The determination of eruptive parameters is crucial in volcanology, not only to document past eruptions, but also for tephra fallout hazard assessments. In most tephra fallout studies, eruptive parameters have been determined either by empirical techniques or analytical models, but the uncertainty of such parameters is usually not well described. We have applied both empirical and analytical models to characterize the climactic phase of the 2450 BP Plinian eruption of Pululagua (BF2 layer) and explore the variations in the total erupted mass, column height and total grain size distribution. Both approaches yield comparable results in the total mass of tephra erupted (4.5 ± 1.5 × 1011 kg), while they show some discrepancies for the determination of the column height (36–20 km from empirical techniques and 30–20 km from analytical techniques). The total grain size distribution of the BF2 layers varies with the different techniques used for the calculation and significantly affects the outputs of analytical models. Furthermore, the determination of the total grain size distribution depends strongly on the number and spatial distribution of the sample location. Inverting tephra fallout deposits on the total accumulation (or thickness) gives a good constraint on the total mass erupted but not on the column height. However, inverting on individual grain size classes better constrains the possible range of column heights (but cannot resolve particle release height). Results from the inversion on individual grain size classes show that large diffusion coefficients are necessary to model the BF2 layer and might be required to model proximal tephra deposits in order not to overestimate the total erupted mass. Additionally, we used a statistical method (smoothed bootstrap approach) to quantify the uncertainty in eruptive parameters such as column height and total erupted mass. Our uncertainty analysis yields a mean total erupted mass of 4.5 ± 0.3 × 1011 kg and a mean column height of 30 ± 3 km. Results from the uncertainty analysis compare well with results from other approaches. Finally, although the climactic phase of the 2450 BP Plinian eruption of Pululagua occurred in relatively calm atmospheric conditions, our results show that the dispersion of the BF2 layer was influenced by slight northeasterly wind conditions.