First principle calculations of H-1 and C-13 NMR chemical shift calculations for un-, mono- and fully-hydrogenated fullerene cages (C-n, CnH, CnHn and CnHn+1, n = 20, 40, 58, 60) are investigated using density functional theory with B3LYP exchange-functional and applying basis set 6-31G(d, p). The results demonstrate that the C-13 NMR chemical shifts are capable of distinguishing between the un-, mono- and fully-hydrogenated fullerene cages, however the H-1 NMR chemical shifts are able to distinct between the three different positions of hydrogen atoms with small fullerene cages: the hydrogen atom located at the center of the fullerene cage, the bonded hydrogen atom to carbon atom and the H-2 molecule located outside the fullerene cages. For comparison, our calculated H-1 NMR and C-13 NMR chemical shift spectra are compared with available experimental results. (C) 2015 Elsevier B.V. All rights reserved.