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/EA-EOM-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.