Theoretical calculations on organic amines widely used as hole-transporting materials (HTMs) in multilayer organic light-emitting diodes have been performed. The calculated I_p and the reorganization energy for hole transport (λ₊) of triphenylamine (TPA), 9-phenyl-9H-carbazole (PC), and their derivatives, are found to be related to their Hammett parameter (σ). In this study, the density functional theory (DFT) calculation is used to optimize 82 TPA and PC derivatives. Electronic structures of these compounds in the neutral and the radical-cation states are obtained based on calculations on optimized geometrical structures. The I_p and λ₊ values are derived from calculated heats of formation (or total energy) of the neutral and the radical-cation states. In particular, the calculated I_ps for these derivatives correlate well with the experimental data. The substitution effect for the mono-substituted TPA and PC is displayed in that the I_ps of the TPA and PC derivatives with electron-donating and -withdrawing substituents are lower and higher than those of TPA and PC, respectively. For the effect of substitution position, the para-substituted TPA derivatives have higher I_p and –E^HOMO than those of meta-substituted TPAs. The substitution effects in di- and tri-substituted TPAs are more pronounced than that of mono-substituted ones. According to the results, the calculated I_ps shows an excellent agreement with the experimental oxidation potentials (E_P/2) in these TPA derivatives. Furthermore, these calculation results can be employed to predict electro-luminescent properties for new and improved HTMs.