# 1.8: 1.8 Dosage Calculations

Learning Objectives

• Calculate drug dosages using conversion factors.

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 (µg) to 300 µg. It is a doctor’s responsibility to prescribe the correct dosage for a patient, and it is a pharmacist’s responsibility to provide the patient with the correct medicine at the dosage prescribed. Thus, proper quantities—which are expressed using numbers and their associated units—are crucial for keeping us healthy.

## Effects are dose-dependent

Chemicals are the most common things for which doses are measured, but there are others, such as radiation exposure. 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, because 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 a given, 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.

## Calculation of dose

Calculating drug dosages for humans based on the doses used in animal studies can be based on weight (e.g., mg/kg) or surface area (e.g., mg/m2) based on weight2/3.

## Drug dosage calculations

Drug dosage calculation is required if the physician’s order is different from what is available.

Example $$\PageIndex{1}$$

1. A physician ordered 100 mg of Demerol. Demerol is available as 50 mg per tablet. How many tablets should the nurse administer?
2. 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

a. 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.

b. 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.

\begin{align*} 1.2 \; \cancel{\rm{g}} \times \dfrac{1,000 \cancel{\rm{mg}}}{1\; \cancel{\rm{g}}} \times \dfrac{1\; \rm{tablet}}{800\; \cancel{ \rm{mg}}} &=1.5 \; \rm{tablets} \end{align*}

Hence, 1.5 tablets should be taken.

Exercise $$\PageIndex{1}$$

Calculate each of the following.

1. The physician ordered 20 mg of Valium. Valium is available as 10 mg per tablet. How many tablets should the nurse administer?
2. 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?

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

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

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

$1000 \cancel{\rm{mg}} \times \dfrac{1\; \rm{tablet}}{500\; \cancel{\rm{mg}}} = 2\; \rm{tablets} \nonumber$

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 to mg (the total mg dose calculated based on body weight). And, finally, the mg dose is converted to the number of tablets. (as in Example 1.8.1).

Example $$\PageIndex{2}$$

1. 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?
2. 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

a. 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.

$220 \cancel{\rm{lbs}} \times \dfrac{1\cancel{\rm{kg}}}{2.2\; \cancel{\rm{lbs}}} \times \dfrac{1.5\cancel{\rm{mg}}}{1\; \cancel{ \rm{kg}}} \times \dfrac{1\; \rm{tablet}}{50\; \cancel{\rm{mg}}}= 3\; \rm{tablets} \nonumber$

Hence, the nurse administers 3 tablets.

b. 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.

\begin{align*} 73.5 \; \cancel{\rm{lbs}} \times \dfrac{1\cancel{\rm{kg}}}{2.2\; \cancel{\rm{lbs}}} \times \dfrac{30\cancel{\rm{mg}}}{1\; \cancel{ \rm{kg}}} \times \dfrac{1\; \rm{tablet}}{500\; \cancel{\rm{mg}}}&=2 \; \rm{tablets} \end{align*}

Hence, the nurse administers 2 tablets.

Exercise $$\PageIndex{2}$$

Calculate each of the following.

1. Vancomycin is ordered 15mg/kg for a patient that is 110 lbs. Vancomycin is available as 250 mg per capsule. How many capsules should the nurse administer? (ans. 3 capsules)
2. A doctor prescribes ampicillin 40mg/kg to a patient weighing 55 lbs. Ampicillin is available as 500 mg tablets. How many tablets should the nurse administer? (ans. 2 tablets)
$110 \cancel{\rm{lbs}} \times \dfrac{1\cancel{\rm{kg}}}{2.2\; \cancel{\rm{lbs}}} \times \dfrac{15\cancel{\rm{mg}}}{1\; \cancel{ \rm{kg}}} \times \dfrac{1\; \rm{tablet}}{250\; \cancel{\rm{mg}}}= 3\; \rm{tablets} \nonumber$
$55 \cancel{\rm{lbs}} \times \dfrac{1\cancel{\rm{kg}}}{2.2\; \cancel{\rm{lbs}}} \times \dfrac{40\cancel{\rm{mg}}}{1\; \cancel{ \rm{kg}}} \times \dfrac{1\; \rm{tablet}}{500\; \cancel{\rm{mg}}}= 2\; \rm{tablets} \nonumber$