Diradical character and excited-state aromaticity serve as guidelines to identify molecules that show nonlinear optical properties. Cumulenes are known to have small singlet-triplet gaps resulting in significant diradical character. Herein, we report a computational investigation on the electronic structure and excited-state properties of cumulenes of different lengths and with various terminal carbene groups. Intriguingly, cumulenes with an even number of cumulative double bonds, which barely have been studied experimentally, are predicted to be thermodynamically more stable than their odd counterparts. We propose that this is due to the stabilizing effect of electron delocalization in the helical Mobius-type frontier orbitals. Accordingly, we delineate how to control the energies of the excited states by the choice of carbene and length of the cumulene. We find that pi-acceptor carbenes decrease the diradical character, whereas donors as well as captodative substitution or potentially biscationic charge leads to an open-shell ground state. We also predict that bent allenes are better in stabilizing organic radicals than carbenes. Eventually, we identify suitable candidates for experimental endeavors toward new singlet fission molecules.