First-principles calculations were performed to compare the energies of 29 different fullerene structures, with mass number from 60 to 240, and of eight nonhelical graphite tubes of different radii. A quantity called the planarity, which indicates the completeness of the pi-bonding, is the single most important parameter determining the energetics of these structures. Empirical equations were constructed for the energies of nonhelical tubes and for those fullerene structures that may be described as balls or capsules. For a given mass number, bail-shaped fullerenes are energetically favored over capsular (tube-like) fullerenes.