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CHAPTER
5 Dosage Calculations
L earning Objectives After completing this chapter, you should be able to:
• Solve one-step pharmaceutical dosage calculations. • Set up a series of ratios and proportions to solve a single dosage calculation. • Determine what information you will need to solve for, in addition to any given information, to properly calculate dosages. • Convert pediatric weights from pounds to kilograms. • Accurately determine dosages based on mg/kg/day. • Define common sig (signa) codes used on prescriptions.
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INTRODUCTION Proper dosing of medications is important to ensure patient safety. Calculating dosages, dosage regimens, and compounding formulas involves the use of simple math principles. You can solve many of these problems by setting up ratios and proportions using the information given in the question and keeping like units consistent.
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Sig Refresher The sig portion of the prescription order, meaning signa, is where the instructions for the patient are written. Pharmacy technicians enter the information from the prescription order into the computer. The sig is an important value to remember in order to properly determine pediatric dosages. The following are some of the more common sigs you will find on prescriptions: qd = every day qod = every other day d = daily bid = twice a day tid = three times a day qid = four times a day q4h = every 4 hr q6h = every 6 hr q8h = every 8 hr q4–6h = every 4–6 hr prn = as needed Depending on the workplace, you may also see sigs such as the following: q3d = every three days qmwf = every Monday, Wednesday, and Friday qw = every week
Dosage Calculations Dosage calculations include calculating the number of doses, dispensing quantities, and ingredient quantities; these calculations are performed in the pharmacy 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 and principles introduced in the previous chapters of this book. You can solve these calculations by setting up ratios and proportions, keeping like units consistent, and cross-multiplying.
CALCULATING THE NUMBER OF DOSES To calculate the number of doses, you should first determine which information presented is actually applicable to the question. Too often mistakes are made on dosage calculations because we overcomplicate them. EXAMPLE 5.1
How many 1-tsp doses are in a 4 oz bottle of Prozac® Liquid Solution 20 mg/5 mL? Rx Prozac® Solution .. TT tsp. po qd Disp. # 4 oz Chapter Five
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Figure 5-1
Drug label for Prozac.
(Courtesy of Eli Lilly and Company.)
Let’s look at the information that has been provided: ✓
.. TT
tsp 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 bottle The question is simply asking how many doses make up the total amount being dispensed. The strength of the drug, frequency of dosage and quantity of 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 to have 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 oz 1 oz = 30 mL x mL Cross-multiply and solve the equation for x. 30 * 4 = 120 and 1 * x = (1) x (1)x = 120 Now that you have both quantities converted to units in mL, we can set up our ratio/proportion and solve. 1 dose x doses = 5 mL 120 mL Cross-multiply 5 * x = 5x and 1 * 120 = 120 4
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Now set up your equation and solve for x. 5x = 120 To solve for x, divide both sides by 5. 120 2x = 2 2 120 , 5 = 24 x = 24 So, there are 24 doses (of 5 mL) in a 4 oz (120 mL) bottle.
CALCULATING THE NUMBER OF DOSES EXAMPLE 5.2
How many doses are provided in the prescription below? Rx—Ibuprofen 400 mg . .. T -TT
po q 6 hr prn pain
Disp. # 120
Let’s look at the information that has been provided: ✓
. .. T -TT
po—the dose
✘ q 6 hr prn pain—the frequency ✓ 120—the quantity dispensed ✘ Ibuprofen 400 mg—the drug name and strength Workplace Wisdom Always use the higher dosage amount when performing dosage calculations on prescriptions that have a range for the dose, as in Example 5.2. This will provide the most conservative solution and ensure the most accurate potential for days supply. Using the information provided, set up the ratio/proportion and solve. 1 dose x doses = 2 tabs 120 tabs Cross-multiply 2 * x = 2x and 1 * 120 = 120 Now set up your equation and solve for x. 2x = 120 To solve for x, divide both sides by 2. 120 2x = 2 2 120 , 2 = 60 x = 60 So, there is a minimum of 60 doses prescribed. Chapter Five
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PRACTICE PROBLEMS 5.1 1. How many dosages are provided in the prescription listed below? ________________ Rx—Cardura® 2 mg .. TT po qd Disp. # 90 2. How many droppersful (a 2.5 mL dosage) are in a 50 mL bottle of EryPed® Drops? ________________
Figure 5-2
Drug 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 q8hr Disp. # 50 4. How many 1 tsp doses are in each bottle of Zithromax® 200 mg/5 mL as listed below, when mixed? ________________
Figure 5-3
Drug 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 qAM Disp. # 1 vial (10mL) 6
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CALCULATING THE QUANTITY TO DISPENSE EXAMPLE 5.3
How many Biaxin® 250 mg tablets should be dispensed? Rx—Biaxin® 250 mg .. TT
po BID 10d
Figure 5-4 Drug label for Biaxin. (Reproduced with permission of Abbott Laboratories.)
Again, to solve this dosage calculation it is important to first determine which information is necessary; it is also critical to know the common SIG codes to perform dosage calculations. Let’s look at what information that has been provided: ✓
.. TT
po—the dose
✓ BID—the frequency ✓ x 10d—the duration ✘ Biaxin® 250 mg—the drug name and strength ✘ 100 tablets—the quantity of the stock bottle To calculate the appropriate quantity to dispense, use the following formula: dose frequency duration quantity to dispense Using the information provided in the prescription, you can set up the calculation as such: 1 2 10 x dose frequency duration quantity to dispense 1 2 10 20 20 x So, 20 tablets of Biaxin® 250 mg should be dispensed.
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CALCULATING THE QUANTITY TO DISPENSE How much Promethazine w/Codeine syrup should be dispensed?
EXAMPLE 5.4
Rx—Promethazine w/Codeine Syrup 6.25/10 .. TT
tsp. po QID 4d
Let’s look at what information has been provided: ✓
.. TT
tsp. po—the dose
✓ QID—the frequency ✓ x 4d—the duration ✘ Promethazine w/Codeine Syrup 6.25/10—the drug name and strength To calculate the appropriate quantity to dispense, use the following formula: dose frequency duration quantity to dispense Using the information provided in the prescription, you can set up the calculation as such: 1tsp 4 dose frequency
4 x duration quantity to dispense
1 4 4 16 16 x So, 16 teaspoonsful, or 80 mL, of promethazine w/codeine should be dispensed.
PRACTICE PROBLEMS 5.2 1. What quantity should be dispensed for the prescription listed below? ________________ Rx—Zoloft® 50 mg .. TT
po qd
Disp. 1 mo. supply 2. What quantity should be dispensed, using the stock medication below, to provide 20 mg of diazepam prior to the procedure and 10 mg following? ________________
Figure 5-5 Drug label for Diazepam. (Used with permission of Roxane Laboratories, Inc.)
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3. What quantity should be dispensed for a three-month supply of the following prescription? ________________ Rx—furosemide 20 mg .. TT
po QOD
4. What quantity should be dispensed if 50 mg of amitriptyline has been prescribed daily for 3 weeks, if the medication listed below is all that is available? ________________
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 following prescription? ________________ Rx—Soma® 350 mg .. TT
po BID – TID prn muscle spasms
CALCULATING THE QUANTITY OF INGREDIENT EXAMPLE 5.5
How much codeine is in each dose of Codeine Phosphate Oral Solution 15 mg/mL? Rx—Codeine Oral Soln. 15 mg/mL .. TT
tbsp po prn pain
Disp. # 4 oz
Figure 5-7 Drug label for Codeine Phosphate Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
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Let’s first look at all of the information provided to determine which will be 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 name and strength ✘ 500 mL—the quantity of the stock bottle To solve this problem, we need to set up a ratio/proportion using the dose and 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 mg 15 mg = 5 mL 1 mL Cross-multiply and then set up the equation to solve for x. 15 * 15 = 225 and 5 * x = 5x 5x = 225
Now divide both sides by 5 to solve for x. 5x 225 = 5 5 x = 45
So, the answer is 45 mg of codeine in each 1 tbsp dose.
PRACTICE PROBLEMS 5.3 Perform the following dosage calculations. 1. Promethazine with codeine syrup contains 6.25 mg promethazine and 10 mg codeine per 5 mL. How many milligrams of promethazine are in 2 tsp? ________________ 2. Rx hydroxycobalamine 10,000 mcg/cc 30 cc Sig: 1 cc IM hs How many milligrams are in each dose?________________ 3. Rx acetaminophen with codeine#3 acetaminophen 300 mg/codeine 30 mg 30 tablets How many grains of codeine are in each tablet? ________________
CALCULATING THE QUANTITY OF INGREDIENT EXAMPLE 5.6
How many mL of stock Dopamine must be added to the IV solution? Rx—Dopamine 400 mg added to 500 mL of NS Stock: Dopamine HCl Injection 80 mg/mL
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Let’s first look at all of the information provided to determine which will be 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 strength To solve this problem, we must determine how many milliliters of the stock Dopamine will need to be added to the normal saline IV solution bag. We must set up a ratio/proportion. 400 mg 80 mg = 1 mL x mL Cross-multiply and then set up the equation to solve for x. 1 * 400 = 400 and 400 = 80x
80 * x = 80x
Now divide both sides by 80 to solve for x. 80x 400 = 80 80 x = 5 So, the answer is 5 mL of the stock Dopamine HCl Injection must be added to the IV solution.
PRACTICE PROBLEMS 5.4 1. Z-Pak®s contain 6 tablets of azithromycin 250 mg, which is taken over the course of five days. How many total mg of active ingredient are contained in a Z-Pak®? ________________ 2. How many mcg of Fentanyl® would be contained in 1.5 mL? ________________
Figure 5-8 Drug label for Fentanyl. (Courtesy of ESI Lederle, a Business Unit of Wyeth Pharmaceuticals, Philadelphia, PA.)
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3. 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 stock bottle (500 mL) below? ________________
Figure 5-9 Drug label for Dexamethasone Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
5. How many mg of hydrocortisone are found in 1 tbsp of Cortef ® 10 mg/5 mL? ________________
Figure 5-10 Drug label for Cortef. (Courtesy of Pharmacia Corporation.)
CALCULATING THE CORRECT DAYS SUPPLY EXAMPLE 5.7
How many days should the following prescription last? Rx—Pamelor® 75 mg .. TT
po BID
Disp. # 50
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Figure 5-11 Drug label for Pamelor. (Copyright Novartis Pharmaceuticals Corporation. Reprinted with permission.)
Let’s determine which information provided will be needed to solve the problem. ✓
.. TT
po—the dose
✓ BID—the frequency ✓ 50—the quantity to dispense ✘ Pamelor® 75 mg—the drug name and strength ✘ 100 capsules—the quantity of the stock bottle To calculate the appropriate days supply, use the following formula: Days Supply =
Qty. Dispensed (Dose * Frequency)
Using the information provided, set up the formula as below. x =
50 (qty. dispensed) (1 * 2) (Dose * Frequency)
This becomes . . . x =
50 or x = 25 2
So, this prescription should last for 25 days.
CALCULATING THE CORRECT DAYS SUPPLY EXAMPLE 5.8
How many days should the following prescription last? Rx—Kaletra® 133.3 mg/33.3mg .. TT
po BID
food.
Disp. # 360
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Let’s determine which information provided will be needed to solve the problem. ..
✓ TT po—the dose ✓ BID—the frequency ✓ 360—the quantity to dispense ✘ Kaletra® 133.3 mg/33.3mg—the drug name and strength To calculate the appropriate days supply, use the following formula: Days Supply =
Qty. Dispensed (Dose * Frequency)
Using the information provided, set up the formula as below. x =
360 (qty. dispensed) (2 * 2) (Dose * Frequency)
This becomes. . . 360 or x = 90 4 So this prescription should last for 3 months, or 90 days. x =
PRACTICE PROBLEMS 5.5 1. How many days will the following prescription last? ________________ Rx—Diabinese® 100 mg .. TT
po qAM
Disp. # 45 2. How many days will a 150 mL bottle of Ceclor® 125 mg>5 mL last, if the patient is to take 2 teaspoonsful three times daily? ________________
Figure 5-12 Drug label for Ceclor. (Courtesy of Eli Lilly and Company.)
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3. How many days will the following prescription last? ________________ Rx—Valium® 5 mg .. TT
po BID
Disp. # 60 4. How many days should 10 tablets of Cialis® 5 mg last, if the prescribed directed to use is a maximum of one tablet q3 days?________________ 5. How many days will the following prescription last? ________________ Rx—Keflex® 250 mg .. TT
po TID
Disp. # 42
PRACTICE PROBLEMS 5.6 1. Rx—Amoxil 250 mg/5 mL .. TT tsp TID 10d a. What is the appropriate quantity to dispense? ________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of amoxicillin, in mg, to be dispensed? ________________ d. How many days should this prescription last? ________________ 2. Rx—Dexamethasone Oral Soln. 0.5 mg>5 mL Give 0.25 mg QOD Disp. 6 mg
Figure 5-13 Drug label for Dexamethasone Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
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a. What is the appropriate quantity to dispense?________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of dexamethasone, in mg, to be dispensed? ________________ d. How many days should this prescription last? ________________ 3. Rx—Proventil® Inhaler 17gm (200 inhalations) .. Use TT puffs BID Disp. # 1 a. What is the appropriate quantity to dispense? ________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of albuterol, in mcg, per inhalation? ________________ d. How many days should this prescription last? ________________ 4. Rx—Xanax 0.25 mg . .. T -TT TID prn 14d a. What is the appropriate quantity to dispense? ________________ b. What is the maximum number of doses available if 60 tablets are dispensed? ________________ c. What is the maximum amount of alprazolam, in mg, to be taken daily? ________________ d. How many days could this prescription last, if 60 tablets are dispensed? ________________
Pediatric Dosing Pediatric patients, which include both infants and children, require special dosing that is adjusted for their body weight. A number of formulas have been used throughout the years to determine the best dose for pediatric patients, but the most commonly used method is stated as mg/kg of body weight. Pediatric Formulas Children need lower dosages of medication compared to adults. Three formulas are used to help calculate a pediatric dosage based on whatever information is available. In some children’s hospitals the pharmacy may have a preferred formula. However, the pharmacy technician should be able to calculate the correct pediatric dosage using each formula. 16
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FORMULA
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Pediatric Dosing
Fried’s Rule Child’s dosage =
Age in months * Adult dosage 150
Young’s Rule Child’s dosage =
Age of child in years * Adult dosage Age of child in years + 12
Clark’s Rule Child’s dosage =
Child’s weight in pounds * Adult dosage 150
CALCULATING PEDIATRIC DOSAGES USING FRIED’S RULE EXAMPLE 5.9
An infant, 15 months old and weighing 20 pounds, needs Streptomycin Sulfate, which is usually administered to adults as 1 gm (1000 mg), as a daily IM injection. What is the appropriate dosage for the infant?
To calculate the pediatric dosage based on a child’s age in months, simply use the formula for Fried’s Rule. Using the information provided, you can set up the calculation as follows: 15 (Age in months) * 1000 mg (Adult Dose) 150 15 Pediatric Dose = * 1000 150 Pediatric Dose = 0.1 * 1000 Pediatric Dose =
Pediatric Dose = 100 mg
So, according to Fried’s Rule, the pediatric dosage appropriate for a 15-month-old would be 100 mg.
PRACTICE PROBLEMS 5.7 1. A child, 24 months old, needs acetaminophen, and the normal adult dose is 650 mg. What is the appropriate dosage for the child?________________ 2. An 18-month-old needs amikacin sulfate, and the normal adult dose is 250 mg. What is the appropriate dosage for the child? ________________ 3. A child, 30 months old, needs erythromycin, and the normal adult dose is 250 mg QID. What is the appropriate dosage for the child? ________________ Chapter Five
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CALCULATING PEDIATRIC DOSAGES USING YOUNG’S RULE EXAMPLE 5.10
Now, let’s reexamine Example 5.9 using Young’s Rule, which uses the child’s age in years. The age of a 15-month-old could be expressed as 1.25 years old, since he or she has lived for 12 months (1 year) 3 months (1/4 or 0.25 of a year).
Using an age of 1.25 years and the information provided in Example 5.5, set up the calculation, using Young’s Rule, as follows: Pediatric Dose =
1.25 (Age in years) * 1000 mg (Adult Dose) 13.25 (Age of child + 12)
Pediatric Dose =
1.25 * 1000 13.25
Pediatric Dose = 0.094 * 1000 Pediatric Dose = 94 mg
So, according to Young’s Rule, the pediatric dosage appropriate for a 15-month-old would be 94 mg.
PRACTICE PROBLEMS 5.8 1. A 2-year-old child is prescribed amoxicillin, and the normal adult dose is 500 mg. What is the appropriate dosage for the child?________________ 2. A 7-year-old needs propylthiouracil, and the normal adult daily dose is 150 mg. What is the appropriate dosage for the child?________________ 3. A child, 10 years old, is prescribed Tavist® syrup, and the normal adult dose is 1.34 mg BID. What is the appropriate dosage for the child?________________
CALCULATING PEDIATRIC DOSAGES USING CLARK’S RULE EXAMPLE 5.11
Now, let’s reexamine Example 5.9 using Clark’s Rule, which uses the child’s weight in pounds.
Using a weight of 20 pounds and the information provided in Example 5.5, set up the calculation, using Young’s Rule, as follows: 20 (Weight in pounds) * 1000 mg (Adult Dose) 150 20 Pediatric Dose = * 1000 150 Pediatric Dose = 0.133 * 1000
Pediatric Dose =
Pediatric Dose = 133 mg 18
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So, according to Clark’s Rule, the pediatric dosage, appropriate for a 15-month-old, weighing 20 pounds, would be 133 mg.
PRACTICE PROBLEMS 5.9 1. A child, weighing 85 pounds, is prescribed hydrochlorothiazide, and the normal adult dose is 50 mg. What is the appropriate dosage for the child?________________ 2. A child, weighing 70 pounds, is prescribed quinine sulfate, and the normal adult dose is 325 mg TID. What is the appropriate dosage for the child?________________ 3. A child, weighing 112 pounds, is prescribed Kaletra®, a protease inhibitor combination therapy. The normal adult dose is 400 mg lopinavir/100 mg ritonavir. What is the appropriate dosage for the child?________________
Converting Pediatric Weight To solve pediatric dosing calculations using the mg/ kg method, you must first determine the patient’s weight in kilograms. To convert weight in pounds to kilograms, use the following formula: FORMULA
Weight Conversion 1 kg = 2.2 lb
CONVERTING WEIGHT FROM POUNDS TO KG EXAMPLE 5.12
If the infant weighs 20 pounds, what is his or her weight in kg?
Using the weight conversion formula, you divide the patient’s weight, which in this case is 20, by 2.2 to convert the weight from pounds to kg. 20 , 2.2 = 9.09 So, the infant weighs 9.09 kg. EXAMPLE 5.13
If a person weighs 180 lb., divide by 2.2 to find weight in kilograms. 180 2.2
= 81.82 kg
So 180 lb. equals 81.82 kg. Chapter Five
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PRACTICE PROBLEMS 5.10 Convert the following. 1. 115 pounds = ________________ kg 2. 18 kg = ________________ pounds 3. 74 pounds = ________________ kg 4. 50 kg = ________________ pounds 5. 41 kg = ________________ pounds 6. 60 pounds = ________________ kg 7. 24 kg = ________________ pounds 8. 100 pounds = ________________ kg
Mg / Kg / Day When the dose is stated in the manufacturer information as mg/kg/day, this means we can calculate the patient’s weight in kilograms, multiply the recommended dose, and take into account the number of times per day the dose is to be given. The goal is to determine how many milligrams can be given in each dose. Step 1: Determine weight in kilograms. Step 2: Multiply by the recommended dose. Step 3: Divide by the number of doses given daily.
CALCULATING DOSAGES USING MG/KG/DAY EXAMPLE 5.14
Using the infant from Example 5.9, determine the pediatric dosage if it is recommended to administer 20 mg/kg/day (maximum of 1gm) of Streptomycin Sulfate.
The infant’s weight in kg has already been calculated as 9.09, so now we will multiply the recommended number of milligrams by her weight in kilograms to calculate the appropriate daily pediatric dosage. 20 mg * 9.09 kg * 1 day = Pediatric Daily Dosage 20 * 9.09 * 1 = Pediatric Daily Dosage 181.8 = Pediatric Daily Dosage
So, according to mg/kg/day, the patient should be given 181.8 mg of Streptomycin Sulfate as a daily IM injection.
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Using the patient from Example 5.13, an order is given for a dose stated as 20 mg/kg tid. Step 1: The weight has been determined to be 81.82 kg. Step 2: Multiply 81.82 by 20 mg, which equals 1634 mg. Step 3: Divide the total number of milligrams for the day by the number of doses for the day: 1634 mg>3 = 544 mg. Based on his weight, the patient should receive 544 mg of drug per dose. The patient used in the preceding example weighs 180 lb. and is probably an adult. The same principles apply to calculating appropriate dosages for a child based on body weight in kilograms.
PRACTICE PROBLEMS 5.11 1. A dose of 4 mg/kg/day of Plaquenil® can be recommended for certain children suffering from lupus. What would be the appropriate dosage for a patient weighing 47 kg? ________________ 2. The daily dose of Omnicef®, in children, is 14 mg/kg, up to a maximum dose of 600 mg/day. What is the appropriate daily dosage for a patient who weighs 98 pounds? ________________ 3. The recommended dosage of fluconazole is 6 mg/kg on day one, followed by 3 mg/kg/day for oropharyngeal candidiasis. What are the appropriate dosages for a child weighing 30 kg? ________________ 4. A child, weighing 76 pounds, is prescribed the antibiotic, Cefaclor. It is recommended for children to receive 20 mg/kg/day in divided doses every 8 hours. How many mg should the child take per dose? ________________ 5. Acute lymphatic leukemia in children can respond well to methotrexate given 2.5 mg/kg every 14 days by IV. What would be the appropriate dosage of methotrexate to administer biweekly to a child weighing 110 pounds? ________________
PRACTICE PROBLEMS 5.12 Perform the following pediatric dosage calculations. 1. Rx tetracycline 25 mg/kg in four equal doses Your patient is 10 years old and weighs 88 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage for this prescription?________________ c. How much is each dose? ________________
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2. Rx amoxicillin/potassium clavulanate 45 mg/kg/day q12h Your patient is 6 years old and weighs 68 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________ 3. Rx furosemide 1 mg>kg daily Your patient is 3 years old and weighs 22 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the daily dose? ________________ 4. Rx albuterol oral syrup 2 mg/5 mL 0.2 mg/kg/day in three divided doses Your patient is 5 years old and weighs 62 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________ 5. Rx amantadine 6.6 mg/kg/day in two doses, not to exceed 150 mg per day Your patient is 6 years old and weighs 54 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________
SUMMARY Dosage calculations are varied, and more than likely will be the pharmacy calculations you perform most often. Dosage calculations include determining the number of doses, dispensing quantities, and ingredient quantities, for both adult and pediatric patients.
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CHAPTER
5 CHAPTER REVIEW QUESTIONS MULTIPLE CHOICE 1. How many 1-tsp doses are in 1 qt. of lactulose solution, USP 10 g/15 mL?________________ a. 32 doses c. 128 doses b. 64 doses d. 192 doses 2. How many milligrams of estradiol are delivered over 72 hours by one 0.075 mg/day patch?________________ a. 0.225 mg c. 8 mg b. 1.6 mg d. 0.075 mg 3. You are asked to compound maldroxyl 60 mL, diphenhydramine elixir 60 mL, and viscous lidocaine 2%, qs to 200 mL. How much viscous lidocaine 2% will you need to prepare the order?________________ a. 60 mL c. 80 mL b. 4 mL d. 200 mL 4. The recommended pediatric dose of ampicillin is 25 mg/kg/day q8h. Your patient is a 4-weekold infant who weighs 8.7 pounds. Which is the best dose for this patient? ________________ a. 15 mg c. 33 mg b. 25 mg d. 45 mg 5. How many days will 4 oz. of clemastine fumerate syrup 0.5 mg/5 mL last if the dose is 1/2 tsp daily?________________ a. 24 days c. 30 days b. 48 days d. 60 days 6. How many grams of drug are in 480 mL of docusate sodium syrup 60 mg/15 mL? ________________ a. 28.8 g c. 1920 g b. 1.92 g d. 2.88 g
7. How many milligrams are in a 2-mL dose of prochlorperazine injection 5 mg/mL given IM for severe nausea and vomiting? ________________ a. 10 mg c. 2.5 mg b. 5 mg d. 15 mg 8. How many milliliters of chloral hydrate syrup 500 mg/5 mL are required for a dose of 100 mg?________________ a. 2.5 mL c. 2 mL b. 5 mL d. 1 mL 9. The recommended pediatric dose for promethazine is 0.25 mg/kg qid. What is the best dose for a 12-year-old male who weighs 95 lb?________________ a. 2.5 mg c. 12.5 mg b. 10 mg d. 15 mg 10. How many total grams of active ingredient are in five syringes of testosterone 4 g/100 g topical gel containing 3 g of gel each? What is the percent strength of the final product? ________________ a. 15 g, 0.4% c. 2.4 g, 40% b. 0.6 g, 4% d. 60 g, 0.04%
TRUE OR FALSE 11. When solving dosage calculations, it is helpful to look for the given. ________________ a. true b. false 12. When setting up ratios and proportions to solve dosage calculations, it is best to keep like units consistent. ________________ a. true b. false Chapter Five
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13. The unknown, x, will always be located in the upper left corner when setting up dosage calculations. ________________ a. true b. false 14. When choosing the answer in a multiple-choice question, you should find the numerical answer regardless of units. ________________ a. true b. false 15. You can solve most dosage calculations by cross-multiplying. ________________ a. true b. false
SHORT ANSWER 16. Describe why proper dosing of medications is important to ensure patient safety. ________________
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17. Name three types of dosage forms. ________________ ___________ ___________ 18. Which dose is larger, 4 mg/mL or 1 mL of 4% gel? ________________ 19. How many milligrams of drug are in 0.5 mL of a cream that is 4 mg/mL? ________________ 20. How many milliliters will be required to provide the necessary dose of albuterol oral syrup 2 mg/5 mL to be given 0.2 mg/kg/day tid for a patient who weighs 88 lb.? ________________
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CHAPTER
5 Dosage Calculations
L earning Objectives After completing this chapter, you should be able to:
• Solve one-step pharmaceutical dosage calculations. • Set up a series of ratios and proportions to solve a single dosage calculation. • Determine what information you will need to solve for, in addition to any given information, to properly calculate dosages. • Convert pediatric weights from pounds to kilograms. • Accurately determine dosages based on mg/kg/day. • Define common sig (signa) codes used on prescriptions.
2
INTRODUCTION Proper dosing of medications is important to ensure patient safety. Calculating dosages, dosage regimens, and compounding formulas involves the use of simple math principles. You can solve many of these problems by setting up ratios and proportions using the information given in the question and keeping like units consistent.
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Sig Refresher The sig portion of the prescription order, meaning signa, is where the instructions for the patient are written. Pharmacy technicians enter the information from the prescription order into the computer. The sig is an important value to remember in order to properly determine pediatric dosages. The following are some of the more common sigs you will find on prescriptions: qd = every day qod = every other day d = daily bid = twice a day tid = three times a day qid = four times a day q4h = every 4 hr q6h = every 6 hr q8h = every 8 hr q4–6h = every 4–6 hr prn = as needed Depending on the workplace, you may also see sigs such as the following: q3d = every three days qmwf = every Monday, Wednesday, and Friday qw = every week
Dosage Calculations Dosage calculations include calculating the number of doses, dispensing quantities, and ingredient quantities; these calculations are performed in the pharmacy 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 and principles introduced in the previous chapters of this book. You can solve these calculations by setting up ratios and proportions, keeping like units consistent, and cross-multiplying.
CALCULATING THE NUMBER OF DOSES To calculate the number of doses, you should first determine which information presented is actually applicable to the question. Too often mistakes are made on dosage calculations because we overcomplicate them. EXAMPLE 5.1
How many 1-tsp doses are in a 4 oz bottle of Prozac® Liquid Solution 20 mg/5 mL? Rx Prozac® Solution .. TT tsp. po qd Disp. # 4 oz Chapter Five
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Figure 5-1
Drug label for Prozac.
(Courtesy of Eli Lilly and Company.)
Let’s look at the information that has been provided: ✓
.. TT
tsp 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 bottle The question is simply asking how many doses make up the total amount being dispensed. The strength of the drug, frequency of dosage and quantity of 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 to have 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 oz 1 oz = 30 mL x mL Cross-multiply and solve the equation for x. 30 * 4 = 120 and 1 * x = (1) x (1)x = 120 Now that you have both quantities converted to units in mL, we can set up our ratio/proportion and solve. 1 dose x doses = 5 mL 120 mL Cross-multiply 5 * x = 5x and 1 * 120 = 120 4
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Now set up your equation and solve for x. 5x = 120 To solve for x, divide both sides by 5. 120 2x = 2 2 120 , 5 = 24 x = 24 So, there are 24 doses (of 5 mL) in a 4 oz (120 mL) bottle.
CALCULATING THE NUMBER OF DOSES EXAMPLE 5.2
How many doses are provided in the prescription below? Rx—Ibuprofen 400 mg . .. T -TT
po q 6 hr prn pain
Disp. # 120
Let’s look at the information that has been provided: ✓
. .. T -TT
po—the dose
✘ q 6 hr prn pain—the frequency ✓ 120—the quantity dispensed ✘ Ibuprofen 400 mg—the drug name and strength Workplace Wisdom Always use the higher dosage amount when performing dosage calculations on prescriptions that have a range for the dose, as in Example 5.2. This will provide the most conservative solution and ensure the most accurate potential for days supply. Using the information provided, set up the ratio/proportion and solve. 1 dose x doses = 2 tabs 120 tabs Cross-multiply 2 * x = 2x and 1 * 120 = 120 Now set up your equation and solve for x. 2x = 120 To solve for x, divide both sides by 2. 120 2x = 2 2 120 , 2 = 60 x = 60 So, there is a minimum of 60 doses prescribed. Chapter Five
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PRACTICE PROBLEMS 5.1 1. How many dosages are provided in the prescription listed below? ________________ Rx—Cardura® 2 mg .. TT po qd Disp. # 90 2. How many droppersful (a 2.5 mL dosage) are in a 50 mL bottle of EryPed® Drops? ________________
Figure 5-2
Drug 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 q8hr Disp. # 50 4. How many 1 tsp doses are in each bottle of Zithromax® 200 mg/5 mL as listed below, when mixed? ________________
Figure 5-3
Drug 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 qAM Disp. # 1 vial (10mL) 6
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CALCULATING THE QUANTITY TO DISPENSE EXAMPLE 5.3
How many Biaxin® 250 mg tablets should be dispensed? Rx—Biaxin® 250 mg .. TT
po BID 10d
Figure 5-4 Drug label for Biaxin. (Reproduced with permission of Abbott Laboratories.)
Again, to solve this dosage calculation it is important to first determine which information is necessary; it is also critical to know the common SIG codes to perform dosage calculations. Let’s look at what information that has been provided: ✓
.. TT
po—the dose
✓ BID—the frequency ✓ x 10d—the duration ✘ Biaxin® 250 mg—the drug name and strength ✘ 100 tablets—the quantity of the stock bottle To calculate the appropriate quantity to dispense, use the following formula: dose frequency duration quantity to dispense Using the information provided in the prescription, you can set up the calculation as such: 1 2 10 x dose frequency duration quantity to dispense 1 2 10 20 20 x So, 20 tablets of Biaxin® 250 mg should be dispensed.
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CALCULATING THE QUANTITY TO DISPENSE How much Promethazine w/Codeine syrup should be dispensed?
EXAMPLE 5.4
Rx—Promethazine w/Codeine Syrup 6.25/10 .. TT
tsp. po QID 4d
Let’s look at what information has been provided: ✓
.. TT
tsp. po—the dose
✓ QID—the frequency ✓ x 4d—the duration ✘ Promethazine w/Codeine Syrup 6.25/10—the drug name and strength To calculate the appropriate quantity to dispense, use the following formula: dose frequency duration quantity to dispense Using the information provided in the prescription, you can set up the calculation as such: 1tsp 4 dose frequency
4 x duration quantity to dispense
1 4 4 16 16 x So, 16 teaspoonsful, or 80 mL, of promethazine w/codeine should be dispensed.
PRACTICE PROBLEMS 5.2 1. What quantity should be dispensed for the prescription listed below? ________________ Rx—Zoloft® 50 mg .. TT
po qd
Disp. 1 mo. supply 2. What quantity should be dispensed, using the stock medication below, to provide 20 mg of diazepam prior to the procedure and 10 mg following? ________________
Figure 5-5 Drug label for Diazepam. (Used with permission of Roxane Laboratories, Inc.)
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3. What quantity should be dispensed for a three-month supply of the following prescription? ________________ Rx—furosemide 20 mg .. TT
po QOD
4. What quantity should be dispensed if 50 mg of amitriptyline has been prescribed daily for 3 weeks, if the medication listed below is all that is available? ________________
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 following prescription? ________________ Rx—Soma® 350 mg .. TT
po BID – TID prn muscle spasms
CALCULATING THE QUANTITY OF INGREDIENT EXAMPLE 5.5
How much codeine is in each dose of Codeine Phosphate Oral Solution 15 mg/mL? Rx—Codeine Oral Soln. 15 mg/mL .. TT
tbsp po prn pain
Disp. # 4 oz
Figure 5-7 Drug label for Codeine Phosphate Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
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Let’s first look at all of the information provided to determine which will be 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 name and strength ✘ 500 mL—the quantity of the stock bottle To solve this problem, we need to set up a ratio/proportion using the dose and 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 mg 15 mg = 5 mL 1 mL Cross-multiply and then set up the equation to solve for x. 15 * 15 = 225 and 5 * x = 5x 5x = 225
Now divide both sides by 5 to solve for x. 5x 225 = 5 5 x = 45
So, the answer is 45 mg of codeine in each 1 tbsp dose.
PRACTICE PROBLEMS 5.3 Perform the following dosage calculations. 1. Promethazine with codeine syrup contains 6.25 mg promethazine and 10 mg codeine per 5 mL. How many milligrams of promethazine are in 2 tsp? ________________ 2. Rx hydroxycobalamine 10,000 mcg/cc 30 cc Sig: 1 cc IM hs How many milligrams are in each dose?________________ 3. Rx acetaminophen with codeine#3 acetaminophen 300 mg/codeine 30 mg 30 tablets How many grains of codeine are in each tablet? ________________
CALCULATING THE QUANTITY OF INGREDIENT EXAMPLE 5.6
How many mL of stock Dopamine must be added to the IV solution? Rx—Dopamine 400 mg added to 500 mL of NS Stock: Dopamine HCl Injection 80 mg/mL
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Let’s first look at all of the information provided to determine which will be 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 strength To solve this problem, we must determine how many milliliters of the stock Dopamine will need to be added to the normal saline IV solution bag. We must set up a ratio/proportion. 400 mg 80 mg = 1 mL x mL Cross-multiply and then set up the equation to solve for x. 1 * 400 = 400 and 400 = 80x
80 * x = 80x
Now divide both sides by 80 to solve for x. 80x 400 = 80 80 x = 5 So, the answer is 5 mL of the stock Dopamine HCl Injection must be added to the IV solution.
PRACTICE PROBLEMS 5.4 1. Z-Pak®s contain 6 tablets of azithromycin 250 mg, which is taken over the course of five days. How many total mg of active ingredient are contained in a Z-Pak®? ________________ 2. How many mcg of Fentanyl® would be contained in 1.5 mL? ________________
Figure 5-8 Drug label for Fentanyl. (Courtesy of ESI Lederle, a Business Unit of Wyeth Pharmaceuticals, Philadelphia, PA.)
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3. 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 stock bottle (500 mL) below? ________________
Figure 5-9 Drug label for Dexamethasone Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
5. How many mg of hydrocortisone are found in 1 tbsp of Cortef ® 10 mg/5 mL? ________________
Figure 5-10 Drug label for Cortef. (Courtesy of Pharmacia Corporation.)
CALCULATING THE CORRECT DAYS SUPPLY EXAMPLE 5.7
How many days should the following prescription last? Rx—Pamelor® 75 mg .. TT
po BID
Disp. # 50
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Figure 5-11 Drug label for Pamelor. (Copyright Novartis Pharmaceuticals Corporation. Reprinted with permission.)
Let’s determine which information provided will be needed to solve the problem. ✓
.. TT
po—the dose
✓ BID—the frequency ✓ 50—the quantity to dispense ✘ Pamelor® 75 mg—the drug name and strength ✘ 100 capsules—the quantity of the stock bottle To calculate the appropriate days supply, use the following formula: Days Supply =
Qty. Dispensed (Dose * Frequency)
Using the information provided, set up the formula as below. x =
50 (qty. dispensed) (1 * 2) (Dose * Frequency)
This becomes . . . x =
50 or x = 25 2
So, this prescription should last for 25 days.
CALCULATING THE CORRECT DAYS SUPPLY EXAMPLE 5.8
How many days should the following prescription last? Rx—Kaletra® 133.3 mg/33.3mg .. TT
po BID
food.
Disp. # 360
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Let’s determine which information provided will be needed to solve the problem. ..
✓ TT po—the dose ✓ BID—the frequency ✓ 360—the quantity to dispense ✘ Kaletra® 133.3 mg/33.3mg—the drug name and strength To calculate the appropriate days supply, use the following formula: Days Supply =
Qty. Dispensed (Dose * Frequency)
Using the information provided, set up the formula as below. x =
360 (qty. dispensed) (2 * 2) (Dose * Frequency)
This becomes. . . 360 or x = 90 4 So this prescription should last for 3 months, or 90 days. x =
PRACTICE PROBLEMS 5.5 1. How many days will the following prescription last? ________________ Rx—Diabinese® 100 mg .. TT
po qAM
Disp. # 45 2. How many days will a 150 mL bottle of Ceclor® 125 mg>5 mL last, if the patient is to take 2 teaspoonsful three times daily? ________________
Figure 5-12 Drug label for Ceclor. (Courtesy of Eli Lilly and Company.)
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3. How many days will the following prescription last? ________________ Rx—Valium® 5 mg .. TT
po BID
Disp. # 60 4. How many days should 10 tablets of Cialis® 5 mg last, if the prescribed directed to use is a maximum of one tablet q3 days?________________ 5. How many days will the following prescription last? ________________ Rx—Keflex® 250 mg .. TT
po TID
Disp. # 42
PRACTICE PROBLEMS 5.6 1. Rx—Amoxil 250 mg/5 mL .. TT tsp TID 10d a. What is the appropriate quantity to dispense? ________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of amoxicillin, in mg, to be dispensed? ________________ d. How many days should this prescription last? ________________ 2. Rx—Dexamethasone Oral Soln. 0.5 mg>5 mL Give 0.25 mg QOD Disp. 6 mg
Figure 5-13 Drug label for Dexamethasone Oral Solution. (Used with permission of Roxane Laboratories, Inc.)
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a. What is the appropriate quantity to dispense?________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of dexamethasone, in mg, to be dispensed? ________________ d. How many days should this prescription last? ________________ 3. Rx—Proventil® Inhaler 17gm (200 inhalations) .. Use TT puffs BID Disp. # 1 a. What is the appropriate quantity to dispense? ________________ b. How many total doses are to be dispensed? ________________ c. What is the total amount of albuterol, in mcg, per inhalation? ________________ d. How many days should this prescription last? ________________ 4. Rx—Xanax 0.25 mg . .. T -TT TID prn 14d a. What is the appropriate quantity to dispense? ________________ b. What is the maximum number of doses available if 60 tablets are dispensed? ________________ c. What is the maximum amount of alprazolam, in mg, to be taken daily? ________________ d. How many days could this prescription last, if 60 tablets are dispensed? ________________
Pediatric Dosing Pediatric patients, which include both infants and children, require special dosing that is adjusted for their body weight. A number of formulas have been used throughout the years to determine the best dose for pediatric patients, but the most commonly used method is stated as mg/kg of body weight. Pediatric Formulas Children need lower dosages of medication compared to adults. Three formulas are used to help calculate a pediatric dosage based on whatever information is available. In some children’s hospitals the pharmacy may have a preferred formula. However, the pharmacy technician should be able to calculate the correct pediatric dosage using each formula. 16
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FORMULA
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Pediatric Dosing
Fried’s Rule Child’s dosage =
Age in months * Adult dosage 150
Young’s Rule Child’s dosage =
Age of child in years * Adult dosage Age of child in years + 12
Clark’s Rule Child’s dosage =
Child’s weight in pounds * Adult dosage 150
CALCULATING PEDIATRIC DOSAGES USING FRIED’S RULE EXAMPLE 5.9
An infant, 15 months old and weighing 20 pounds, needs Streptomycin Sulfate, which is usually administered to adults as 1 gm (1000 mg), as a daily IM injection. What is the appropriate dosage for the infant?
To calculate the pediatric dosage based on a child’s age in months, simply use the formula for Fried’s Rule. Using the information provided, you can set up the calculation as follows: 15 (Age in months) * 1000 mg (Adult Dose) 150 15 Pediatric Dose = * 1000 150 Pediatric Dose = 0.1 * 1000 Pediatric Dose =
Pediatric Dose = 100 mg
So, according to Fried’s Rule, the pediatric dosage appropriate for a 15-month-old would be 100 mg.
PRACTICE PROBLEMS 5.7 1. A child, 24 months old, needs acetaminophen, and the normal adult dose is 650 mg. What is the appropriate dosage for the child?________________ 2. An 18-month-old needs amikacin sulfate, and the normal adult dose is 250 mg. What is the appropriate dosage for the child? ________________ 3. A child, 30 months old, needs erythromycin, and the normal adult dose is 250 mg QID. What is the appropriate dosage for the child? ________________ Chapter Five
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CALCULATING PEDIATRIC DOSAGES USING YOUNG’S RULE EXAMPLE 5.10
Now, let’s reexamine Example 5.9 using Young’s Rule, which uses the child’s age in years. The age of a 15-month-old could be expressed as 1.25 years old, since he or she has lived for 12 months (1 year) 3 months (1/4 or 0.25 of a year).
Using an age of 1.25 years and the information provided in Example 5.5, set up the calculation, using Young’s Rule, as follows: Pediatric Dose =
1.25 (Age in years) * 1000 mg (Adult Dose) 13.25 (Age of child + 12)
Pediatric Dose =
1.25 * 1000 13.25
Pediatric Dose = 0.094 * 1000 Pediatric Dose = 94 mg
So, according to Young’s Rule, the pediatric dosage appropriate for a 15-month-old would be 94 mg.
PRACTICE PROBLEMS 5.8 1. A 2-year-old child is prescribed amoxicillin, and the normal adult dose is 500 mg. What is the appropriate dosage for the child?________________ 2. A 7-year-old needs propylthiouracil, and the normal adult daily dose is 150 mg. What is the appropriate dosage for the child?________________ 3. A child, 10 years old, is prescribed Tavist® syrup, and the normal adult dose is 1.34 mg BID. What is the appropriate dosage for the child?________________
CALCULATING PEDIATRIC DOSAGES USING CLARK’S RULE EXAMPLE 5.11
Now, let’s reexamine Example 5.9 using Clark’s Rule, which uses the child’s weight in pounds.
Using a weight of 20 pounds and the information provided in Example 5.5, set up the calculation, using Young’s Rule, as follows: 20 (Weight in pounds) * 1000 mg (Adult Dose) 150 20 Pediatric Dose = * 1000 150 Pediatric Dose = 0.133 * 1000
Pediatric Dose =
Pediatric Dose = 133 mg 18
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So, according to Clark’s Rule, the pediatric dosage, appropriate for a 15-month-old, weighing 20 pounds, would be 133 mg.
PRACTICE PROBLEMS 5.9 1. A child, weighing 85 pounds, is prescribed hydrochlorothiazide, and the normal adult dose is 50 mg. What is the appropriate dosage for the child?________________ 2. A child, weighing 70 pounds, is prescribed quinine sulfate, and the normal adult dose is 325 mg TID. What is the appropriate dosage for the child?________________ 3. A child, weighing 112 pounds, is prescribed Kaletra®, a protease inhibitor combination therapy. The normal adult dose is 400 mg lopinavir/100 mg ritonavir. What is the appropriate dosage for the child?________________
Converting Pediatric Weight To solve pediatric dosing calculations using the mg/ kg method, you must first determine the patient’s weight in kilograms. To convert weight in pounds to kilograms, use the following formula: FORMULA
Weight Conversion 1 kg = 2.2 lb
CONVERTING WEIGHT FROM POUNDS TO KG EXAMPLE 5.12
If the infant weighs 20 pounds, what is his or her weight in kg?
Using the weight conversion formula, you divide the patient’s weight, which in this case is 20, by 2.2 to convert the weight from pounds to kg. 20 , 2.2 = 9.09 So, the infant weighs 9.09 kg. EXAMPLE 5.13
If a person weighs 180 lb., divide by 2.2 to find weight in kilograms. 180 2.2
= 81.82 kg
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PRACTICE PROBLEMS 5.10 Convert the following. 1. 115 pounds = ________________ kg 2. 18 kg = ________________ pounds 3. 74 pounds = ________________ kg 4. 50 kg = ________________ pounds 5. 41 kg = ________________ pounds 6. 60 pounds = ________________ kg 7. 24 kg = ________________ pounds 8. 100 pounds = ________________ kg
Mg / Kg / Day When the dose is stated in the manufacturer information as mg/kg/day, this means we can calculate the patient’s weight in kilograms, multiply the recommended dose, and take into account the number of times per day the dose is to be given. The goal is to determine how many milligrams can be given in each dose. Step 1: Determine weight in kilograms. Step 2: Multiply by the recommended dose. Step 3: Divide by the number of doses given daily.
CALCULATING DOSAGES USING MG/KG/DAY EXAMPLE 5.14
Using the infant from Example 5.9, determine the pediatric dosage if it is recommended to administer 20 mg/kg/day (maximum of 1gm) of Streptomycin Sulfate.
The infant’s weight in kg has already been calculated as 9.09, so now we will multiply the recommended number of milligrams by her weight in kilograms to calculate the appropriate daily pediatric dosage. 20 mg * 9.09 kg * 1 day = Pediatric Daily Dosage 20 * 9.09 * 1 = Pediatric Daily Dosage 181.8 = Pediatric Daily Dosage
So, according to mg/kg/day, the patient should be given 181.8 mg of Streptomycin Sulfate as a daily IM injection.
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Using the patient from Example 5.13, an order is given for a dose stated as 20 mg/kg tid. Step 1: The weight has been determined to be 81.82 kg. Step 2: Multiply 81.82 by 20 mg, which equals 1634 mg. Step 3: Divide the total number of milligrams for the day by the number of doses for the day: 1634 mg>3 = 544 mg. Based on his weight, the patient should receive 544 mg of drug per dose. The patient used in the preceding example weighs 180 lb. and is probably an adult. The same principles apply to calculating appropriate dosages for a child based on body weight in kilograms.
PRACTICE PROBLEMS 5.11 1. A dose of 4 mg/kg/day of Plaquenil® can be recommended for certain children suffering from lupus. What would be the appropriate dosage for a patient weighing 47 kg? ________________ 2. The daily dose of Omnicef®, in children, is 14 mg/kg, up to a maximum dose of 600 mg/day. What is the appropriate daily dosage for a patient who weighs 98 pounds? ________________ 3. The recommended dosage of fluconazole is 6 mg/kg on day one, followed by 3 mg/kg/day for oropharyngeal candidiasis. What are the appropriate dosages for a child weighing 30 kg? ________________ 4. A child, weighing 76 pounds, is prescribed the antibiotic, Cefaclor. It is recommended for children to receive 20 mg/kg/day in divided doses every 8 hours. How many mg should the child take per dose? ________________ 5. Acute lymphatic leukemia in children can respond well to methotrexate given 2.5 mg/kg every 14 days by IV. What would be the appropriate dosage of methotrexate to administer biweekly to a child weighing 110 pounds? ________________
PRACTICE PROBLEMS 5.12 Perform the following pediatric dosage calculations. 1. Rx tetracycline 25 mg/kg in four equal doses Your patient is 10 years old and weighs 88 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage for this prescription?________________ c. How much is each dose? ________________
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2. Rx amoxicillin/potassium clavulanate 45 mg/kg/day q12h Your patient is 6 years old and weighs 68 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________ 3. Rx furosemide 1 mg>kg daily Your patient is 3 years old and weighs 22 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the daily dose? ________________ 4. Rx albuterol oral syrup 2 mg/5 mL 0.2 mg/kg/day in three divided doses Your patient is 5 years old and weighs 62 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________ 5. Rx amantadine 6.6 mg/kg/day in two doses, not to exceed 150 mg per day Your patient is 6 years old and weighs 54 lb. a. What is the patient’s weight in kilograms? ________________ b. What is the total dosage per day? ________________ c. How much is each dose? ________________
SUMMARY Dosage calculations are varied, and more than likely will be the pharmacy calculations you perform most often. Dosage calculations include determining the number of doses, dispensing quantities, and ingredient quantities, for both adult and pediatric patients.
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CHAPTER
5 CHAPTER REVIEW QUESTIONS MULTIPLE CHOICE 1. How many 1-tsp doses are in 1 qt. of lactulose solution, USP 10 g/15 mL?________________ a. 32 doses c. 128 doses b. 64 doses d. 192 doses 2. How many milligrams of estradiol are delivered over 72 hours by one 0.075 mg/day patch?________________ a. 0.225 mg c. 8 mg b. 1.6 mg d. 0.075 mg 3. You are asked to compound maldroxyl 60 mL, diphenhydramine elixir 60 mL, and viscous lidocaine 2%, qs to 200 mL. How much viscous lidocaine 2% will you need to prepare the order?________________ a. 60 mL c. 80 mL b. 4 mL d. 200 mL 4. The recommended pediatric dose of ampicillin is 25 mg/kg/day q8h. Your patient is a 4-weekold infant who weighs 8.7 pounds. Which is the best dose for this patient? ________________ a. 15 mg c. 33 mg b. 25 mg d. 45 mg 5. How many days will 4 oz. of clemastine fumerate syrup 0.5 mg/5 mL last if the dose is 1/2 tsp daily?________________ a. 24 days c. 30 days b. 48 days d. 60 days 6. How many grams of drug are in 480 mL of docusate sodium syrup 60 mg/15 mL? ________________ a. 28.8 g c. 1920 g b. 1.92 g d. 2.88 g
7. How many milligrams are in a 2-mL dose of prochlorperazine injection 5 mg/mL given IM for severe nausea and vomiting? ________________ a. 10 mg c. 2.5 mg b. 5 mg d. 15 mg 8. How many milliliters of chloral hydrate syrup 500 mg/5 mL are required for a dose of 100 mg?________________ a. 2.5 mL c. 2 mL b. 5 mL d. 1 mL 9. The recommended pediatric dose for promethazine is 0.25 mg/kg qid. What is the best dose for a 12-year-old male who weighs 95 lb?________________ a. 2.5 mg c. 12.5 mg b. 10 mg d. 15 mg 10. How many total grams of active ingredient are in five syringes of testosterone 4 g/100 g topical gel containing 3 g of gel each? What is the percent strength of the final product? ________________ a. 15 g, 0.4% c. 2.4 g, 40% b. 0.6 g, 4% d. 60 g, 0.04%
TRUE OR FALSE 11. When solving dosage calculations, it is helpful to look for the given. ________________ a. true b. false 12. When setting up ratios and proportions to solve dosage calculations, it is best to keep like units consistent. ________________ a. true b. false Chapter Five
Dosage Calculations
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13. The unknown, x, will always be located in the upper left corner when setting up dosage calculations. ________________ a. true b. false 14. When choosing the answer in a multiple-choice question, you should find the numerical answer regardless of units. ________________ a. true b. false 15. You can solve most dosage calculations by cross-multiplying. ________________ a. true b. false
SHORT ANSWER 16. Describe why proper dosing of medications is important to ensure patient safety. ________________
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Chapter Five
Dosage Calculations
17. Name three types of dosage forms. ________________ ___________ ___________ 18. Which dose is larger, 4 mg/mL or 1 mL of 4% gel? ________________ 19. How many milligrams of drug are in 0.5 mL of a cream that is 4 mg/mL? ________________ 20. How many milliliters will be required to provide the necessary dose of albuterol oral syrup 2 mg/5 mL to be given 0.2 mg/kg/day tid for a patient who weighs 88 lb.? ________________
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