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5

DosageCalculat ions

Key Termsapothecary systemClark’s RuleconversionFried’s Rulemetric systemratio and proportionYoung’s Rule

To determine the correct dose of a particular drug for a pa-tient, one should take into consideration the patient’s sex,weight, age, and physical condition, as well as the other drugsthat the patient is taking. Frequently, the dose that is needed fora patient is not the dose that is available, and it is necessary toconvert the dosage form available into the prescribed dosage.Doing the necessary mathematical calculations to determinewhat should be given is the responsibility of the prescriber whoorders the drug, the pharmacist who dispenses the drug, andthe nurse who administers the drug. This provides for a goodset of checks on the dosage being given before the patient ac-tually receives the drug. In many institutions, drugs arrive atthe patient care area in unit-dose form, prepackaged for eachindividual patient. The nurse who will administer the drug maycome to rely on the prepackaged unit-dose that is sent from thepharmacy and may not even recalculate or recheck the dose tomatch the order that was written. But mistakes still happen,and the nurse, as the person who is administering the drug, islegally and professionally responsible for any error that mightoccur. It is necessary for practicing nurses to know how to con-vert drug orders into available forms of a drug to ensure thatthe right patient is getting the right dose of a drug.

MEASURING SYSTEMS

At least four different systems are currently used in drugpreparation and delivery: the metric system, the apothecarysystem, the household system, and the avoirdupois system.With the growing number of drugs available and increasingawareness of medication errors that occur in daily practice, ef-forts have been made to decrease the dependence on so manydifferent systems. In 1995, the United States PharmacopeiaConvention established standards requiring that all prescrip-tions, regardless of the system that was used in the drug

dosage, include the metric measure for quantity and strengthof drug. It was also established that drugs may be dispensedonly in the metric form. Prescribers are not totally convertedto this new standard, and the nurse must be able to covert whatis ordered into the available form to ensure patient safety. It isimportant to be able to perform conversions within each sys-tem of measure and between systems of measure.

Metric System

The metric system is the most widely used system of meas-ure. It is based on the decimal system, so all units are deter-mined as multiples of 10. This system is used worldwide andmakes the sharing of knowledge and research informationpossible. The metric system uses the gram as the basic unitof solid measure and the liter as the basic unit of liquid meas-ure. Table 5–1 lists the standard units of the metric system.

Apothecary System

The apothecary system is a very old system or measure thatwas specifically developed for use by apothecaries or phar-macists. The apothecary system uses the minim as the basicunit of liquid measure and the grain as the basic unit of solidmeasure. This system is much harder to use than the metricsystem and is rarely seen in most clinical settings. Occa-sionally a prescriber will write an order in this system andthe dosage will have to be converted to an available form.An interesting feature of this system is that it uses Romannumerals placed after the unit of measure to denote amount.For example, 15 grains would be written “gr xv.” Table 5–1lists the standard units of the apothecary system.

Household System

The household system is the measuring system that is foundin recipe books. Many people are familiar with the teaspoon

C H A P T E R 5 Dosage Calculations 45

TABLE 5–1 Basic Units of Measure of the Metric, Apothecary, and Household Measuring Systems

System Solid Measure Liquid Measure

Metric gram (g) liter (L)1 milligram (mg) � 0.001 g 1 milliliter (mL) � 0.001 L1 microgram (�g) � 0.000001 g 1 mL � 1 cubic centimeter � 1 cc1 kilogram (kg) � 1000 g

Apothecary grain (gr) minim (min)60 gr � 1 dram (dr) 60 min � 1 fluidram (f dr)8 dr � 1 ounce (oz) 8 f dr � 1 fluidounce (f oz)

Household pound (lb) pint (pt)1 lb � 16 ounces (oz) 2 pt � 1 quart (qt)

4 qt � 1 gallon (gal)16 oz � 1 pt � 2 cups (c)32 tablespoons (tbsp) � 1 pt3 teaspoons (tsp) � 1 tbsp60 drops (gtt) � 1 tsp

and the cup as units of measure. This system uses the tea-spoon as the basic unit of fluid measure and the pound as thebasic unit of solid measure. Although efforts have been madein recent years to standardize these measuring devices, widevariations have been noted in the capacity of some of theseunits. Patients need to be advised that flatware teaspoons anddrinking cups vary tremendously in the volume that they con-tain. A flatware teaspoon could hold up to two measuring tea-spoons of quantity. When a patient is using a liquid medica-tion at home, it is important to clarify that the measuresindicated in the instructions refer to a standardized measuringdevice. Table 5–1 lists the standard units of the householdsystem.

Avoirdupois System

The avoirdupois system is another older system that was verypopular when pharmacists routinely had to compound med-ications on their own. This system uses ounces and grains, butthey measure differently than those of the apothecary andhousehold systems. The avoirdupois system is seldom usedby prescibers but may be used for bulk medications that comedirectly from the manufacturer.

Other Systems

Some drugs are measured in units other than those already dis-cussed. These measures may reflect chemical activity or biolog-ical equivalence. One of these measures is the unit (U). A unitusually reflects the biological activity of the drug in 1 mL of so-lution. The unit is unique for the drug it measures; a unit of he-parin would not be comparable to a unit of insulin. Milliequiva-lents (mEq) are used to measure electrolytes (eg, potassium,sodium, calcium, fluoride). The milliequivalent refers to theionic activity of the drug in question; the order is usually writtenfor a number of milliequivalents instead of a volume of drug. In-ternational units (IU) are sometimes used to measure certain vi-tamins or enzymes. These are also unique to each drug and can-not be converted to another measuring form.

CONVERTING BETWEEN SYSTEMS

The simplest way to convert measurements from one systemto another is to set up a ratio and proportion equation. Theratio containing two known equivalent amounts is placed onone side of an equation, and the ratio containing the amountyou wish to convert and its unknown equivalent is placed onthe other side. To do this, it is necessary to first check a tableof conversions to determine the equivalent measure in the twosystems you are using. Table 5–2 presents some acceptedconversions between systems of measurement. It is a goodidea to post a conversion guide in the medication room or onthe medication cart for easy access. When conversions areused frequently, it is easy to remember them. When conver-sions are not used frequently, it is best to look them up.

Try the following conversion using Table 5–2. Convert 6 foz (apothecary system) to the metric system of measure. Ac-cording to Table 5–2, 1 f oz is equivalent to 30 mL. Use thisinformation to set up a ratio:

�

The known ratio, 1 f oz (apothecary system) is equivalent to30 mL (metric system), is on one side of the equation. Theother side of the equation contains 6 f oz, the amount (apothe-cary system) that you want to convert, and its unknown (met-ric system) equivalent, X. Because the fluidounce measure-ment is in the numerator (top number) on the left side of theequation, it must also be in the numerator on the right side ofthe equation. This equation would read as follows: One flu-idounce is to thirty milliliters as six fluidounces is to howmany milliliters?

The first step in the conversion is to cross multiply (multi-ply the numerator from one side of the equation times the de-nominator from the other side, and vice-versa):

�

1 f oz � X � 6 f oz � 30 mL

This could also be written

(1 f oz)(X) � (6 f oz)(30 mL)

After multiplying the numbers, you have

1 (f oz) X � 180 (f oz)(mL)

Next, rearrange the terms to let the unknown quantity standalone on one side of the equation:

6 f oz�

X1 f oz�30 mL

6 f oz�

X1 f oz�30 mL

46 P A R T I Introduction to Nursing Pharmacology

TABLE 5–2 Some Commonly AcceptedConversions Between Systems ofMeasurement

Metric System Apothecary System Household System

SOLID MEASURE

1 kg 2.2 lb

454 g 1.0 lb

1 g � 1000 mg 15 gr (gr xv)

60 mg 1 gr (gr i)

30 mg 1/2 gr (gr ss)

LIQUID MEASURE

1 L � 1000 mL about 1 qt

240 mL 8 f oz (f oz viii) 1 c

30 mL 1 f oz (f oz i) 2 tbsp

15–16 mL 4 f dr (f dr iv) 1 tbsp � 3 tsp

8 mL 2 f dr (f dr ii) 2 tsp

4–5 mL 1 f dr (f dr i) 1 tsp � 60 gtt

1 mL 15–16 min (min xv or min xvi)

0.06 mL 1 min (min i)

X �

Whenever possible, cancel out numbers as well as units ofmeasure. In this example, canceling out leaves

X � 180 mL

By canceling out, you are left with the appropriate amountand unit of measure. The answer to the problem is that 6 f ozis equivalent to 180 mL.

Try another conversion. Convert 32 gr (apothecary sys-tem) to its equivalent in the metric system, expressing theanswer in milligrams. First, find the conversion on Table5–2: 1 gr is equal to 60 mg. Set up the ratio:

�

Cross multiply:

(1 gr)(X) � (32 gr)(60 mg)

1 (gr) X � 1920 (gr)(mg)

Rearrange:

X �

Finally, cancel out units and numbers:

X � 1920 mg

Therefore, 32 gr is equivalent to 1920 mg.

CALCULATING DOSAGE

As mentioned earlier, because there are several systems ofmeasurement available that might be used when ordering adrug and because drugs are made available only in certainforms or dosages, it may be necessary to calculate what thepatient should be receiving when interpreting a drug order.

Oral Drugs

Frequently, tablets or capsules for oral administration are notavailable in the exact dose that has been ordered. In these situ-ations, the nurse who is administering the drug must calculatethe number of tablets or capsules that should be given to makeup the ordered dose. The easiest way to determine this is onceagain to set up a ratio and proportion equation. The ratio con-taining the two known equivalent amounts is put on one side ofthe equation, and the ratio containing the unknown value is puton the other side. The known equivalent is the amount of drugavailable in one tablet or capsule; the unknown is the numberof tablets or capsules that are needed for the prescribed dose:

The phrase “amount of drug” serves as the unit, so this in-formation must be in the numerator of each ratio.

Try this example: An order is written for 10 grains of as-pirin (gr x, aspirin). The tablets that are available each con-tain 5 grains. How many tablets should be given? First, setup the equation:

�

Cross multiply the ratio:

5 (gr) X � 10 (gr)(tablet)

Rearrange and cancel units and numbers:

X �

X � 2 tablets

Try another example: An order is written for 0.05 g Al-dactone to be given orally (PO). The Aldactone is availablein 25-mg tablets. How many tablets would you have to give?First, you will need to convert the grams to milligrams.

�

Cross multiply:

1 (g) X � (0.05 � 1000) (g)(mg)

Simplify:

X �

X � 50 mg

The order has been converted to the same measurement asthe available tablets. Now solve for the number of tabletsthat you will need, letting X be the desired dose.

�

25 (mg) X � (50 � 1) (mg)(tablet)

X �

X � 2 tablets

Sometimes the desired dose will be a fraction of a tabletor capsule, 1/2 or 1/4. Some tablets come with score markingsthat allow them to be cut. Pill cutters are readily available inmost pharmacies to help patients cut tablets appropriately.One must use caution when advising a patient to cut a tablet.Many tablets today come in a matrix system that allows forslow and steady release of the active drug. These drugs can-not be cut, crushed, or chewed. A drug reference should al-ways be consulted before cutting a tablet. However, as aquick reference, any tablet that is designated as having de-layed or sustained release may very well be one that cannotbe cut. Capsules can be very difficult to divide precisely, andsome of them also come with warnings that they cannot becut, crushed, or chewed. If the only way to deliver the cor-

50 (mg) (tablet)��

25 (mg)

50 mg�

X25 mg�1 tablet

50 (g)(mg)��

1 (g)

0.05 g�

X1 g

�1000 mg

10 (gr) (tablet)��

5 (gr)

10 gr�

X5 gr

�1 tablet

1920 (gr) (mg)��

1 gr

32 gr�

X1 gr�60 mg

180 (mL) (f oz)��

1 f oz

C H A P T E R 5 Dosage Calculations 47

�

amount of drug prescribed����number of tablets or capsules to give

amount of drug available���

one tablet or capsule

rect dose to a patient is by cutting one of these preparations,a different drug or a different approach to treating the patientshould be tried.

Other oral drugs come in liquid preparations. Many of thedrugs used in pediatrics and for adults who might have dif-ficulty swallowing a pill or tablet are prepared in a liquidform. Some drugs that do not come in a standard liquid formcan be prepared as a liquid by the pharmacist. If the patientis not able to swallow a tablet or capsule, check for otheravailable forms and consult with the pharmacist about thepossibility of preparing the drug in a liquid as a suspensionor a solution. The same principle used to determine the num-ber of tablets needed to arrive at a prescribed dose can beused to determine the volume of liquid that will be requiredto administer the prescribed dose. The ratio on the left of theequation shows the known equivalents, and the ratio on theright side contains the unknown. The phrase “amount ofdrug” must appear in the numerator of both ratios, and thevolume to administer is the unknown (X).

Try this example: An order has been written for 250 mgsulfisoxazole. The bottle states that the solution contains 125mg/5 mL. How much of the liquid should you give?

�

Cross multiply:

125 (mg) X � (250 � 5) (mg)(mL)

Simplify:

X �

So the desired dose is

X � 10 mL

Even if you are working in an institution that providesunit-dose medications, practice your calculation skills occa-sionally to make sure that you can figure out the dose of adrug to give. Power can be lost, computers can go down, andthe ability to determine conversions is a skill that anyonewho administers drugs should have in reserve.

Parenteral Drugs

All drugs administered parenterally must be administered inliquid form. The person administering the drug needs to cal-culate the volume of the liquid that must be given to admin-ister the prescribed dose. The same formula can be used forthis determination that was used for determining the dose ofan oral liquid drug:

Try this example: An order has been written for 75 mgmeperidine to be given intramuscularly (IM). The vial statesthat it contains meperidine, 1.0 mL � 50.0 mg. Set up theequation just as before:

�

50 (mg) X � (75 � 1) (mg)(mL)

X �

X � 1.5 mL

Intravenous Solutions

Intravenous (IV) solutions are used to deliver a prescribedamount of fluid, electrolytes, vitamins, nutrients, or drugs di-rectly into the bloodstream. Although most institutions nowuse electronically monitored delivery systems, it is still im-portant to be able to determine the amount of an IV solutionthat should be given using standard calculations. Most IV de-livery systems come with a standard control called a micro-drip, by which each milliliter delivered contains 60 drops.Macrodrip systems, which deliver 15 drops/mL, are alsoavailable; they are usually used when a large volume must bedelivered quickly. In giving IV drugs, the microdrip systemis most commonly encountered. Check the packaging of theIV tubing if you have any doubts or are unfamiliar with thepackaging. The ratio that is used to determine how manydrops of fluid to administer per minute is the following:

drops/minute � mL of solution prescribed per hour � drops delivered per mL����

60 minutes/1 hour

That is, the number of drops per minute, or the rate that youwill set by adjusting the valve on the IV tubing, is equal tothe amount of solution that has been prescribed per hourtimes the number of drops delivered per mL divided by 60minutes in an hour.

Try this example: An order has been written for a patientto receive 400 mL of 5% dextrose in water (D5W) over a pe-riod of 4 hours in a standard microdrip system (ie, 60drops/mL). Calculate the correct setting (drops per minute).

X �

Simplify:

X �

X �

Therefore,

X � 100 drops/min

Now calculate the same order for an IV set that delivers15 drops/mL:

6000 drops/h��

60 min/h

100 mL/h � 60 drops/mL���

60 min/h

400 mL/4 h� 60 drops/mL���

60 min/h

75 (mg)(mL)��

50 (mg)

75 mg�

X50 mg�1 mL

1250 (mg)(mL)��

125 mg

250 mg�

X125 mg�

5 mL

48 P A R T I Introduction to Nursing Pharmacology

�amount of drug prescribed���

volume of administeramount of drug available���

volume available

�amount of drug prescribed���

volume to administeramount of drug available���

volume available

X �

X �

X �

X � 25 drops/min

If a patient has an order to be given a IV drug, the sameprinciple can be used to calculate the speed of the delivery.

For example, an order is written for a patient to receive 50mL of an antibiotic over 30 minutes. The IV set used dis-penses 60 drops/mL, which allows greater control. Calculatehow fast the delivery should be.

X �

X �

X �

X � 100 drops/min

Pediatric Considerations

Children require different dosages of most drugs than adultsdo. The “standard” drug dosage that is listed on package in-serts and in many references refers to the dose that has beenfound to be most effective in the adult male. An adult’s bodyhandles drugs differently and may respond to drugs differ-ently than a child’s. A child’s body may handle a drug dif-ferently in all areas of pharmacokinetics—absorption, distri-bution, metabolism, and excretion. The responses of thechild’s organs to the effects of the drug also may vary be-cause of the immaturity of the organs. Most of the time achild requires a smaller dose of a drug to achieve the com-parable critical concentration. On rare occasions, a childmay require a higher dose of a drug. For ethical reasons,drug research per se is not done on children. Over time, how-ever, enough information can be accumulated from experi-ence with the drug to have a recommended pediatric dosage.The drug guide that you have selected to use in the clinicalsetting will have the pediatric dose listed if this informationis available. Sometimes there is no recommended dosage buta particular drug is needed for a child. In these situations,there are established formulas that can be used to estimatethe appropriate dosage. These methods of determining a pe-diatric dose take into consideration the child’s age, weight,or body surface.

Fried’s Rule applies to a child younger than 1 year ofage. The rule assumes that an adult dose would be appropri-ate for a child who is 12.5 years (150 months) old. Fried’sRule states

child’s dose (age �1 year) �

� average adult dose

Young’s Rule,which applies to children age 1 to 12 yearsof age, states

child’s dose (age 1–12 years) �

� average adult dose

Clark’s Rule uses the child’s weight to calculate the ap-propriate dose and assumes that the adult dose is based on a150-lb person. It states

child’s dose �

� average adult dose

The child’s surface area may also be used to determinethe approximate dosage that should be used. To do this, thechild’s surface area is determined with the use of a nomo-gram (Figure 5–1). The height and weight of the child aretaken into consideration in this chart. The following formulais then used:

weight of child (in pounds)���

150 pounds

child’s age (in years)���child’s age (in years) � 12

infant’s age (in months)���

150 months

6000 drops/h��

60 min/h

100 mL/h � 60 drops/mL���

60 min/h

50 mL/0.5 h � 60 drops/mL���

60 min/h

1500 drops/h��

60 min/h

100 mL/h � 15 drops/mL���

60 min/h

400 mL/4h � 15 drops/mL���

60 min/h

C H A P T E R 5 Dosage Calculations 49

FIGURE 5–1. The West nomogram for calculating body surface area(BSA). Draw a straight line connecting the child’s height (left scale) tothe child’s weight (right scale). The BSA value, which is calculated insquare meters, is found at the point where the line intersects the SAcolumn. The formula for estimating a child’s dose is: Child’s BSA (in m2)� adult dose � 1.73. Normal values are shown in the box.

child’s dose �

� average adult dose

For example, a 3-year-old child weighing 30 lb is to re-ceive a therapeutic dose of aspirin. The average adult dose is5 gr, and the dose to be given is the unknown (X). The calcu-lation may be made from the child’s age, by Young’s Rule:

X � � 5 gr

X �

X � 1 gr

Alternatively, the calculation may be based on the child’sweight, using Clark’s Rule:

X � � 5 gr

X �

X � 1 gr

With small children, even a tiny dosage error can be crit-ical. When working in pediatrics, it is important to becomefamiliar with at least one of these methods of determiningthe drug dose to use. Many institutions require that twonurses check critical pediatric dosages. This is a good prac-tice when working with small children. Box 5–1 summarizesthe pediatric conversion formulas.

CHAPTER SUMMARY

• At least four different systems are currently used in drugpreparation and delivery. These include the metric system,the apothecary system, the household system, and the av-oirdupois system.

• The metric system is the most widely used system of meas-ure. The United States Pharmacopeia Convention estab-lished standards requiring that all prescriptions, regardlessof the system that was used in the drug dosage, include themetric measure for quantity and strength of drug. All drugsare dispensed in the metric system.

• It is important to know how to convert dosages from onesystem to another. The method of ratio and proportion,which uses basic principles of algebra to find an unknown,is the easiest method of converting doses within and be-tween systems.

• Children require different dosages of most drugs thanadults do because of the way that their bodies handle drugsand the way that drugs affect their tissues and organs.

• Standard formulas can be used to determine the approximatedose that should be given to a child when the average adultdose is known. These include Fried’s Rule (which considersage less than 1 year), Clark’s Rule (which considers thechild’s weight), Young’s Rule (which considers weight andage greater than 1 year), and the surface area rule, which re-quires the use of a nomogram to determine body surface area.

Review Questions1. Digoxin 0.125 mg is ordered for a patient who is having

trouble swallowing. The bottle of digoxin elixir reads 0.5mg/2 mL. How much would you give?a. 5 mLb. 0.5 mLc. 1.5 mLd. 1 mL

2. The usual adult dose of Benadryl is 50 mg. What wouldbe the safe dose for a child weighing 27 lb?a. 0.9 mgb. 1.8 mgc. 9.0 mgd. 18 mg

3. An order is written for 700 mg ampicillin PO. The drug issupplied in liquid form as 1 g/3.5 mL. How much of theliquid should be given?a. 5 mLb. 2.5 mLc. 6.2 mLd. 2.45 mL

4. An order is written for 1000 mL of normal saline to be ad-ministered over 10 hr. The drop factor on the IV tubingstates 15 drops/mL. What is the IV flow rate?a. 50 mL/ hr at 50 drops/minb. 100 mL/hr at 25 drops/minc. 100 mL/hr at 100 drops/mind. 100 mL/hr at 15 drops/min

150 (gr)(lb)��

150 lb

30 lb�150 lb

15 (y)(gr)��

15 y

3 y�3 � 12 y

surface area in square meters���

1.73

50 P A R T I Introduction to Nursing Pharmacology

B O X 5 – 1

Formulas Used for CalculatingPediatric Dosages

FRIED’S RULE

child’s dose (age �1 year) �

� average adult dose

YOUNG’S RULE

child’s dose (age 1–12 years) �

� average adult dose

CLARK’S RULE

child’s dose � � average adult dose

SURFACE AREA CALCULATION

child’s dose � � average adult dosesurface area in square meters���

1.73

weight of child (in pounds)���

150 pounds

child’s age (in years)���

childs age (in years) � 12

infant’s age (in months)���

150 months

5. The average adult dose of meperidine is 75 mg. Whatdose would be appropriate for a 10-month-old infant?a. 50 mgb. 5 mgc. 25 mgd. 0.5 mg

6. A patient needs to take 0.75 g tetracycline PO. The drugcomes in 250-mg tablets. How many tablets should thepatient take?a. 2 tabletsb. 3 tabletsc. 4 tabletsd. 30 tablets

7. Aminophylline is supplied in a 500 mg/2.5 mL solution.How much would be given if an order were written for100 mg aminophylline IV?a. 5 mLb. 1.5 mLc. 2.5 mLd. 0.5 mL

8. Heparin 800 U is ordered for a patient. The heparin issupplied in a multidose vial that is labeled 10,000 U/mL.How many cubic centimeters of heparin would be neededto treat this patient?a. 0.8 ccb. 0.08 ccc. 8.0 ccd. 0.4 cc

B I B L I O G R A P H YBroussard, M. C., & Pire, S. (1996). Medication problems in the

elderly: A home healthcare nurse’s perspective. Home Health-care Nurse, 14, 441–443.

Hardman, J. G., Limbird, L. E., Molinoff, P. B., Ruddon, R. W., &Gilman, A. G. (Eds.). (1996). Goodman and Gilman’s the pharma-cological basis of therapeutic (9th ed.). New York: McGraw-Hill.

Lee, M. (1996). Drugs and the elderly: Do you know the risks?American Journal of Nursing, 96 (7), 25–32.

Morrison, G. (1996). Drug dosing in the intensive care unit: Thepatient with renal failure. In J. M. Rippe, R. S. Irwin, & M. P.Fink, Intensive care medicine (3rd ed.). Boston: Little, Brown.

C H A P T E R 5 Dosage Calculations 51