Alligation Calculator (mix two strengths to a target %: parts and amounts)

Understanding the alligation calculator — concept and principle

Alligation is a quick method, long used in pharmacy, for mixing two strengths of a product to get a strength in between. This calculator gives the parts and the actual amounts of the stronger and weaker products needed for a desired total.

Each strength is used in proportion to how far the other is from the target: 20 parts of 95% to 25 parts of 50%.

How it is calculated

Parts of the stronger = desired − weaker.
Parts of the weaker = stronger − desired.
Amount of each = total × its parts ÷ (sum of parts).
This is the same as the mass balance Cs·Vs + Cw·Vw = Ct·(Vs + Vw).

The principle

Mixing averages the concentrations, weighted by amount. To land on the target, each strength must be used in proportion to how far the other one is from the target: the farther the weaker one is from the target, the more of the stronger one you need. Writing the target in the middle of a grid and subtracting diagonally ("alligation alternate") produces exactly those proportions without algebra.

Worked example

Default inputs: stronger 95%, weaker 50%, desired 70%, total 900 mL.

Parts of the stronger = 70 − 50 = 20.
Parts of the weaker = 95 − 70 = 25.
Amount of the stronger = 900 × 20 ÷ 45 = 400 mL; share = 44.44%.
Amount of the weaker = 900 × 25 ÷ 45 = 500 mL; weaker parts per 1 part stronger = 1.25.
Check: (0.95 × 400 + 0.50 × 500) ÷ 900 = 630 ÷ 900 = 70%.

Each point is the calculator re-run with only “Total amount wanted (mL or g)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Total amount wanted (mL or g)	Amount of the stronger one
225	100
450	200
675	300
900	400
1,125	500
1,350	600
1,800	800

How to read the result

The parts can be scaled to any batch size. The method only works if the desired strength lies between the two starting strengths. Use the same basis (w/w, w/v or v/v) for all three percentages. Some liquids, such as ethanol and water, shrink slightly when mixed, so check the final volume and strength if accuracy matters.

Common mistakes

Choosing a target outside the range of the two strengths.
Mixing w/w and v/v percentages.
Treating a diluent such as water as having a strength other than 0%.
Forgetting volume contraction for alcohol–water mixtures.

Keep in mind: For medicines and compounding, follow professional standards and have calculations checked. This calculator is not a substitute for a pharmacist's verification.

Frequently asked questions

How does alligation work?

Subtract diagonally: stronger parts = target − weaker, weaker parts = stronger − target.

Can I use alligation to dilute with water?

Yes. Enter 0% as the weaker strength.

Why is it called alligation alternate?

Because the differences are written alternately (diagonally) against the opposite strength.

Sources: Ansel, H. C., Pharmaceutical Calculations, 15th ed. Wolters Kluwer · United States Pharmacopeia, General Chapter <1160> Pharmaceutical Calculations in Pharmacy Practice

Checked 9 Nov 2026. Alligation alternate (mixing two strengths) as taught in pharmaceutical calculations; it follows directly from the conservation of solute, C₁V₁ + C₂V₂ = C(V₁ + V₂) — standard method.

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