Topic overview

Start with the big picture

Set up an alligation grid by placing the higher and lower strengths on the left and the desired strength in the center. Diagonal subtraction gives the relative parts: the difference between the higher and desired strengths, and between the desired and lower strengths. Scale those parts to the total quantity required, then convert each part into an actual mass or volume. Before setting up the grid, express all strengths in common units; for alcohol, convert proof to % v/v by dividing proof by two. Alligation assumes additive masses or volumes and a linear relationship between concentration and strength. These assumptions suit dilute solutions and solids, but may not hold when liquid densities differ significantly or potency depends nonlinearly on concentration. A parts-based verification can help identify calculation errors.