these relations which predicts that the division site would be located closer to the cell end with the larger radius of curvature. By combining genetics and quantitative imaging, we tested experimentally whether altered shapes of cell end correlate with a displaced division site, leading to asymmetric cell division. Our results show that the division site position depends on the radii of curvatures of both ends. This new geometrical mechanism for the proper division plane positioning could be essential to achieve even partitioning of cellular material at each cell division.