Raman scattering and optical absorption spectroscopy are used for the chirality characterization of HiPco single wall carbon nanotubes (SWNTs) dispersed in aqueous solution with the surfactant sodium dodecylbenzene sulfonate. Radial breathing mode (RBM) Raman peaks for semiconducting and metallic SWNTs are identified by directly comparing the Raman spectra with the Kataura plot. The SWNT diameters are calculated from these resonant peak positions. Next, a list of (n, m) pairs, yielding the SWNT diameters within a few percent of that obtained from each resonant peak position, is established. The interband transition energies for the list of SWNT (n, m) pairs are calculated based on the tight binding energy expression for each list of the (n, m) pairs, and the pairs yielding the closest values to the corresponding experimental optical absorption peaks are selected. The results reveal (1, 11), (4, 11), (5, 12), and (5, 9) among the most probable chiralities for the semiconducting nanotubes. The results also reveal that (4, 16), (6, 12) and (8, 8) are the most probable chiralities for the metallic nanotubes. Directly relating the Raman scattering data to the optical absorption spectra, the present method is considered the simplest technique currently available. Another advantage of this technique is the use of the, E11S, E33S, and E22M peaks in the optical absorption spectrum in the analysis to enhance the accuracy in the results.