Stable, homogeneous, aqueous dispersions of single-walled carbon nanotubes (SWNTs) are prepared by nonspecific physical adsorption of surfactants enhanced by sonication. Upon centrifugation, supernatant and precipitate phases are obtained. The initial weights of the SWNTs and the surfactant are divided between these two phases, and the respective SWNT concentration in each phase is unknown. The focus of this work is on the determination of the true concentration of raw, exfoliated HiPCO SWNTs in the supernatant phase. A UV-visible absorption-based approach is suggested for a direct measurement of the SWNT and the surfactant concentration in the supernatant. UV-visible absorbance spectra of SWNTs-surfactant dispersions and surfactants alone reveal that the intensity of a certain peak, attributed to the pi-plasmon resonance absorption, is unaffected by the presence of most surfactants. A calibration plot is then made by monitoring the intensity of the peak as a function of the true concentration of the exfoliated SWNTs. Thus, we are able to determine the unknown concentration of surfactant-dispersed HiPCO SWNTs in the supernatant solution, simply by measuring its optical absorbance. Moreover, we can now calculate the surfactant efficiency in dispersing SWNTs. Cryogenic-transmission electron microscopy and thermogravimetric analysis techniques are used for the characterization of these dispersions and to complement the UV-visible measurements.