We compute the electrostatic potential at the surface, or zeta potential \(\zeta\), of a charged particle embedded in a colloidal suspension using a hybrid mesoscopic model. We show that for weakly perturbing electric fields, the value of \(\zeta\) obtained at steady state during electrophoresis is statistically indistinguishable from \(\zeta\) in thermodynamic equilibrium. We quantify the effect of counterions concentration on \(\zeta\). We also evaluate the relevance of the lattice resolution for the calculation of \(\zeta\) and discuss how to identify the effective electrostatic radius.