The Alligation Calculator determines the ratio in which two solutions of different concentrations must be mixed to produce a desired intermediate concentration. Used in pharmacy compounding, chemistry, food science, and industrial mixing — providing exact volumes needed for any target concentration.
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The calculator for alligation determines how to mix two solutions of different concentrations to produce a target concentration between the two. The alligation method is a classical calculation technique used in pharmacy, chemistry, food science, and industrial production wherever two stock solutions must be blended to a specified intermediate concentration.
For solutions with concentrations C₁ (higher) and C₂ (lower) being mixed to produce concentration C_T (target):
Example: mixing 70% ethanol and 30% ethanol to produce 50%: Parts of 70% = 50 − 30 = 20; Parts of 30% = 70 − 50 = 20; equal volumes of each. The ratio is always the difference between the target and the other component. The percent solution calculator handles concentration calculations for single-component solutions.
Alligation is taught in every pharmacy curriculum because compounding pharmacists regularly blend stock solutions to custom concentrations. Clinical applications include:
Use this online calculator for any two-component concentration mixing problem. The solution mixture calculator and mixing ratio calculator provide related tools.
The inverse problem — finding the concentration resulting from mixing known volumes — uses alligation medial:
C_result = (C₁ × V₁ + C₂ × V₂) / (V₁ + V₂)
This is a weighted average of the two concentrations. Mixing 200 mL of 70% ethanol with 300 mL of 40% ethanol produces: (70 × 200 + 40 × 300) / 500 = 52% ethanol. Note that alligation assumes ideal mixing with no volume change — for non-ideal systems like alcohol-water, actual concentrations should be verified by measurement.
Beyond pharmacy, alligation appears in food production (blending beverages to target alcohol or sugar content), petroleum refining (blending crude streams to product specifications), and paint manufacturing (tinting base paints to custom colors). Any process requiring two components with different concentrations to be blended to a target value uses the alligation principle — the mathematics is identical regardless of industry. The solution and mixture calculators category covers the complete toolkit for concentration and dilution calculations.
The alligation method is based on the principle of mass balance. When two solutions are mixed, the total amount of solute is the sum of the solute in each individual solution, and the total volume is the sum of both volumes. The formula used is:
C_mix = (V₁ × C₁ + V₂ × C₂) / (V₁ + V₂)
Where C₁ and C₂ are the concentrations of solutions 1 and 2 (in percent), and V₁ and V₂ are their respective volumes. This equation assumes that the volumes are additive (which is approximately true for dilute aqueous solutions) and that no chemical reaction occurs between the components.
The alligation medial method finds the weighted average concentration, while the alligation alternate method determines the ratio in which two solutions must be mixed to achieve a desired concentration. The mixing ratio is simply V₁/V₂. In pharmacy, this technique is essential for compounding prescriptions when the exact concentration needed is not commercially available. The calculator also reports the total volume so you can plan container sizes and verify that the preparation meets volume requirements.
The mixture concentration will always fall between the two input concentrations. If both solutions have the same concentration, the result equals that concentration regardless of volumes. A higher volume of the more concentrated solution shifts the mixture concentration upward. The mixing ratio tells you how many parts of Solution 1 are used per part of Solution 2. Use these results to verify your compounding calculations before physically mixing solutions.
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Mixing 200 mL of 10% solution with 100 mL of 50% solution yields 300 mL at 23.33% concentration. The 2:1 ratio means twice as much dilute solution is used.
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When equal volumes of 20% and 80% solutions are mixed, the result is exactly 50% — the arithmetic mean of the two concentrations.
Alligation is an arithmetic method for solving problems related to mixing solutions of different concentrations. It has two forms: alligation medial (finding the average concentration of a mixture) and alligation alternate (finding the ratio needed to achieve a target concentration). It is widely used in pharmaceutical compounding and chemical preparation.
Yes. The same formula applies when using masses instead of volumes: C_mix = (m₁ × C₁ + m₂ × C₂) / (m₁ + m₂). Simply substitute mass values for volume values. This is particularly useful for solid mixtures or w/w percent calculations.
The method assumes that volumes (or masses) are additive upon mixing and that no chemical reaction changes the solute amount. For most dilute aqueous solutions this is an excellent approximation, but for concentrated solutions of certain solutes (like ethanol-water mixtures), volume contraction can introduce small errors.
Yes, the formula generalizes to any number of solutions: C_mix = Σ(Vᵢ × Cᵢ) / Σ(Vᵢ). This calculator handles the two-solution case, which is the most common scenario in practice.
Nurses and pharmacists use alligation to prepare IV solutions at specific concentrations from available stock solutions. For example, mixing D5W (5% dextrose) with D50W (50% dextrose) to obtain D10W at a required volume. The alligation method quickly provides the volumes of each stock solution needed.
Alligation medial calculates the final concentration from known volumes and concentrations. Alligation alternate works in reverse — given a desired final concentration and two stock concentrations, it determines the ratio of volumes needed. This calculator performs alligation medial.
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