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Joh Ch05.qxd8/31/072:39 PMPage 2CHAPTER5Dosage CalculationsL earning ObjectivesAfter completing this chapter, youshould be able to: Solve one-step pharmaceuticaldosage calculations. Set up a series of ratios andproportions to solve a singledosage calculation. Determine what informationyou will need to solve for, inaddition to any giveninformation, to properlycalculate dosages. Convert pediatric weights frompounds to kilograms. Accurately determine dosagesbased on mg/kg/day. Define common sig (signa)codes used on prescriptions.2INTRODUCTIONProper dosing of medications is important to ensure patientsafety. Calculating dosages, dosage regimens, andcompounding formulas involves the use of simple mathprinciples. You can solve many of these problems by settingup ratios and proportions using the information given in thequestion and keeping like units consistent.

Joh Ch05.qxd8/31/072:39 PMPage 3Sig RefresherThe sig portion of the prescription order, meaning signa, is where the instructions for the patient are written. Pharmacy technicians enter the informationfrom the prescription order into the computer. The sig is an important valueto remember in order to properly determine pediatric dosages. The followingare some of the more common sigs you will find on prescriptions:qd every dayqod every other dayd daily bid twice a daytid three times a dayqid four times a dayq4h every 4 hrq6h every 6 hrq8h every 8 hrq4–6h every 4–6 hrprn as neededDepending on the workplace, you may also see sigs such as the following:q3d every three daysqmwf every Monday, Wednesday, and Fridayqw every weekDosage CalculationsDosage calculations include calculating the number of doses, dispensingquantities, and ingredient quantities; these calculations are performed in thepharmacy on a daily basis. The pharmacy technician must have a full working knowledge of how to perform these calculations.To perform dosage calculations, you will utilize the information andprinciples introduced in the previous chapters of this book. You can solvethese calculations by setting up ratios and proportions, keeping like unitsconsistent, and cross-multiplying.CALCULATING THE NUMBER OF DOSESTo calculate the number of doses, you should first determine which information presented is actually applicable to the question. Too often mistakes aremade on dosage calculations because we overcomplicate them.EXAMPLE 5.1How many 1-tsp doses are in a 4 oz bottle of Prozac LiquidSolution 20 mg/5 mL?Rx Prozac Solution.TT tsp. po qdDisp. # 4 ozChapter FiveDosage Calculations3

Joh Ch05.qxd8/31/072:39 PMPage 4Figure 5-1Drug label for Prozac.(Courtesy of Eli Lilly and Company.)Let’s look at the information that has been provided: .TTtsp po—the dose qd—the frequency 4 oz—the quantity dispensed Prozac Solution 20 mg/5 mL—the drug name and strength 120 mL—the quantity of the stock bottleThe question is simply asking how many doses make up the total amountbeing dispensed. The strength of the drug, frequency of dosage and quantityof the stock bottle have no relevance in performing this calculation.So now we know that we are working with 1 tsp. doses and a total quantity of 4 oz, but to solve this calculation using a ratio/proportion we have tohave similar units of measure—in this case mL.We know that 1 tsp 5 mL and we should also know that 4 oz. 120 mL,but if you didn’t that could also be solved by using a ratio/proportion.4 oz1 oz 30 mLx mLCross-multiply and solve the equation for x.30 * 4 120 and 1 * x (1) x(1)x 120Now that you have both quantities converted to units in mL, we can setup our ratio/proportion and solve.1 dosex doses 5 mL120 mLCross-multiply5 * x 5x and 1 * 120 1204Chapter FiveDosage Calculations

Joh Ch05.qxd8/31/072:39 PMPage 5Now set up your equation and solve for x.5x 120To solve for x, divide both sides by 5.1202x 22120 , 5 24x 24So, there are 24 doses (of 5 mL) in a 4 oz (120 mL) bottle.CALCULATING THE NUMBER OF DOSESEXAMPLE 5.2How many doses are provided in the prescription below?Rx—Ibuprofen 400 mg. .T -TTpo q 6 hr prn painDisp. # 120Let’s look at the information that has been provided: . .T -TTpo—the dose q 6 hr prn pain—the frequency 120—the quantity dispensed Ibuprofen 400 mg—the drug name and strengthWorkplace Wisdom Always use the higher dosage amount when performing dosage calculations on prescriptions that have a range for the dose, as inExample 5.2. This will provide the most conservative solution and ensurethe most accurate potential for days supply.Using the information provided, set up the ratio/proportion and solve.1 dosex doses 2 tabs120 tabsCross-multiply2 * x 2x and 1 * 120 120Now set up your equation and solve for x.2x 120To solve for x, divide both sides by 2.1202x 22120 , 2 60x 60So, there is a minimum of 60 doses prescribed.Chapter FiveDosage Calculations5

Joh Ch05.qxd8/31/072:39 PMPage 6PRACTICE PROBLEMS 5.11. How many dosages are provided in the prescription listed below?Rx—Cardura 2 mg.TT po qdDisp. # 902. How many droppersful (a 2.5 mL dosage) are in a 50 mL bottle ofEryPed Drops?Figure 5-2Drug label for EryPed Drops.(Reproduced with permission of Abbott Laboratories.)3. How many dosages are provided in the prescription listed below?Rx—Vicodin 5/500.TT po q8hrDisp. # 504. How many 1 tsp doses are in each bottle of Zithromax 200 mg/5 mL aslisted below, when mixed?Figure 5-3Drug label for Zithromax.(Registered Trademark of Pfizer Inc. Reproduced with permission.)5. How many dosages are provided in the prescription listed below?Rx—Regular Insulin U-100 (100 units/mL)Inject 20 units qAMDisp. # 1 vial (10mL)6Chapter FiveDosage Calculations

Joh Ch05.qxd8/31/072:39 PMPage 7CALCULATING THE QUANTITY TO DISPENSEEXAMPLE 5.3How many Biaxin 250 mg tablets should be dispensed?Rx—Biaxin 250 mg.TTpo BID 10dFigure 5-4 Drug label for Biaxin.(Reproduced with permission of Abbott Laboratories.)Again, to solve this dosage calculation it is important to first determinewhich information is necessary; it is also critical to know the common SIGcodes to perform dosage calculations.Let’s look at what information that has been provided: .TTpo—the dose BID—the frequency x 10d—the duration Biaxin 250 mg—the drug name and strength 100 tablets—the quantity of the stock bottleTo calculate the appropriate quantity to dispense, use the followingformula:dose frequency duration quantity to dispenseUsing the information provided in the prescription, you can set up thecalculation as such:1 2 10 xdosefrequencydurationquantity to dispense1 2 10 2020 xSo, 20 tablets of Biaxin 250 mg should be dispensed.Chapter FiveDosage Calculations7

Joh Ch05.qxd8/31/072:39 PMPage 8CALCULATING THE QUANTITY TO DISPENSEHow much Promethazine w/Codeine syrup should be dispensed?EXAMPLE 5.4Rx—Promethazine w/Codeine Syrup 6.25/10.TTtsp. po QID 4dLet’s look at what information has been provided: .TTtsp. po—the dose QID—the frequency x 4d—the duration Promethazine w/Codeine Syrup 6.25/10—the drug name and strengthTo calculate the appropriate quantity to dispense, use the following formula:dose frequency duration quantity to dispenseUsing the information provided in the prescription, you can set up thecalculation as such:1tsp 4 dosefrequency4 xdurationquantity to dispense1 4 4 1616 xSo, 16 teaspoonsful, or 80 mL, of promethazine w/codeine should bedispensed.PRACTICE PROBLEMS 5.21. What quantity should be dispensed for the prescription listed below?Rx—Zoloft 50 mg.TTpo qdDisp. 1 mo. supply2. What quantity should be dispensed, using the stock medication below,to provide 20 mg of diazepam prior to the procedure and 10 mgfollowing?Figure 5-5 Drug label forDiazepam.(Used with permission ofRoxane Laboratories, Inc.)8Chapter FiveDosage Calculations

Joh Ch05.qxd8/31/072:39 PMPage 93. What quantity should be dispensed for a three-month supply of thefollowing prescription?Rx—furosemide 20 mg.TTpo QOD4. What quantity should be dispensed if 50 mg of amitriptyline has beenprescribed daily for 3 weeks, if the medication listed below is all that isavailable?Figure 5-6 Drug label for Amitriptyline HCL.(Courtesy of Geneva Pharmaceuticals.)5. What quantity should be dispensed for a 30-day supply of the followingprescription?Rx—Soma 350 mg.TTpo BID – TID prn muscle spasmsCALCULATING THE QUANTITY OF INGREDIENTEXAMPLE 5.5How much codeine is in each dose of Codeine Phosphate OralSolution 15 mg/mL?Rx—Codeine Oral Soln. 15 mg/mL.TTtbsp po prn painDisp. # 4 ozFigure 5-7 Drug label forCodeine Phosphate OralSolution.(Used with permission ofRoxane Laboratories, Inc.)Chapter FiveDosage Calculations9

Joh Ch05.qxd8/31/072:39 PMPage 10Let’s first look at all of the information provided to determine which willbe used in solving the problem:. TT tbsp po—the dose prn—the frequency 4 oz—the quantity to dispense Codeine Phosphate Oral Solution 15 mg/mL—the drug nameand strength 500 mL—the quantity of the stock bottleTo solve this problem, we need to set up a ratio/proportion using the doseand strength, but again remember that units of measure must be the same.The dose (1 tbsp) is equivalent to 15 mL—which you should know.Now we can set up the ratio/proportion.15 mg15 mg 5 mL1 mLCross-multiply and then set up the equation to solve for x.15 * 15 225 and 5 * x 5x5x 225Now divide both sides by 5 to solve for x.5x225 55x 45So, the answer is 45 mg of codeine in each 1 tbsp dose.PRACTICE PROBLEMS 5.3Perform the following dosage calculations.1. Promethazine with codeine syrup contains 6.25 mg promethazine and10 mg codeine per 5 mL. How many milligrams of promethazine are in2 tsp?2. Rx hydroxycobalamine 10,000 mcg/cc 30 cc Sig: 1 cc IM hsHow many milligrams are in each dose?3. Rx acetaminophen with codeine#3 acetaminophen 300 mg/codeine30 mg 30 tabletsHow many grains of codeine are in each tablet?CALCULATING THE QUANTITY OF INGREDIENTEXAMPLE 5.6How many mL of stock Dopamine must be added to the IV solution?Rx—Dopamine 400 mg added to 500 mL of NSStock: Dopamine HCl Injection 80 mg/mL10Chapter FiveDosage Calculations

Joh Ch05.qxd8/31/072:39 PMPage 11Let’s first look at all of the information provided to determine which willbe used in solving the problem: 400 mg—the dose 500 mL—the quantity to dispense Dopamine HCl Injection 80 mg/mL—the drug name and strengthTo solve this problem, we must determine how many milliliters of the stockDopamine will need to be added to the normal saline IV solution bag.We must set up a ratio/proportion.400 mg80 mg 1 mLx mLCross-multiply and then set up the equation to solve for x.1 * 400 400 and400 80x80 * x 80xNow divide both sides by 80 to solve for x.80x400 8080x 5So, the answer is 5 mL of the stock Dopamine HCl Injection must beadded to the IV solution.PRACTICE PROBLEMS 5.41. Z-Pak s contain 6 tablets of azithromycin 250 mg, which is taken overthe course of five days. How many total mg of active ingredient arecontained in a Z-Pak ?2. How many mcg of Fentanyl would be contained in 1.5 mL?Figure 5-8 Drug label forFentanyl.(Courtesy of ESI Lederle, a BusinessUnit of Wyeth Pharmaceuticals,Philadelphia, PA.)Chapter FiveDosage Calculations11

Joh Ch05.qxd8/31/072:39 PMPage 123. How many milligrams of acetaminophen are contained in 2 Lortab 2.5(2.5 mg hydrocodone/500 mg acetaminophen) tablets?4. How many milligrams of dexamethasone are contained in the stockbottle (500 mL) below?Figure 5-9 Drug label forDexamethasone Oral Solution.(Used with permission of RoxaneLaboratories, Inc.)5. How many mg of hydrocortisone are found in 1 tbsp of Cortef 10 mg/5 mL?Figure 5-10 Drug label forCortef.(Courtesy of PharmaciaCorporation.)CALCULATING THE CORRECT DAYS SUPPLYEXAMPLE 5.7How many days should the following prescription last?Rx—Pamelor 75 mg.TTpo BIDDisp. # 5012Chapter FiveDosage Calculations