A Superfat Margin That Cannot Go Negative: Weighing Tolerances and Saponification Uncertainty in Home Soap Making

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. The computed lye requirement for the recipe is 150.8 grams before any discount. Saponification uncertainty alone can raise the true requirement by 3.0 percent, and adverse weighing errors add a further 1.27 percent, giving a worst-case guarantee threshold of 4.27 percent superfat. The traditional 5 percent discount therefore meets the guarantee, with little to spare for this recipe and equipment. At half batch size the threshold rises to 6.17 percent, and with a scale accurate only to 5 grams it rises to 6.87 percent. A superfat of 8 percent satisfies the worst case with a small additional allowance for spillage and residue on the weighing vessel. The proposed arrangement is as follows. The deliverable is a margin rule: compute the requirement from the recipe, add the percentage contributions of saponification uncertainty and weighing error for the equipment actually in use, and set superfat at or above the sum. A small table for three grades of scale lets a maker read off a safe figure without repeating the analysis. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.