We examine under what conditions cavity ring-down spectroscopy (CRDS) can be used for quantitative diagnostics of molecular species. We show that CRDS is appropriate for diagnostics of species whose absorption features are wider than the spacing between longitudinal modes of the optical cavity. For these species, the absorption coefficient can be measured by CRDS without a knowledge of the pulse characteristics provided that the cavity ring-down decay is exponential. We find that the exponential ring-down decay is obeyed when the linewidth of the absorption feature is much broader than the linewidth of the light circulating in the cavity. This requirement for exponential decay may be relaxed when the sample absorption constitutes only a small fraction of the cavity loss and, consequently, the sample absorbance is less than unity during the decay time. Under this condition the integrated area of a CRDS spectral line approximates well the integrated absolute absorption coefficient, which allows CRDS to determine absolute number densities (concentrations). We determine conditions useful for CRDS diagnostics by analyzing how the absorption loss varies with the sample absorbance for various ratios of the laser pulse linewidth to the absorption linewidth for either a Gaussian or a Lorentzian absorption line shape.