The longitudinal polarizabilities of carbon nanotubes are determined using first principles density functional theory. These results demonstrate that the polarizability per atom of a nanotube in the axial direction is primarily determined by the band gap. In fact, polarizability per atom versus inverse band gap yields a linear trend for all nanotubes and methods utilized in this study, creating a universal relationship for longitudinal polarizability. This can be explained by examining the terms in the sum over states equation used to determine polarizability and noting that the vast majority of the polarizability arises from a few elements near the band gap. This universal trend is then used with experimentally determined band gaps to predict the experimental polarizability of carbon nanotubes.