Gauging free carrier generation (FCG) in optically excited, charge-neutral single-walled carbon nanotubes (SWNTs) has important implications for SWNT-based optoelectronics that rely upon conversion of photons to electrical current. Earlier investigations have largely provided only qualitative insights into optically triggered SWNT FCG, due to the heterogeneous nature of commonly interrogated SWNT samples and the lack of direct, unambiguous spectroscopic signatures that could be used to quantify charges. Here, employing ultrafast pump-probe spectroscopy in conjunction with chirality-enriched, length-sorted, ionic-polymer-wrapped SWNTs, we develop a straightforward approach for quantitatively evaluating the extent of optically driven FCG in SWNTs. Owing to the previously identified trion transient absorptive hallmark (Tr-11(+) -> Tr-nm(+))) and the rapid nature of trion formation dynamics (<1 ps) relative to established free-carrier decay time scales (>ns), we correlate FCG with trion formation dynamics. Experimental determination of the trion absorptive cross section further enables evaluation of the quantum yields for optically driven FCG [Phi(E-nn -> h(+)+e(-))] as a function of optical excitation energy and medium dielectric strength. We show that (i) E-33 excitons give rise to dramatically enhanced Phi(E-nn -> h(+)+e(-)) relative to those derived from E-22 and E-11 excitons and (ii) Phi(E-33 -> h(+)+e(-)) monotonically increases from similar to 5% to 18% as the solvent dielectric constant increases from similar to 32 to 80. This work highlights the extent to which the nature of the medium and excitation conditions control FCG quantum yields in SWNTs: such studies have the potential to provide new design insights for SWNT-based compositions for optoelectronic applications that include photodetectors and photovoltaics.