Alligation Calculator

Mix two solutions of different concentrations to achieve a target intermediate concentration using alligation ratios. This calculator gives you the proportion and actual volumes needed. Essential for pharmacy compounding, lab solution preparation, and any mixing by concentration.

Lower concentration solution

Higher concentration solution

Desired intermediate concentration

If specified, calculate actual volumes

ALLIGATION METHOD: 1. CONCENTRATION DIFFERENCES: Part of higher = Target - Lower Part of lower = Higher - Target 2. FORMULA: Ratio = Part Lower : Part Higher = (Target - Lower conc) : (Higher - Target conc) 3. FOR SPECIFIC VOLUME: Total parts = Part Lower + Part Higher Vol Lower = Target Vol × (Part Lower / Total parts) Vol Higher = Target Vol × (Part Higher / Total parts) 4. VERIFICATION: Check: (Vol1 × C1 + Vol2 × C2) / (Vol1 + Vol2) = Target
Example: Mix 5% and 20% solutions to get 10% 1. Target (10%) is between 5% and 20% - valid 2. Part of high = 10 - 5 = 5 parts of 20% 3. Part of low = 20 - 10 = 10 parts of 5% 4. Ratio = 10:5 = 2:1 For 300 mL: - Total parts = 10 + 5 = 15 - Part size = 300/15 = 20 mL - Use 10 × 20 = 200 mL of 5% - Use 5 × 20 = 100 mL of 20% - Total: 300 mL at ~10% Verification: (200×5 + 100×20)/300 = (1000+2000)/300 = 3000/300 = 10%

What is an alligation calculator?

Alligation is a method for mixing solutions of different concentrations to get a desired intermediate concentration. The alligation ratio tells you how much of each stock solution to combine. It's widely used in pharmacy, chemistry, and food preparation when you need a specific concentration but only have other concentrated forms.

How does the alligation method work?

The alligation method is "allegation" or "alligation"—the ancient proportion method. Steps: (1) Write concentrations: lower, higher, target in a diamond pattern. (2) Calculate differences: target minus lower = part of higher, higher minus target = part of lower. (3) The parts give the mixing ratio. For example, target 10% from 5% and 20%: 10-5=5 parts 20%, 20-10=10 parts 5%, ratio 10:5 or 2:1.

What if I need a specific final volume?

Once you have the ratio (say 2:1 for 5%:20% → 10%), scale to your volume. If you need 300 mL: total parts = 2+1=3, divide 300 mL by 3: 100 mL per part. Use 2×100=200 mL of 5%, 1×100=100 mL of 20%, total 300 mL at ~10%. The slight error comes from volume changes on mixing—usually negligible.

Can I use more than two solutions?

Yes, the method extends. With three solutions, you might mix two at one ratio, then mix that result with the third. For complex requirements, you can iteratively use alligation. Many pharmacy compounding problems use just two stock solutions, though.

What applications use alligation?

Pharmacy: making specific-percent solutions from concentrates. Chemistry: diluting stock solutions. Food: adjusting recipe concentrations. Industrial: mixing chemical solutions. The method is universal for any concentration blending where precise ratios matter.

Does alligation account for volume changes?

Alligation assumes volumes are additive (which is approximate). Exact mixing sometimes has slight contraction or expansion, especially with water/alcohol. For most purposes this is fine—it's precise enough. For very precise work, measure final concentration with a refractometer or titration and adjust.

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