A new electrical conductivity model is developed for unassociated electrolyte solutions based on the Debye-Hückel-Onsager theory. In this model, we assume that a single cation and a single anion with their crystallographic ionic radii are in a continuum medium of the solvent(s). We compare the predictions of the developed model with the experimental measurements of binary 1:1, 2:1, 1:2, 2:2, 1:3, 3:1, 2:3, 3:2, 3:3, 1:4, and 2:4 aqueous solutions in the temperature range 273.15-373.15 K. Our results are in good agreement with the experimental data. An extension of the model was formulated to incorporate ion pairing, and its effectiveness was evaluated across three essential systems: 2:2 aqueous sulfate solutions, ionic liquid-co-solvent systems, and NaCl-water-1,4-dioxane solutions. This adaptation demonstrated a strong correlation with experimental data, highlighting the broad applicability.