Dosage calculation - Ratio and proportion method: Nursing pharmacology

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 milligrams or 1 liter equals 1000 milliliters.

Let’s look at some medication calculations using the R&P method. First, you’ll read the order, which is: furosemide 20 milligrams IV twice daily.

Then, check the medication label. Since the vial contains 40 milligram per 4 milliliter, 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 milligrams, which was obtained from the health care provider’s order; H is 40 milligrams, which was obtained from the medication label; and V, is 4 milliliters, 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 milligrams over 4 milliliters equals 20 milligrams over X milliliters.

When you cross multiply, you get 40X equals 80. Next, divide both sides by 40 to solve for X.

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

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 milligrams per capsule, you will calculate how many capsules to administer to achieve the Desired dose.

To do this, first, identify the components, D, H, and V. In this case, D is 1 gram, which was obtained from the health care provider’s order; H is 500 milligrams, which was obtained from the medication label; and V, is 1 capsule, which was also obtained from the label.

Next, you’ll determine if a conversion factor is required. Because D and H are in different units, a conversion is needed.

In this case, you’ll use the following conversion factor to convert milligrams to grams: 1000 milligrams equals 1 gram. So, to complete the conversion, convert the H which is 500 milligrams to 0.5 grams.

Then, set up the equation, where X is the dose 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 0.5 grams over 1 capsule equals 1 gram over X number of capsules.

When you cross multiply, you get 0.5X equals 1. Then, divide both sides by 0.5 and solve for X.

The answer is 2 capsules, meaning, you'll administer 2 capsules of cephalexin 500 milligrams to achieve the ordered dose of 1 gram.

Let’s look at another example. First, you’ll read the order, which is: lorazepam 1 milligram PO every 4 hours PRN.

Then, look at the following label. Since the available dose is 2 milligrams per one tablet, you will calculate how many tablets to administer to achieve the Desired dose.

To do this, first, identify the components, D, H, and V. In this case, D is 1 milligram, which was obtained from the health care provider’s order.

H is 2 milligrams, which was obtained from the medication label. And V, is 1 tablet, which was also obtained from the label.

Next, you’ll determine if a conversion factor is required. Because both D and H are in milligrams, no conversion factor is needed.

Then, set up the equation, where X is the dose 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 2 milligrams over 1 tablet equals 1 milligram over X.

When you cross multiply, you'll get 2X equals 1. Then, divide both sides by 2 and solve for X.

The answer is one half or 0.5 tablets, meaning, you'll administer one-half tablet of lorazepam to achieve the ordered dose of 1 milligram.

Because the answer is a partial dose, you’ll cut the pill in half and discard the other half according to your facility protocol.

Alright, as a quick recap...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