Centrality determination remains one of the major sources of systematic uncertainty in intermediate-energy heavy-ion collision analyses, especially for probing the nuclear equation of state (EOS) at suprasaturation densities, to quantitatively assess the uncertainties associated with different centrality determination methods, and to investigate their effects on final-state EOS-sensitive observables. Within the ultrarelativistic quantum molecular dynamics model, $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=2.4$ GeV are performed within a soft and a hard EOS. Event centrality is determined using the multiplicity of all charged particles ($M_{\mathrm{ch}}$) and two impact parameter-based centrality filters, one based on a geometrical interpretation and the other based on the Glauber Monte Carlo (MC) model, denoted as $b_f$ and $b_r$, respectively. It is shown that there exist significant differences between the real impact parameter distributions of event samples selected by $M_{\mathrm{ch}}, b_f$, and $b_r$, particularly between $M_{\mathrm{ch}}$ and $b_r$. When the $b_f$ is employed, uncertainties associated with centrality selection have a weaker influence on observables than the effects induced by the EOS. In contrast, when the $b_r$ is used, the influence of centrality-related uncertainties becomes more pronounced than that of the EOS. These results demonstrate that a rigorous and consistent mapping between $M_{\mathrm{ch}}$ and impact parameter is essential to impose quantitative constraints on the high-density nuclear EOS. Furthermore, our study indicates that the geometrical interpretation of centrality remains valid and consistent with dynamical multiplicity selection, whereas the Glauber MC-based centrality determination becomes unreliable at the investigated energy.

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• Charged-particle multiplicity
• Collective flow
• Equations of state of nuclear matter
• Nuclear reactions
• Relativistic heavy-ion collisions
• Transport in heavy-ion collisions