How to Perform Alligation Calculations: Grid Method

When faced with complex dosing problems, understanding alligation calculations can be crucial for determining the right proportions of solutions in pharmaceutical preparations.

Clinical scenario:

The neonatologist orders D12% for a 2 day old neonate. What would you do? Chat GPT or Google? On a 2 day old? Even the most trusted clinical calculators have the disclaimer that results they generate must be re-checked and should not be used alone to guide patient care, nor should they substitute for clinical judgment. In good faith we should have at least some understanding of how to perform alligation calculations.

Alligation is one of those calculation techniques you won’t use often but when it is needed it’s non negotiable.

There are 2 ways to perform alligation:

1. Alligation Grids
2. Alligation Equations

This unit focuses on the use of alligation grids. Alligation via intuitive equations is covered in another unit. Take a look at both strategies, decide which one works best for your style of learning.

What is Alligation?

Alligation is a mathematical technique used to determine the quantity of 2 concentrations needed to create a desired concentration. The desired concentration will have a value somewhere in the range of the 2 starting concentrations.

Clinical Application

As we’ve seen alligation is useful in specific patient populations where standard concentrations of fluids are not ideal, like NICU.

It is also useful when there are drug shortages. For instance there have been times when we are not able to get bags of 3% saline for acute hyponatremia but we have vials of concentrated saline (23.4%). We can use alligation to compound lower concentration from the higher concentration.

An understanding of alligation is also needed when compounding custom TPNs.

Terminology

As always terminology is important. It allows us to all to be oriented in the same direction as we work through concepts.

Alligation Tic-Tac-Toe

An alligation table is a well coordinated version of tic-tac-toe. The grid for alligation is in fact the very way you would set up tic-tac-toe. Alligation grids work by condensing a complex mathematical concept into a standardized table.

Your desired concentration will be some value between your initial higher concentration and lower concentration. Once you’ve organized your concentrations on the grid, the next step is a series of diagonal differences.

Diagonal Differences

Vertical Sum

You’ve organized your grid, calculated differences diagonally, now we add vertically. The sum of Δ₁ and Δ₂ is the combined quantity (parts) that will result from the combination of the 2 starting solutions.

We will place these 4 components on one grid to determine the quantity of 2 concentrations that must be mixed to obtain a desired concentration (alligation)

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Horizontal Quantities

Once we have those 6 values placed on the grid we calculate the quantities needed of each concentration horizontally.

Note that we are using the diagonal difference of the lower concentration to calculate the quantity of the higher concentration.

Again, note that we are using the diagonal difference of the higher concentration to calculate the quantity of the lower concentration.

You can then convert these ratios to the desired unit of measurement, usually volume or weight, to calculate the amount of each solution needed. Let’s look at some example calculations.

Alligation Calculations

Disadvantages of Alligation Grid

As you have seen alligation grids require some memorization. You must orient the 3 concentrations and the differences in concentrations correctly on the grid for it to work. You must subtract diagonally, add vertically then work horizontally. Any misstep and your calculation will be incorrect.

This may be a non-issue if you are studying for a test next week but when you are actually working and haven’t used alligation in weeks, months or even years, it will be hard to remember what goes where.

There is a more intuitive way to solve alligation problems. This method is covered here. If alligation grids work for you, great! If not, consider alligation equations.

GlobalRph offers an alligation calculator. As always no calculator will assume your responsibilities in patient dosing. It is always a good idea to understand what you are plugging into calculators and why.

I hope this unit has provided more context to the usual plug and chug explanation of alligation grids. It will always be easier to retain information when it is connected to already established concepts rather than just memorization. Take the time to walk through the steps diligently and build your confidence in alligation calculations.

The information on this website is intended to be used solely for educational and informational purposes. While the content may be about specific medical and health care issues, it is not a substitute for or replacement of personalized medical advice and is not intended to be used as the sole basis for making individualized medical or health-related decisions.