1.11: Dosage Calculations II

Learning Objectives

• Calculate drug dosages using metric prefixes and conversion factors.

Effects are dose-dependent

For humans, most doses of micronutrients and medications are measured in milligrams (mg), but some are measured in micrograms because of their potency. Nonmedicinal poisons span the measurement scale; some poisons are so dangerous that a single microgram of it could be deadly, whereas other substances take much more. For example, even water is toxic when consumed in large enough quantities.

Dosage (the size of each dose) determines the strength and duration of the health benefits of nutrients, and also of the therapeutic effects of medical treatments. Dosage also determines the severity of adverse effects of treatments and toxins.

Duration of exposure, that is, the period of time over which the dose was received (all at once or gradually) also determines its effects (the body may build tolerance to gradual exposure to a drug, while a large immediate dose could be deadly).

The route by which a dose is exposed to may affect the outcome. Some medications have different effects depending on whether they are inhaled, ingested, taken transdermally, injected, or inserted.

The dosage, route, concentration, and division over time may all be critical considerations in the administering of drugs, or in responding to exposure to a toxin. In nutrition, the route is usually implied, as nutrients are generally eaten; while dosage and the frequency of ingestion of nutrients are very important variables in preventing disease and promoting overall health.

Drug dosage calculation is required if the physician’s order is different from what is available. Here we will see examples where the medications are administered as fluids or tablets.

Example \(\PageIndex{1}\)

Neomycin is an antibiotic. A patient needs 2.5 grams of Neomycin sulfate. 500 mg tablets are available. How many tablets will you give to the patient?

Solution

It is important to set up a concept map, so as to plan the steps involved:

We will set up a series of conversion factors so that each conversion factor produces the next unit in the sequence.

In each step, the previous unit is cancelled and the next unit in the sequence is produced, each successive unit canceling out until only the unit needed in the answer is left.

The patient requires 5 tablets of neomycin.

Example \(\PageIndex{2}\)

Epinephrine is used to treat peanut allergies. A 5 year old patient needs an immediate treatment of 120 mcg of epinephrine. The solution is available in concentration of 0.50 mg/mL. Calculate the volume (mL) required for the patient?

Solution

It is important to set up a concept map, so as to plan the steps involved:

We will set up a series of conversion factors so that each conversion factor produces the next unit in the sequence.

In each step, the previous unit is cancelled and the next unit in the sequence is produced, each successive unit canceling out until only the unit needed in the answer is left.

The 5 year old patient requires 0.24 ml of epinephrine.

Example \(\PageIndex{3}\)

The doctor’s order is 1.2 g of Folic Acid. Folic Acid is available as 800 mg per tablet. How many tablets should be taken?

Solution

We start with the given, 1.2 g and we want to change grams to number of tablets. First, we convert 1.2 g to mg and then convert mg to tablets. We need a

conversion factor for each step.

Hence, 1.5 tablets should be taken.

Example \(\PageIndex{4}\)

The doctor’s order is 1 g of Calcium. What is on hand is Calcium as 500 mg per tablet. How many tablets should be taken?

Solution

Start with 1 g (1000 mg) of Calcium. For the conversion factor, we know that 500 mg Calcium = 1 tablet

\[1000 \cancel{\mathrm{mg}} \times \dfrac{1 \text { tablet }}{500 ~ \cancel{\mathrm{mg}}}=2 ~ tablets \nonumber\]

Hence, 2 tablets should be taken.

Note

Drug Dosage Calculation based on Body Weight.

Many drugs (especially in children) are dosed according to body weight (mg/kg). These calculations are carried in 3-step conversions. The first step is to convert the body weight from pounds (lbs) to kg. The second step is to convert kg of body weight to mg of dose (the total mg dose calculated based on body weight). Finally, the mg dose is converted to the number of tablets.

Example \(\PageIndex{5}\)

Demerol is ordered 1.5mg/kg for a patient that is 220 lbs. Demerol is available as 50 mg per tablet. How many tablets should the nurse administer?

Solution

We start with the given, 220 lbs. We want to change the unit from lbs to kg, and then, from kg to total dose (mg) and then the mg dose to tablets. The first conversion factor will cancel out the original unit, lbs, and introduce the unit we are converting to, which is kg. The second conversion factor will cancel out kg, and introduce the unit of the dose (usually mg) and then mg to tablet.

Hence, the nurse administers 3 tablets.

Example \(\PageIndex{6}\)

A doctor prescribes amoxicillin 30mg/kg to a child weighing 73.5 lbs. Amoxicillin is available as 500 mg tablets. How many tablets should the nurse administer?

Solution

Start with the given, 73.5 lbs. We want to change the unit from lbs to kg, and then, from kg to total dose (mg) and then mg to tablets. The first conversion factor will cancel out the original unit, lbs, and convert to kg. The second conversion factor will cancel out kg, and convert to the total mg dose and the final conversion will cancel mg to introduce the final unit, tablet.

Hence, the nurse administers 2 tablets.

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.)

Summary

In multi-step conversion problems, the previous unit is canceled for each step and the next unit in the sequence is produced, each successive unit canceling out until only the unit needed in the answer is left.