Dimensional Analysis 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 drug calculations are the basic formula, also called Desired over Have; ratio and proportion; and dimensional analysis. Let’s take a deeper look into the dimensional analysis method.

As with the other methods for drug calculation, the three components involved in dimensional analysis, or DA for short, are D, for the Desired dose, or dose ordered by the health care provider; H, for Have, or the dosage you have available; and V, for Vehicle or the form and amount in which the medication comes, like tablets or liquid.

The dimensional analysis method is set up like this:

X = Vehicle x Desired Have

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

Let’s look at some drug calculations using the DA method. First, you’ll read the order, which is: acetaminophen 1 gram PO one time. Now, let’s look at the following label. Since the medication comes in 500 mg per 1 tablet, you’ll calculate how many tablets to administer to achieve the desired dose. To do this, first identify your components, Desired, Have, and Vehicle. In this case, D is 1 gram, which was obtained from the health care provider’s order. H is 500 mg, 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. To do this, compare the units of D with the units of H; and if they're the same, no conversion factor is needed. Because D is in grams and H is in mg, a conversion factor is needed. In this case you’ll use the following conversion factor for mg to grams: 1 gram = 1000 mg

Now, set up the equation, where X is the dose you’ll administer, written out like this: X number of tablets equals Vehicle over Have, multiplied by Desired multiplied by the conversion factor for mg to grams

X tablets = V x D x Conversion factor mg H Conversion factor grams

Remember, you should put the units you’re trying to convert to in the denominator so you can cancel, or cross out, “mg” and “grams”.

Now, plug in the values for the components to get X equals 1 tablet multiplied by 1 gram multiplied by 1000 mg divided by 500 mg multiplied by 1 gram.

X = 1 tablet x 1 gram x 1000 mg
500 mg x 1 gram

Now, cross out the units of the numerator that match the units of the denominator because they cancel out.

X = 1 tablet x 1 gram x 1000 mg
500 mg x 1 gram

Then, multiply the numbers in the numerator and then the numbers in the denominator to get X equals 1000 tablets divided by 500.

X = 1000 tablets 500

Next, divide 1000 by 500 to solve for X.

X = 2

The answer is 2 tablets, meaning, you will administer two 500 mg tablets of acetaminophen to achieve the ordered dose of 1 gram.

Let’s look at another example. First, you’ll read the order, which is: alprazolam 0.5 mg PO every 12 hours PRN for anxiety. Now let’s look at the medication label. Since the medication comes in 1 mg per 1 tablet, you’ll calculate how many tablets you should administer to achieve the Desired dose. To do this, first identify your components, Desired, Have, and Vehicle. In this case, D is 0.5 mg, which was obtained from the health care provider’s order. H is 1 mg, 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.

Now, set up the equation, where X is the dose you’ll administer, written out like this:

X equals Vehicle over Have, multiplied by Desired.

X = V x D H

Now, plug in the values for the components to get X equals 1 tablet multiplied by 0.5 mg divided by 1 mg.

X = 1 tablet x 0.5 mg 1 mg

Remember, cross out the units of the numerator that match the units of the denominator because they cancel out.

X = 1 tablet x 0.5 mg 1 mg

Now, you’ll multiply 1 by 0.5 and divide by 1 to solve for X.

X = 0.5

The answer is 0.5 tablets, meaning, you’ll administer one half of a 1 mg tablet to achieve the ordered dose of 0.5 mg. Because the answer is a partial dose, you’ll cut the pill in half.

Let’s look at another example. First, you’ll read the order which is: cefdinir 7 mg/kg PO every 12 hours for 10 days. Now let’s look at the medication label. Since the medication comes in 125 mg per 5 mL, you’ll calculate how many mL you should administer to achieve the Desired dose. To do this, first identify your components Desired, Have, and Vehicle. In this case, D is 7 mg/kg which was obtained from the health care provider’s order, H is 125 mg which was obtained from the medication label, and V is 5 mL which was also obtained from the label. Now, since this order is a weight-based dose, you’ll check the electronic health record, or EHR, and see that your patient’s weight was obtained today and is 15 kg. Next, you’ll determine if a conversion factor is required. Because both D and H are in milligrams, no conversion factor is needed.