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# Section One Calculating Drug Dosages

Section One: Calculating Drug Dosages

It is very important to give the correct dose of a medicine. While many drugs now come already packaged in the correct dosage for the patient, at other times or places of employment, you may need to accurately calculate the dosage using basic math formulas or a calculator. Even a small error in dosage may produce a big error. (Many of you may remember that the twin 74babies of actor Dennis Quaid were accidentally given a huge overdose of heparin in the neonatal intensive care unit, which made the babies’ blood fail to clot.) Accuracy with dosage is one of the things the nurse does that helps ensure safety.

Although most nurses feel comfortable with addition and subtraction, many can profit from a review of basic concepts in multiplication and division, as well as fractions, percentages, and proportions and ratios, to increase their speed. These number relationships form important building blocks for tasks the nurse must master. For example, these math processes are the basic concepts in calculating ratio and proportion, an important procedure in drug calculations. By memorizing and drilling on these basic mathematical facts, you will have confidence and speed in calculating dosages and converting from one system of measures for drugs to another. Even if one uses a calculator, it is important to know how to manually do the math problem so you can recheck calculations at the bedside when necessary to make sure you are not making a mistake.

Please review Roman numerals because they may sometimes be used in the writing of prescriptions. You should have a good awareness of common abbreviations and symbols used to interpret and solve medication problems, as well as the units used in the apothecaries’, metric, and household measurement systems. For some nurses, using the metric system will be a new experience, especially when you have to use the metric system to convert from one measure to another. This includes not only the calculation of drug dosages but also the conversion of Fahrenheit to Celsius while taking temperatures and converting pounds to kilograms when weighing patients and using the metric system.

The following section is a brief review of essential information to master in calculating drug dosages.

Calculation Methods

Calculating dosages involves the following three steps:

1. Determine whether the drug dosage desired (what is written in the prescriber’s order) is in the same measurement system as the drug dosage available. If they are not in the same measurement system, convert between the two systems.

2. Simplify by reducing to the lowest terms whenever possible.

3. Calculate the dosage quantity to be administered. This may be done by using fractions, ratios, or proportions. All of these calculation methods arrive at the same answer. It is simply a matter of finding which method works best for you as the nurse.

Fraction Method

When you are using fractions to compute drug dosages, write an equation consisting of two fractions. First, set up a fraction showing the number of units to be given over x, the unknown number of tablets or milliliters. For example, if the physician’s order states, “ibuprofen 600 mg,” you would write . On the other side of the equation, write a fraction showing the drug dosage as listed on the medication bottle over the number of tablets or milliliters. The ibuprofen bottle label states, “200 mg per tablet,” so the second fraction is . The equation then reads:

600

mg

x

tablets

=

200

mg

1

tablet

Note that the same units of measure are in both numerators and the same units of measure are in both denominators. Now solve for x:

Ratio and Proportion Method

In using the ratio method, first write the amount of the drug to be given and the quantity of the dosage (x) as a ratio. Using the previous example, this is 600 mg:x tablets. Next, complete the equation by forming a second ratio consisting of the number of units of the drug in the dosage form and the quantity of that dosage form as taken from the bottle. Again, using the previous example, the second ratio is 200 mg:1 tablet. Expressed as a proportion, this is:

600

mg

:

x

tablets

:

:

200

mg

:

1

tablet

(Or: 600 mg over x tablets is proportional to 200 mg over 1 tablet.)

Solving for x determines the dosage:

600×1=200×x 600=200x x=600 / 200 x=3

This method, again, gives a dosage of 3 tablets.

Insulin

Insulin is a parenteral medication given to replace insulin not being made by the patient’s own body. Great accuracy is important in preparing and administering insulin because the quantity given is very small, and even minor variations in dosage may produce adverse symptoms in the patient.

Intravenous Infusions

Flow rates.

Regulating the intravenous (IV) infusion rate is a common nursing task. Some institutions have automatic infusion pumps that make flow-rate calculations easy. Each nurse will learn to use the equipment available. However, all nurses must learn to calculate infusion rates without relying on equipment, in case of power or equipment failures or when working in agencies where no automatic pumps are available. The completeness of physicians’ orders for IV infusions varies widely. Some physicians are more specific in their instructions than others. A complete order specifies not only the type of solution and the volume to be infused (usually 500 or 1000 mL) but also the length of 76time the medication should be given. More commonly, the nurse is left to calculate the flow rate, or how fast, the medication will be infused.

There are three mathematical procedures the nurse must be familiar with regarding IV infusions:

1. Calculating the flow rates for IV fluid administration

2. Making modifications in flow rates for infants

3. Calculating total administration time for IV fluid

To calculate the flow rate for IV fluid administration, two concepts must be understood: the flow rate and the drop factor. The rate at which IV fluids are given is the flow rate, and this is measured in drops per minute. The drop factor is the number of drops per milliliter of liquid and is determined by the size of the drops. The drop factor is different for different manufacturers of IV infusion equipment, and it must be checked by reading it on the infusion set itself. Regular infusion sets generally range between 10 and 15 drops/mL. Infusion sets have different drop factors for use with blood infusion sets (usually 10 to 12 drops/mL) because the drops are larger, whereas pediatric setups use very small drops called microdrops (often with 50 or 60 microdrops/mL).

Once the nurse has learned the drop factor for the equipment being used, the flow rate may be calculated by using the following formula:

Drop factor×Milliliters / minute =Flow rate (drops / minute)

To illustrate, here are a few examples:

The order reads: “IV infusion to run at a slow rate to keep vein open.” The rate to keep a vein open is 2 mL/min. The IV infusion set delivers 10 drops/mL. The goal is to determine the flow rate in drops/minute:

10

drops

/

mL

(

drop

factor

)

×

2

mL

/

min

=

20

drops

/

min

The order reads: “1000 mL NS to be administered in 5 hours.” The drop factor is 15. To calculate the flow rate, use:

Flow rates for infants and children.

Infants and small children are very sensitive to extra amounts, or volumes, of fluids. Smaller total amounts of IV fluids are often ordered, and the infusions are given in very small drops to avoid quickly overloading the infant’s circulation. This is a built-in safety mechanism to try to prevent fluid overloading as a result of accidental delivery of too much fluid.

The drop factor must be determined from the infusion setup. Usually 60 microdrops/mL is the drop factor for infants. For calculating the flow rates in infants, the same formula is used, but the microdrop drop factor must be substituted into the formula for the adult drop factor:

Total

of

fluid

to

give

Total

time

(

minutes

)

×

Drop

factor

(

microdrops

/

milliliter

)

=Flow rate (drops / minute)

For example, the order reads: “Give 50 mL D5W [5% dextrose in water] IV in 4 hours.” The drop factor is 60 microdrops/mL. Thus:

50

mL

240

min

×60 microdrops / mL=

300

24

=12.5 microdrops / min

Total infusion time.

Sometimes physicians’ orders tell how fast they want infusions to run. To plan nursing care of the patient and to anticipate when new IV bottles may be needed, you need to calculate the total time the infusion will run.

Calculating the total administration time for IV fluid depends on calculating the total number of drops to be infused. Using this information, plus the drop factor, the total infusion time can be easily determined by using the following formula:

Total

drops

to

be

infused

Flow

rate

(

drops

/

minute

)

×60 (drops / hour) =Total infusion time (hours and minutes)

To calculate the total infusion time:

1. Determine the total number of drops ordered. The total number of drops to be infused comes from the physician’s order for the amount of fluid. This amount is multiplied by the drop factor (read from the infusion setup) to determine the total number of drops.

2. Determine the number of minutes the IV is to flow. The number of drops per minute (50) is multiplied by 60 to give the number of drops infused in 1 hour (3000). This figure is then divided into the total number of drops. This will give the number of hours and minutes for the total infusion.

For example, the order reads: “1000 mL D5W to be given at 50 drops/min with a drop factor of 10 drops/mL.” Thus:

1000 mL×10 drops / mL=10,000 drops

10

,

000

drops

3000

drops

/

hr

=3.33 hr or 3 hr, 20 min

Other factors influencing flow rates.

There are many other factors that influence the flow rate of an infusion. The nurse has no control over many of them, such as the age, size, and condition of the patient; the size of the vein; the type of fluid; and the need for the fluid. Other factors may be changed or altered to assist in infusion of IV fluids: the size of the needle, the needle’s position in the vein, the height of the IV pole, the condition of the filter, the air in the air vent, and movement of the patient. If the fluid does not infuse at the calculated rate, the IV setup should be carefully checked from the IV bottle to the site of the needle’s insertion.

Calculating Dosages for Infants and Children

Drug dosages are calculated to give the highest possible blood and tissue concentration of a medication without causing overdosage or adverse effects. Because infants are very sensitive to medications, and because infants and children are so much smaller than adults, almost all dosages given to infants and children are smaller than those given to adults. Most pharmaceutical companies list the recommended dosages of their drugs for a child or infant. If this information is not listed in the instructional material provided with the medication, the nurse should question whether the medication may safely be given to a child.

Although children’s dosages were once frequently calculated, there remain only a few medications that require the nurse to determine how much to give a child. In past years, there were several general rules developed to calculate these special reduced dosages for infants and children. Some were based on age, and these have fallen out of usage because children of different ages vary so much in size. With the growing attention on having better information available for giving medications to children, there has been greater focus on accurate drug calculation for them. The Joint Commission (TJC) now asks that all dosages for children be weight based, preferably in kilograms.

One of the most widely accepted methods for determining children’s dosages based on body weight is known as Clark’s rule. Again, ratios and proportions may be used to calculate the pediatric value. If we assume that an average adult weighs 150 pounds (lb) and we know the adult dosage, it follows that if we know the child’s weight, we can calculate the child’s dosage:

Adult weight:Adult dosage:: Child’s weight:x (Child’s dosage)

For example, if the 150-lb adult dose of meperidine is 100 mg, what is the dose for a 50-lb child?

Weight

of

child

Weight

of

adult

×

Adult’s

dose

=

Child’s

dose

So

50

lb

150

lb

×

100

mg

=

100

3

=

33

mg

Other formulas substitute kilograms for pounds in calculating the correct dose. The formula remains the same. Using the problem information in the preceding column, the nurse simply divides the weight of the adult and the weight of the child by 2.2 to obtain the weights in kilograms. Clark’s rule is by far the most popular method of assessing children’s dosages and should be the formula used.

Medications that require very careful dosage use the body surface area (BSA), or total tissue area, of the child. This is the most accurate method for determining pediatric dosages. The reason for using the BSA is that children have a greater surface area than adults in relation to their weight. For drugs that require careful dosage, charts known as nomograms are used to calculate the BSA in square meters. A nomogram is a chart that displays the relationships between two different types of data so that complex calculations are not necessary. BSA charts are constructed from height and weight data. The ratio of BSA to weight varies inversely (opposite) to length. Thus infants would have proportionally more surface area, because they weigh less and are shorter than children. These charts may be used only if the child has normal height for weight. Even with the use of standardized charts, the calculated dosages are more accurate for children than for very young infants.

An example of a nomogram used to calculate BSA is shown in Figure 7-3. A straight edge is placed from the patient’s height in the left column to his weight in the right column, and the intersection on the BSA column indicates the patient’s BSA. The total BSA value is determined and is put into the following formula:

FIGURE 7-3 Nomogram for body surface area of a child. SA, Surface area. (From Kleigman RM, Stanton BF, St. Geme III JW, et al, editors: Nelson textbook of pediatrics, ed 19, Philadelphia, 2011, Saunders.)

Surface area of the child (

m

2

)×Usual adult dose÷ Surface area of an adult (1.73

m

2

)=Child dose

Use the nomogram to solve these two sample problems, using the BSA to calculate pediatric dosages (use 1.73 m2 as the accepted adult BSA):

1. If the adult dose of kanamycin is 0.5 g, what is the pediatric dose for a 10-month-old child who weighs 22 lb and is 29 inches long?

2. If the adult dose of sulfisoxazole is 500 mg, what is the pediatric dose for an 8-year-old child who weighs 48 lb and is 47 inches tall?

Dimensional analysis is a technique used in a select number of LPN/LVN programs. If your program uses dimensional analysis for drug calculations, see the Evolve website (http://evolve.elsevier.com/Edmunds/LPN/) for information on using this calculation procedure and sample problems.

The Student Study Guide that can be purchased with this text includes an expanded basic review of mathematical principles involved in multiplication and division, calculation of ratio and proportion, percentages, as well as an overview of the apothecary, metric, and household measurement systems. Please review these optional learning resources as needed, and then use the quizzes to test your knowledge and measure your mastery of the content. If, after reading these materials and taking the quizzes, you feel you need additional review, please go to Evolve for additional chapters to help you master this content.