The determination of the electronic states of single-walled carbon nanotubes (SWNTs) with a specific chirality has been a central issue in the science of SWNTs. Here we present the empirical equations with fitting parameters for the determination of the reduction and oxidation potentials of SWNTs for a wide range of diameters and chiral angles. In these equations, a distinct chirality family dependence of the reduction potentials is observed, while the oxidation potentials show a simple diameter dependence nearly proportional to the inversed nanotube diameter. Based on observations of the asymmetric chirality dependence between the reduction and oxidation potentials, the Fermi levels of the SWNTs were revealed to have a definite chirality family dependence, which indicates that the work functions of the SWNTs with small diameters deviate from the values for the large diameter SWNTs and graphene. We also performed quantum chemical calculations to compare the experiment to the calculations.