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Alligation Calculator

Chemistry

Calculate mixing proportions of two solutions with different concentrations to achieve a desired intermediate concentration using the alligation method. Pharmacy and chemistry tool.

10 %
%
2 %
%
5 %
%
1,000 mL
mL

Volume of Higher Conc. Solution (mL)

375
Volume of Lower Conc. Solution (mL)
625
Parts of Higher Conc. Solution
3
Parts of Lower Conc. Solution
5

Breakdown

How the total splits

Volume of Higher Conc. Solution (mL)
375
Volume of Lower Conc. Solution (mL)
625

This calculator computes your Volume of Higher Conc. Solution (mL), Volume of Lower Conc. Solution (mL), Parts of Higher Conc. Solution, Parts of Lower Conc. Solution from the values you enter.

Inputs
Higher Concentration (C₁)Lower Concentration (C₂)Target Concentration (C_target)Total Volume Required
Outputs
Volume of Higher Conc. Solution (mL)Volume of Lower Conc. Solution (mL)Parts of Higher Conc. SolutionParts of Lower Conc. Solution

What is a Alligation?

The Alligation Calculator determines the exact volumes of two solutions at different concentrations that must be mixed to achieve a specified intermediate concentration. Using the alligation alternate method — a classic pharmacy and chemistry calculation — it takes the concentrations of a higher-strength and lower-strength solution plus a target concentration, and computes precisely how many mL of each are required to make any desired total volume.

Alligation is indispensable whenever two stocked solutions bracket the target concentration and direct dilution from a single stock won't produce the required strength. A hospital pharmacist preparing a custom glucose drip from 5% and 50% dextrose to reach 10% uses alligation. A compounding chemist blending 70% and 40% ethanol to prepare a 60% topical solution uses alligation. A chemical plant mixing two process streams of different acid concentrations to achieve a reactor feed specification uses alligation.

The method avoids algebraic setup by using a geometric cross arrangement to directly read off the parts. It is faster and less error-prone than setting up mass balance equations, especially when working quickly in a pharmacy dispensing environment or on a production floor. For the simpler case where one component is pure water, the Solution Dilution Calculator or Dilution Factor Calculator may be more direct — but alligation is the correct tool when both components contain active substance.

The alligation alternate method is part of the standard syllabus in B.Pharm and D.Pharm programmes at Indian universities, covered under Pharmaceutical Calculations. It also appears in GPAT preparation material, making this calculator useful for both clinical compounding and exam practice.

How to use this Alligation calculator

  1. Identify your two stock solutions and their concentrations. Enter the higher-concentration value (e.g. 10%) in the Higher Concentration (C₁) field.
  2. Enter the lower-concentration value (e.g. 2%) in the Lower Concentration (C₂) field. This may be 0% if one component is pure water or diluent.
  3. Enter the desired intermediate concentration (e.g. 5%) in the Target Concentration (C_target) field. It must lie between C₁ and C₂.
  4. Enter the total volume of the finished blend you need to prepare in the Total Volume Required field (in mL).
  5. Read Volume of Higher Conc. Solution and Volume of Lower Conc. Solution — measure out these exact volumes using calibrated cylinders and combine them.
  6. Verify the result: the pie chart shows the proportion of each component visually. Check that the two volumes sum to your specified total volume before committing to a large-batch preparation.

Formula & Methodology

Alligation alternate rule:

Parts of C₁ (higher) = C_target − C₂ Parts of C₂ (lower)  = C₁ − C_target Total parts           = (C_target − C₂) + (C₁ − C_target) = C₁ − C₂

Volume calculation:

V_high = [Parts C₁ / Total Parts] × V_total V_low  = [Parts C₂ / Total Parts] × V_total

Verification (must equal C_target):

C_blend = (V_high × C₁ + V_low × C₂) / V_total

Worked example — preparing 5% povidone-iodine from 10% and 2% stocks:

A ward needs 1,000 mL of 5% w/v povidone-iodine surgical scrub, and the pharmacy stocks 10% and 2% solutions.

Parts of 10% solution = 5 − 2 = 3 parts Parts of 2% solution  = 10 − 5 = 5 parts Total parts = 3 + 5 = 8 parts  V_high (10%) = (3/8) × 1,000 = 375 mL V_low  (2%)  = (5/8) × 1,000 = 625 mL

Verification: (375 × 10 + 625 × 2) / 1,000 = (3,750 + 1,250) / 1,000 = 5,000/1,000 = 5% ✓

Mix 375 mL of 10% povidone-iodine with 625 mL of 2% to produce 1,000 mL of 5% solution. For the Mixing Ratio Calculator, these volumes correspond to a 3:5 ratio (375 mL : 625 mL) of the two components.

Frequently Asked Questions

Alligation is a mathematical method for determining the proportions in which two solutions of different concentrations must be mixed to produce a desired intermediate concentration. It avoids the need to set up algebraic equations by using a geometric arrangement (the alligation cross) to read off the required parts directly. Alligation is widely used in pharmacy compounding, hospital dispensing, and industrial chemical blending wherever two concentrations need to be blended to a specific target.
Alligation alternate is the most commonly used form of alligation. It determines the ratio of volumes needed when mixing two solutions (one above the target concentration, one below) to achieve an intermediate concentration. The rule is: Parts of the higher-concentration solution = Target − Lower Concentration; Parts of the lower-concentration solution = Higher Concentration − Target. These parts, when expressed as volumes, give the correct mixing proportions.
Alligation medial is used to find the resulting concentration when you mix two solutions in known quantities — it is the inverse problem. Alligation alternate is used when the resulting concentration is specified and the mixing volumes are unknown. The Alligation Calculator uses the alternate method: you specify concentrations and a target, and the tool gives you the volumes to use.
Parts of higher-concentration solution: p₁ = C_target − C_low. Parts of lower-concentration solution: p₂ = C_high − C_target. Volume of each = (parts / total parts) × total volume required. The resulting blend concentration can be verified by: C_blend = (V₁ × C₁ + V₂ × C₂) / (V₁ + V₂), which should equal the target concentration to within rounding precision.
Dilution (C₁V₁ = C₂V₂) always mixes a solution with pure water (or a zero-concentration diluent) to reduce concentration. Alligation mixes two solutions both of which may have a non-zero concentration, and the target concentration lies between them. If your lower-concentration solution is pure water (0%), alligation and dilution give identical answers. For any case where both components have active substance, alligation is the correct method.
Use alligation when you need a specific intermediate concentration and have two stocks — one above and one below the target — and do not want to set up an algebraic equation. Common scenarios include: diluting 70% ethanol with 40% ethanol to get 60%; blending 10% w/v povidone-iodine with 2% w/v to achieve 5%; or mixing 15% and 5% glucose IV solutions to give 10%. When one component is pure water, the [Solution Dilution Calculator](/solution-dilution-calculator/) may be simpler.
Enter the concentration of your more concentrated solution in the 'Higher Concentration (C₁)' field (in %). Enter the concentration of your less concentrated solution in the 'Lower Concentration (C₂)' field. Enter the desired intermediate concentration in the 'Target Concentration (C_target)' field. Enter the total volume of blend you need in 'Total Volume Required' (mL). The calculator gives you the exact mL of each component and the ratio of parts.
Standard alligation alternate handles exactly two components. For three or more components, the problem requires linear programming or matrix methods, as there is no unique solution — multiple combinations can achieve the target. In practice, three-component blending is handled by fixing one ratio and applying two-component alligation to the remaining pair, or by using algebraic methods. This calculator is designed for the common two-component case.
Yes — alligation is a standard topic in B.Pharm, D.Pharm, and Pharm.D curricula across India, covered under Pharmaceutical Calculations and Compounding subjects. It appears in GPAT (Graduate Pharmacy Aptitude Test) and state-level pharmacy entrance examinations. The method is taught using both the cross diagram and algebraic approach, with the alligation cross being the faster method for multiple-choice exam contexts.
Common Indian pharmacy applications include: mixing 70% v/v Industrial Methylated Spirit (IMS) with 40% v/v spirit to get 60% for a hand sanitiser; blending 10% w/v povidone-iodine solution with 2% w/v to prepare 5% w/v surgical scrub; combining different-strength dextrose IV solutions (5% and 50%) to prepare 10% or 25% glucose drips; and diluting 15% salicylic acid lotion with a 2% base to achieve 5% for keratolytic preparations.
The alligation alternate method is only valid when the target concentration lies strictly between the two stock concentrations (C_low < C_target < C_high). If the target equals either stock concentration, you simply use the matching stock solution directly. If the target is above the high concentration or below the low concentration, you cannot achieve it by mixing these two stocks — you need a higher or lower-concentration stock. The calculator enforces this constraint and clamps the target within the valid range.
Alligation alternate is mathematically identical to the lever rule used in binary phase diagrams (e.g. VLE diagrams in chemical engineering). In a phase diagram, the relative amounts of two phases at a given overall composition are determined by the inverse-lever-arm principle — exactly the same cross method as alligation. Students familiar with one method can directly apply the same calculation to the other context.