In most applications of carbon nanotubes and fullerenes, molecules are attached to either external or internal surface of carbon nanotubes and fullerenes to functionalize them. Therefore, the chemical reactions on nanotubes or fullerenes play an important role in understanding how to functionalize nanotubes and fullerenes. We have analyzed and compared the chemical reactivity of both external and internal surfaces of carbon nanotubes and fullerenes. The chemical reactivity analysis can be used to control the localized functionalization process as well as to predict energies and configurations of chemical reactions. Also this analysis can be applied to examine the storage capacity of carbon nanotubes and fullerenes. The chemical reactivity of carbon nanotubes and fullerenes can be characterized by a pyramidal angle, which is defined as the angle between @sigma@ bond and @pi@ orbital minus 90 degree. We analyze the chemical reactivity in terms of pyramidal angle. All analyses have been done by total energy density functional theory pseudo-potential method, and we have used a hydrogen atom as a point probe to investigate the chemical reactivity. We have developed a way to express the chemical relativity as function of pyramidal angle. We have found that the external chemical reactivity depends strongly on the initial pyramidal angle but the internal chemical reactivity is less sensitive to it. And we have also found that the internal chemical reactivity has more complex behavior than external chemical reactivity.