Ratio and Proportion Method for Dosage Calculation

As the nurse, you’ll perform medication calculations to ensure the correct dose of a prescribed medication is administered. The three methods for medication calculations are the basic formula method; dimensional analysis; and the ratio and proportion method, or R&P for short.

R&P is a method of dosage calculation using a ratio, which shows the relationship between two quantities, like 1:2; and a proportion, which shows the relationship between two ratios.

Ratios and proportions can be set up two ways: vertically with fractions, or horizontally with colons.

To solve an R&P problem set up as fractions, you'll cross-multiply the numerator of the first fraction by the denominator of the second fraction, and then cross-multiply the denominator of the first fraction by the numerator of the second fraction. After that, division is needed as the final step to solve for the dose.

To solve an R&P problem when it’s set up horizontally, the inside numbers, which are called means, are multiplied and then the outside numbers, which are called extremes, are multiplied. Then division is used to solve for the dose.

Now, as with the other methods for medication calculation, the three components involved in Ratio and Proportion are D, for the Desired dose, which is the dose ordered by the health care provider; H, for Have, or amount you have available; and V, for Vehicle or the form in which the medication comes, like tablets or liquid.

Now, before the drug dosage can be calculated, all units of measurement must be converted into one system of measurement, so they’re all the same. For example, if the medication is ordered in grams and comes in milligrams, then grams are converted to milligrams or milligrams are converted to grams. To do this, you'll use conversion factors, which are simply equivalents of measurements, like 1 gram equals 1000 mg or 1 liter equals 1000 mL.

Let’s look at some medication calculations using the R&P method.

First, you’ll read the order, which is: furosemide 20 mg IV twice daily.

Then, check the medication label:

Since the vial contains 40 mg per 4 mL, you will calculate how many milliliters you need to achieve the Desired dose.

To do this, first, identify the components, D, H, and V.

In this case, D is 20 mg, which was obtained from the health care provider’s order; H is 40 mg, which was obtained from the medication label; and V, is 4 mL, which was also obtained from the medication label.

Next, you’ll determine if a conversion factor is required. To determine this, compare the units of D with the units of H, and if they’re the same, no conversion factor is needed. Because both D and H are in milligrams, no conversion factor is needed.

Now, set up the equation, where X is the dose in milliliters you’ll administer, written out like this: Have over Vehicle equals Desired over X.

Now, plug in the values for the components. This gives you 40 mg over 4 mL equals 20 mg over X mL.

When you cross multiply, you get 40X equals 80.

Next, divide both sides by 40 to solve for X.

The answer is 2 mL, meaning, you'll administer 2 mL of furosemide to achieve the ordered dose of 20 mg.

Let’s look at another example, where a conversion is required.

First, you’ll read the order, which is: cephalexin 1 gram PO once and then every 12 hours.

Then, check the medication label:

Since the available dose is 500 mg per capsules, you will calculate how many capsules to administer to achieve the Desired dose.