Alligation Calculator

Alligators are a method for mixed calculations. They answer two common questions that arise in laboratories, pharmacies and kitchens: What ratio of two starting substances is required to achieve a given concentration? What concentration results from mixing known amounts? This tool supports both types of calculations, shows the calculation process, and converts the ratio into actual quantities.

Two types of mixtures:

This term refers to two interrelated methods that perform opposite calculations.

The cross method is used to design a mixture. It is employed when the concentrations of two starting materials and the desired target concentration are known, and the mixing ratio needs to be determined. The mean value method is used to check a mixture. It is employed when the amounts of individual components are known, and the resulting concentration should be calculated as a weighted average of the amounts used.

Cross-mix method:

The cross method is typically represented in a cross diagram. The concentrations of the two starting substances are given on the left side, the target concentration in the middle and two diagonals are drawn along which subtractions are performed. In each case the positive difference is taken. What's clever about this method is that the amount of each starting substance is equal to the distance between that starting substance and the target concentration.

The mixing ratio can be directly derived from the two results. To convert this ratio into actual amounts, the required total amount is divided according to the ratio.

This method is only applicable if the target concentration falls between the concentrations of the two starting solutions. It is not possible to achieve a 30% concentration. Even mixing the 10% and 25% solutions will result in mixtures that fall somewhere between 10% and 25%. For higher concentrations, you need a more concentrated component. For lower concentrations, you need a more dilute component such as pure water or an inert carrier material with a concentration of 0%.

Example:

Suppose you need to make 1,000 mL of a 5% solution and have available 10% and 2% stock solutions.

The ratio of the mixture is therefore 3 to 5 for a total of eight parts. If you divide up the 1000 mL, the 10% solution will provide 1000 × 3/8 or 375 mL and the remaining 625 mL will be from the 2% solution. By writing out and checking your calculations, you can see that the resulting concentration is indeed 5%.

Start with a set amount.

Preparation almost never begins with an empty beaker; more often the situation is that you want to know how much of one particular stock solution needs to be added to another when you already have a stock solution available. The ratio remains an important calculation factor in this case.

For example: To increase the concentration of a 20% solution from 150mL to 25%, you can use a 50% stock solution. The cross-multiplication method states that 5 "parts" of the 50% solution is equivalent to 25 "parts" of the 20% solution. If 150mL represents these 25 parts, then one part would be equal to 6mL. Adding five parts, or 30mL, of the 50% solution will result in a new total volume of 180mL. This method can be used if the reference for volumes is changed on this tool.

Medium-weighted mixture and resulting concentration

In calculating the mean-weighted mixture, the direction is reversed. The amount of each component is multiplied by its concentration, these products are summed and then divided by the total amount.

If you mix 200 mL of a 12% solution, 300 mL of an 8% solution and 500 mL of a 5% solution, it will be (2.400 + 2.400 + 2.500) divided by 1,000 which gives you 7.3%. This is a weighted average so the result will always be between the least concentrated and most concentrated solutions and will tend toward the solution with the larger volume.

Customize units.

The mixing procedures deal with ratios, so it doesn't matter if the concentrations are given as mass-volume percent, mass-mass percent, parts per million or milligrams per milliliter; the calculation method remains the same. The only requirement is that all of the concentrations use the same units. Mixing percentages and ppm will give you nonsense results, so convert all values to the same scale first.

The same goes for the quantities. This tool treats the quantities as volumes and allows you to switch between milliliters, liters, and gallons but the same ratio can also be applied to masses. If you are making a salve by weight then you can simply treat each quantity as grams and use the values directly. When dissolving a solid in a liquid and the volume does not add up easily, use mass for accuracy.

Applications of mixing methods

Pharmacists rely on this method to prepare the concentration required for a prescription based on the concentration of stock solutions available in storage. They can also adjust the contents of infusion bags without having to discard them. Chemists use this method to dilute or concentrate reagents to the desired working concentration. The same cross diagram is used to solve classic commercial problems, i.e. mixing two product qualities with different prices where the unit price plays a role in reaching a target price.

This tool is a general educational tool. It assumes an ideal mixture and requires a single consistent unit of measure and does not take into account volume contractions, compounding differences or rounding rules set by the pharmacopoeia. If you are making something for clinical use follow pharmacy validated procedures and have it checked by a qualified assessor.