Alligation Calculator
Blend two strengths of the same solute to hit a target strength. Classic alligation alternate for pharmacy compounding.
Recipe
50 of 70% stock + 50 of 30% stock → 100 at 50%
Frequently asked questions
It's a centuries-old pharmacy technique formalized in 19th-century compounding texts. Mathematically it's just a weighted average solved backwards: if you have stocks at strengths H and L and want a target T, the part ratio between them is |T - L| : |H - T|. The 'alligation' visual (drawing a tic-tac-toe with the numbers) is a quick mnemonic for this.
Yes — same math. Use grams instead of mL. To make 100 g of 5% hydrocortisone ointment from 2.5% and 10% stocks: |10 - 5| = 5 parts of 2.5%, |5 - 2.5| = 2.5 parts of 10%, total 7.5 parts. 5/7.5 × 100 = 67 g of 2.5%, 2.5/7.5 × 100 = 33 g of 10%.
Yes if both stocks are in the same unit. Two stocks at 10 mg/mL and 50 mg/mL blended to make 25 mg/mL works identically — just use the numbers directly. The 'percentage' framing is convention; the math is the same for any pair of strengths in the same unit.
Three-component alligation (also called 'alligation medial' followed by an alternate step) is more complex and not always uniquely solvable. For practical compounding with three stocks, fix the proportion of one stock first, then alligation the other two against the resulting two-component problem. The tool currently supports the standard two-stock case only.
For percentages by weight/weight (w/w), no. For percentages by volume/volume (v/v), temperature and the specific solvent can change the actual blend volume slightly because alcohol-water mixing isn't perfectly additive (it contracts). For typical pharmacy compounding the math holds within ±1%; for research-grade work, account for non-ideal mixing.
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