The universal variation pattern of the total energy of various fullerenes including single-walled carbon nanotubes with respect to their extra charge is revealed by the density-functional-theory calculations. The parabolic energy-charge curve with its lowest energy value corresponding to a negatively charged fullerene indicates that these carbon materials have positive electron affinity and are not in the most stable state. The positive electron affinity seems to originate from the pi-electrons and is found to be related to the aggregation property of fullerenes. (C) 2004 American Institute of Physics.