## Defining the formula

This short video is the first of three videos in the Nursing calculations - Finding the volume required section. It explains how to define the formula for calculating medication dosage, how to understand the formula structure and how to use the formula with practical examples provided.

The volume required formula combines two key sorts of values. Firstly, there are the values for drug strength. Think of that as the mass of the drug… The more of the drug you have… the stronger the dose is. The amount of medication—which is often in powder form in its original state—gives an indication of the dosage. Mass is measured in units such as kilograms or grams, but, of course, in medication, this is more likely to be in milligrams or micrograms.

Another way to measure the amount of mass of a medication is units. That is, there is an alternative to milligrams or micrograms and it's called units.The other value that the formula uses is volume… Volume measures the amount of liquid. For example, a bottle contains one litre of water or 600 mls of juice. Litres, millilitres, and microlitres are units of volume.

A certain amount of drug, 100 milligrams for example, can be diluted to any number of volumes. You might put 100 milligrams of drug into 1 ml of liquid for an intravenous injection. Or you might put 100 milligrams of drug into a 500 ml bag of saline, which will be infused into a patient over a period of hours.

The milligrams indicates the amount of the drug that the patient receives. The mLs, then, indicates the volume of the liquid. The milligrams per ml indicates the concentration of the solution.Milligrams per ml is the unit for the concentration of the solution. A few milligrams put into a small volume of mls creates a high concentration. A few milligrams put into a large volume creates a low concentration.

So, with this formula, you are seeking the volume required... You want to know how much of the medication solution you should give to the patient… This depends on the strength required, which is how many milligrams or micrograms of the drug the patient must be given.

The stock strength is how many milligrams or micrograms of the drug there are in the original bottle, or ampoule, or capsule. And, finally, the stock volume tells us how much liquid is in the original bottle, or ampoule, or capsule.

All in all, what we are finding is the proportion of the drug we need out of what we have available to begin with. And that is the proportion—or the fraction—that we want out of the original stock bottle of liquid... Put simply, if we only need half of the drug that is available in the bottle, then we only need half of the liquid solution that it comes in!

When preparing a medication of a prescribed strength, you need to know how much of the liquid solution you need to draw up. The volume of the solution required can be be calculated using this formula. Using the strength of the drug required, the strength available, and finding the volume that is available in the stock bottle, vial, or ampoule… And it can be written in the abbreviated form like this...

It is useful, though, to understand why the formula has this shape. The formula is helpful, but, what is more important is the logic behind the formula, and if you understand that for simple calculations, you may not need to rely on the formula.

Here’s a sample problem to solve: The doctor has ordered 25 milligrams of Drugafloxin. This drug is available in solution form… And there is 100 milligrams of the drug in 120 mls of liquid solution in the vial. Now, thinking about this first… We only need 25 out of the available 100 milligrams. That is only one quarter of the strength. We need one quarter—or one fourth—of the available solution. So, consequently, we only need one quarter of the liquid that it comes in. One quarter of 120mls is… 30 mls. Let's demonstrate this.

We only need 25 milligrams out of the total 100 milligrams of the Drugafloxin, so we only need the same proportion of the liquid. A quarter of the original 120 mls will be 30 mls… And hopefully that is the answer that we calculate. Now let’s write this down using the formula. So the fraction of the drug needed out of what is available is the same as the fraction of the volume needed, out of what is available. And now for some clever algebra: if we want to get the volume required on one side of the equal side on it’s own, then we can multiply that side with the stock volume. But we must do this to both sides if want to keep the equation balanced. And why did we do this? This gives us the opportunity to cancel the stock volume on the left hand side of the equation, and there we have the equation in the form that we normally see it.

This is the form that is most useful for finding the value for the volume required, but the important message behind it... Is that whatever fraction you need out of the available drug strength... That is the same fraction you need out of the available volume of the medicated solution. The volume required is what we are looking for. The strength required is 25 milligrams… And the stock strength is 100 milligrams. Let’s finish substituting into the formula and the stock volume is 120 mls.

Now mg and mg cancel. 25 and 100 can cancel. 25 goes into 25 once, and into 100 four times. There is your quarter. Now we want a quarter of the 120 mls. We can cancel the four with the 120. Four goes into 120... 30 times. The remaining unit is mls. The volume required is 30 mls. We only need 25 out of the available 100 milligrams, that is only one quarter of the strength, so it makes sense that the amount of solution we need is also a quarter of the available solution.

We can understand that the proportion of the drug we need is equal to the proportion of the liquid we need in comparison to the drug amount or the liquid amount we have. We know we need 25 out of the 100 milligrams. This is equivalent to needing the 30 out of the 120 mls. Both of these proportions reduce to a quarter.

Let’s rearrange this equation to get the volume required on its own. We can do this if we multiply by stock volume or SV. But whatever we do to one side of the equation we must do to the other so that it keeps the equation balanced. On the left side, the SV will cancel. One the right side it will remain. And there we have it, the usual form of the volume required formula. This more common form of the formula–as well as the equal fractions shown above–are both true. They are actually expressions of the same formula… They have just undergone some rearrangement. The message that is hiding inside these formulas is that the fraction of the drug you need out of what you have is the same fraction in terms of the liquid solution.