In this paper, we apply equation-of-motion coupled cluster (EOM-CC) methods in the studies of the vertical ionization potentials (IPs) and electron affinities (EAs) for a series of single-walled carbon nanotubes (SWCNT). The EOM-CC formulations for IPs and EAs employing excitation manifolds spanned by single and double excitations (IP/EAEOM-CCSD) are used to study the IPs and EAs of the SWCNTs as a function of the nanotube length. Several armchair nanotubes corresponding to C20nH20 models with n = 2-6 have been used in benchmark calculations. In agreement with previous studies, we demonstrate that the electronegativity of C20nH20 systems remains, to a large extent, independent of the nanotube length. We also compare IP/EA-EOM-CCSD results with those obtained with coupled cluster models with single and double excitations corrected by perturbative triples, CCSD(T), and density functional theory (DFT) using global and range separated hybrid exchange correlation functionals.