The geometrical and electronic structures of 44 squarate and croconate derivatives are computationally studied by quantum chemistry methods, in the pursuit of new singlet fission sensitizers. A non-negligible singlet open-shell diradical character is observed for most of the studied molecules, which can be controlled through chemical substitution as well as by the size of the central ring. Such a diradical character is related to small singlet-triplet energy gaps, facilitating the accomplishment of the singlet fission energetic requirements. In general, the present results indicate that squarates hold superior singlet fission capabilities than croconates, although we have identified several derivatives within both families as promising singlet fission sensitizers.