that when single-wall CNTs (SWCNTs) are sorted by diameter [7-10] or atomic structure [i.e., (n,m)], [11-14] they strikingly exhibit various distinct colors in suspension. More recently, colorful SWCNT thin films were produced by a novel one-step fabrication procedure, [15] enabling the direct synthesis of colorful SWCNTs that were previously thought impossible. Despite numerous studies on SWCNT colors, the coloration mechanism has not been fully understood. Currently, no theoretical model can reliably predict the color of a given SWCNT film. Namely, predicting the range of possible SWCNT colors has not been possible, nor has explaining why SWCNTs with certain atomic structures [specified by (n,m)] display stronger colors than other CNT species. This lack of understanding largely prevents us from further elaborating the controlled synthesis of color-specified SWCNT materials. Here, we report the results of both experimental and theoretical studies providing answers to these long-standing questions. First, by studying colored thin films with varying thicknesses, we established a quantitative relationship between the obtained colors and the optical absorption spectra of the films. This relationship confirms the absorption-dominated coloration mechanism of SWCNT-based films. Based on this finding, in combination with SWCNT optical absorption studies, we constructed a comprehensive theoretical model that can describe Although single-wall carbon nanotubes (SWCNTs) exhibit various colors in suspension, directly synthesized SWCNT films usually appear black. Recently, a unique one-step method for directly fabricating green and brown films has been developed. Such remarkable progress, however, has brought up several new questions. The coloration mechanism, potentially achievable colors, and color controllability of SWCNTs are unknown. Here, a quantitative model is reported that can predict the specific colors of SWCNT films and unambiguously identify the coloration mechanism. Using this model, colors of 466 different SWCNT species are calculated, which reveals a broad spectrum of potentially achievable colors of SWCNTs. The calculated colors are in excellent agreement with existing experimental data. Furthermore, the theory predicts the existence of many brilliantly colored SWCNT films, which are experimentally expected. This study shows that SWCNTs as a form of pure carbon, can display a full spectrum of vivid colors, which is expected to complement the general understanding of carbon materials.