Octane numbers (ON) and derived cetane numbers (DCN) are widely used as indicators to quantify the ignition qualities of gasoline- and diesel-type fuels, respectively. In this study, a chemical kinetics-based methodology is proposed for quantitatively relating ignition delay times (IDTs) to the ON and subsequently deriving correlations to predict DCN. The methodology is based on the ignition-delay-time equivalence principle, according to which fuels exhibiting ignition delay times identical to those of primary reference fuel (PRF) mixtures under well-defined RON-like thermodynamic conditions are assigned the same octane number. To assess the predictive capability of this methodology, ignition delay times of both test fuels and PRF mixtures were simulated under RON-like conditions using detailed chemical kinetic mechanisms for toluene primary reference fuels (TPRF) developed independently by various research groups. The predicted ON values were validated against experimentally measured ON data obtained using standard ASTM methods. For PRF, TRF, and TPRF blends under RON-like conditions over 30–80 bar at φ = 1.0, the best overall correlation was achieved at 40 bar, with an R2 of 0.988 and an RMSE of 1.322. The validation results confirm that the proposed kinetic modeling approach provides reliable and accurate predictions of ON, with improved accuracy correlating closely with the precision of simulated ignition delay times. Subsequently, a linear correlation between the predicted ON and DCN values, measured in accordance with ASTM D6890 standards, was established. The predicted DCN values exhibit satisfactory agreement with experimental data under the specified RON-like conditions. The developed kinetic-based methodology provides valuable theoretical insights for engine design and operation, as well as the development of future fuels.