2.7: Dosage Calculations I

Learning Objectives

• Calculate drug dosages using conversion factors.

To Your Health: Dosages

A medicine can be more harmful than helpful if it is not taken in the proper dosage. A dosage (or dose) is the specific amount of a medicine that is known to be therapeutic for an ailment in a patient of a certain size. Dosages of the active ingredient in medications are usually described by units of mass, typically grams or milligrams, and generally are equated with a number of capsules or teaspoonfuls to be swallowed or injected. The amount of the active ingredient in a medicine is carefully controlled so that the proper number of pills or spoonfuls contains the proper dose.

Most drugs must be taken in just the right amount. If too little is taken, the desired effects will not occur (or will not occur fast enough for comfort); if too much is taken, there may be potential side effects that are worse than the original ailment. Some drugs are available in multiple dosages. For example, tablets of the medication levothyroxine sodium, a synthetic thyroid hormone for those suffering from decreased thyroid gland function are available in 11 different doses, ranging from 25 micrograms (mcg) to 300 mcg. It is a doctor’s responsibility to prescribe the correct dosage for a patient; it is a pharmacist’s responsibility to provide the patient with the correct medicine at the dosage prescribed; and it is the nurse's or caregivers responsibility to check and provide the patient with the medication. Thus, proper quantities—which are expressed using numbers and their associated units—are crucial for keeping us healthy.

Drug dosage calculations

Drug dosage calculation is required if the physician’s order is different from what is available. The medication may be administered as fluid or tablet.

Example \(\PageIndex{1}\)

Epinephrine is used to treat peanut allergies. A 5 year old patient needs an immediate treatment of 0.12 mg of epinephrine. The solution is available in concentration of 0.50 mg/ml. Calculate the volume in ml required for the patient.

Solution

The first step is to understand the meaning of concentration of solution. There are 0.50 mg in 1 mL of solution. From this relationship, we can construct the conversion factor. We use the conversion factor that will cancel out the original unit, mg, and introduce the unit we are converting to, which is mL.

\[ 0.12 \cancel{\rm{mg}} \times \dfrac{1\; \rm{mL}}{0.50\; \cancel{\rm{mg}}} = 0.24\; \rm{mL} \nonumber \]

Thus the patient requires 0.24 mL of epinephrine.

Example \(\PageIndex{2}\)

A physician ordered 100 mg of Demerol. Demerol is available as 50 mg per tablet. How many tablets should the nurse administer?

Solution

We start with the given, 100 mg. We want to change the unit from mg to tablets. There are 50 mg in 1 tablet (Remember that per tablet means one tablet. From this relationship, we can construct the conversion factor. We use the conversion factor that will cancel out the original unit, mg, and introduce the unit we are converting to, which is tablet.

\[ 100 \cancel{\rm{mg}} \times \dfrac{1\; \rm{tablet}}{50\; \cancel{\rm{mg}}} = 2\; \rm{tablets} \nonumber \]

Hence, the nurse should administer 2 tablets.

Example \(\PageIndex{3}\)

The physician ordered 20 mg of Valium. Valium is available as 10 mg per tablet. How many tablets should the nurse administer?

Solution

Start with 20 mg of Valium. For the conversion factor, we know that 10 mg Valium = 1 tablet

\[ 20 \cancel{\rm{mg}} \times \dfrac{1\; \rm{tablet}}{10\; \cancel{\rm{mg}}} = 2\; \rm{tablets} \nonumber \]

Career Focus: Pharmacist

A pharmacist dispenses drugs that have been prescribed by a doctor. Although that may sound straightforward, pharmacists in the United States must hold a doctorate in pharmacy and be licensed by the state in which they work. Most pharmacy programs require four years of education in a specialty pharmacy school. Pharmacists must know a lot of chemistry and biology so they can understand the effects that drugs (which are chemicals, after all) have on the body. Pharmacists can advise physicians on the selection, dosage, interactions, and side effects of drugs. They can also advise patients on the proper use of their medications, including when and how to take specific drugs properly. Pharmacists can be found in drugstores, hospitals, and other medical facilities. Curiously, an outdated name for pharmacist is chemist, which was used when pharmacists formerly did a lot of drug preparation, or compounding. In modern times, pharmacists rarely compound their own drugs, but their knowledge of the sciences, including chemistry, helps them provide valuable services in support of everyone’s health.

A woman consulting with a pharmacist. (Public Domain; Rhoda Baer via National Cancer Institute, an agency part of the National Institutes of Health.)