Alligation Calculator - Two-Solution Mixing Ratio

An alligation calculator turns a higher-concentration stock, a lower-concentration stock, a target percent, and a total amount into the parts of each stock to mix plus the volume or mass of each to pipette. The parts of the higher stock equal the target minus the lower concentration and the parts of the lower stock equal the higher minus the target, so a student or technician stops doing the cross arithmetic by hand and reads a defensible bench answer from the alligation calculator.

• • Compound a 70% alcohol dilution from 95% and 50% stocks: Target 70% for a pharmacy prep. The tool returns the mL of each to mix.
• • Dilute a strong acid to a working percent: Use 37% HCl and water as 0% to reach a 10% working solution.
• • Blend two syrup strengths to hit a target Brix: Mix two syrup batches of different percent solids to reach a target.
• • Work a homework alligation problem quickly: Plug textbook percents to read the part ratio and the scaled volumes.

Alligation is taught as a shortcut for the algebra of how much of each of two known solutions to mix to land at a third concentration. The arithmetic is simple once you see the cross, but most students slip on the direction of subtraction, so this kind of tool is useful from undergraduate chemistry through pharmacy technician training.

After you read the parts ratio from the alligation cross you still need to know the percent strength of each stock on the same percent w/w scale, and the same percent-by-mass arithmetic that defines a stock solution sits behind a Mass Percent Calculator.

The alligation calculator applies the classical alligation cross in percent. It subtracts the lower stock from the target to get the parts of the higher stock, the target from the higher stock to get the parts of the lower stock, then divides each part by the total parts to scale into the chosen total volume or mass.

• Higher stock concentration (%): Strength of the stronger stock. Must exceed the target.
• Lower stock concentration (%): Strength of the weaker stock. Must be below the target; pure water counts as 0.
• Target concentration (%): Strength of the mixture; must lie strictly between the two stocks.
• Total amount (mL or g): Volume or mass of the final mixture; converts the parts ratio into pipette volume or weigh mass.

The two part values always sum to the difference between the two stocks and reduce to a small integer pair when the stock strengths are on a percent grid.

According to Omni Calculator - Alligation, the alligation method sets the parts of the higher stock equal to the target minus the lower concentration and the parts of the lower stock equal to the higher minus the target

According to Wikipedia - Alligation, alligation is a historical arithmetic method that places the target percent at the center of a cross and the two stock percents at the ends to read the parts along the diagonals

The percent numbers you type into the alligation cross come from the percent w/v or percent w/w recipes that a Percent Solution Calculator prepares, so the percent-of-solute-in-solvent arithmetic feeds the stocks that alligation then blends.

Four ideas come up every time you set up an alligation problem: what the rule really says, how to read the cross, where the rule fails, and why a parts ratio beats a single ratio.

These four ideas cover a typical undergraduate chemistry homework set on alligation, so the calculator pairs naturally with the dilution and percent tools. When the lower stock is pure water at 0% the rule collapses to C1V1 = C2V2, and the same dilution arithmetic sits behind a Dilution Formula Calculator.

Five quick steps take you from two stock bottles and a percent target to the exact mL or g of each to measure. The defaults match a classic textbook problem so the first answer is useful without changing anything.

1. 1 Enter the higher stock percent: Percent strength of the stronger stock. Pharmacy examples use 95% alcohol, 37% HCl, or 70% isopropyl alcohol.
2. 2 Enter the lower stock percent: Percent strength of the weaker stock. Pure water is 0%; dilute stocks run 5% to 50%.
3. 3 Enter the target percent: Percent strength of the mixture you want to make. The target must lie strictly between the two stocks.
4. 4 Enter the total amount: Total volume (mL) or mass (g) of the final mixture. This converts the parts ratio into an actual pipette or weigh amount.
5. 5 Read the parts ratio and amounts: Read the parts of each stock, the reduced higher:lower ratio, and the volume or mass to pipette.

For 70% and 10% stocks at a 50% target with 100 mL total, the calculator returns 40 parts of 70%, 20 parts of 10%, a 2:1 ratio, 66.67 mL of the 70% stock, and 33.33 mL of the 10% stock.

Once the prep is mixed you can record the dilution factor from the higher stock to the final mixture for a lab notebook, and the same ratio-of-final-to-initial arithmetic that a Dilution Factor Calculator reports sits behind the same workflow.

The tool turns a published alligation cross into a specific mL or g for your exact stocks and total, so you stop re-doing the arithmetic on scratch paper.

• • Skip the diagonal subtraction by hand: Type two stock percents and a target percent and read both the parts and the amounts.
• • Match USP compounding practice: The cross layout and parts-to-volume scaling match the United States Pharmacopeia compounding standards for two-solution preparations.
• • Surface invalid setups before you pipette: If the target is outside the bracket of the two stocks, the status line flags the error before you measure anything.
• • Scale the parts ratio to any total amount: Whether you compound 10 mL of a 10% buffer or 5 L of a 30% syrup, the same parts ratio scales to the total amount.
• • Move between percent strength and dilution setups: The same alligation rule covers water (0%) plus a concentrated reagent, two strengths of the same solvent, or two syrup batches.
• • Hand off to a downstream percent or molarity tool: The mix percent feeds a percent-solution, mass-percent, or molarity workflow without recomputing parts.

Once you have the mL or g number, measure each stock into a clean vessel, mix, and verify the final percent with a refractometer or assay if the prep is critical.

If you need to convert the percent strengths into moles per liter for an analytical prep, the same gram-to-mole stoichiometry that defines molarity sits behind a Grams to Moles Calculator.

Four variables move the parts ratio and pipette amounts the most, plus two caveats when the target is not a percent w/w or w/v.

• • The rule assumes percent is linear on the amount you measure. For percent w/v the solute volume is small and the rule is a good approximation, but for percent w/w with dense solutes an alligation cross can drift a few tenths of a percent.
• • The calculator treats the two stocks as pure solutions of the same solute. Mixing reagents that react, or stocks with impurities or stabilizers, will drift from the alligation answer; verify reactive or buffered systems with an assay.

If the bench answer disagrees with a refractometer or assay, re-check the stock percents, confirm the units (w/w vs w/v), and confirm the stocks are miscible in the proportions you are mixing.

According to United States Pharmacopeia (USP) Compounding Standards, pharmacy technicians use alligation calculations to determine the quantities of two stock preparations of known strength needed to compound an intermediate-strength preparation

When the prep has to be reported in molarity instead of percent, the same percent-to-molar conversion that fixes a lab notebook entry sits behind a Percentage Concentration to Molarity Calculator.