Drug Dosage Calculations

8 Drug Dosage Calculations OUTLINE Overview Dosage and Doses The Desired Dose Calculating the Amount to Administer OBJECTIVES Upon completion of this chapter, the student should be able to: 1. Distinguish between the dosage ordered and a dose. 2. Convert the dosage ordered to the by using the conversion factor or the ratio-proportion method. 3. Determine the amount of a medication to administer by using the ratio and proportion, proportion, or formula methods. GLOSSARY The amount of medication that is to be administered to the patient. dosage ordered The exact amount of medication that the prescriber has ordered along with the frequency with which it is given. dose The strength of a drug that is present in one dosage unit.

72 CHAPTER 8 Drug Dosage Calculations OVERVIEW The ability to calculate drug dosages is a skill that should not be taken lightly. In fact, the pharmacy technicians who deal with dispensing and preparing medications should aim for 100% success in performing this task. When a technician receives an order for a medication in a dosage that is different from that of the medications in stock, he must be able to use his skill to accurately calculate by using formulas, mathematical tables, or calculators. Learning to correctly calculate drug dosages is an extremely important skill, because it can often be the difference between life and death for a patient. DOSAGE AND DOSES The dosage ordered is the exact amount of medication that the prescriber has ordered along with the frequency with which it is given. This information may be found on the prescription or through a verbal order by the cian. A dose is the strength of a drug that is present in one dosage unit; this is generally the amount of drug that the physi- pharmacy has on hand to prepare the dosage ordered. red When a pharmacy technician receives a physician s order, the dosage and dose of the medication must be identified. For example, review the following information on how to determine the dosage ordered and the dose on hand: Order: Supply: Lopid 0.6 g p.o. b.i.d. Lopid 600 mg tablets In this example, the dosage is 0.6 g. The dose on hand is 600 mg (as determined from the drug label). These two lead to the same result. When a physician orders a medication wherein the amount of drug ordered equals the amount given to the patient, the ratio will be equal to 1. Dosage ordered Therefore, dosage ordered 1 EXAMPLE: The dosage ordered: The : 15 mg 15 mg 1 15 mg 15 mg The Conversion Factor Method When the is unknown, use the conversion factor formula. EXAMPLE: The dosage ordered is 0.5 mg. The dose on hand is in mcg. You want to find the. dosage ordered 0.5 mg X 0.5 mg conversion factor X The conversion factor should relate mg to mcg. You know that 1 mg 1000 mcg, therefore: 1 mg 1000 mcg 0.5 mg 1 mg X 1000 mcg If you cross multiply, you arrive at the result of: 0.5 1000 X 1 X 0.5 * 1000 1 X 0.5000 500 mcg (Courtesy of Parke-Davis) The Desired Dose To calculate the (the amount of medication to be administered to the patient), one of two methods can be used. One is the conversion factor method by using fraction proportion. Another is the ratio and proportion. The Ratio and Proportion Method Ratio and proportion form the basis for nearly all calculation and is a concept that seems to be generally understood and used. However, many pharmacy technicians have difficulty in problem interpretation and identifying a place to start. Recall from Chapter 3 that a ratio states the relation of one quantity to another and may be written as

CHAPTER 8 Drug Dosage Calculations 73 a common fraction (implying division) or with a colon between the two numbers. For example, three parts compared with four parts is written as 3/4, 3 : 4, or three is to four. Two equal ratios that are set equal to each other result in an equation called a proportion. For example, 3 4 15 20 3 : 4 : : 15 : 20 The first and last terms of a proportion are called the extremes, and the second and third terms are called the means. 3 : 4 : : 15 : 20 means extremes EXAMPLE 1: If 100 g of a drug costs $2.60, how much will 25 g cost? 100 g : 25 g : : 2.60 : X 25 g * 2.60 X 100 g X 65 100 00.65 Remember To find the : Use the conversion factor formula Use the ration and proportion method STOP AND Calculating the Desired Dose REVIEW 1. Ordered: Synthroid 0.05 mg On hand: Synthroid 50 mcg tablets 2. Ordered: Aspirin gr v p.o. q.d. On hand: Aspirin 325 mg tablets 3. Ordered: Levoxyl 0.15 mg On hand: Levoxyl 300 mcg tablets 4. Ordered: Phenobarbital gr 1/2 p.o. q.d. On hand: Phenobarbital 15 mg 5. Ordered: Duricef 0.75 g p.o. q.i.d. a.c. On hand: Duricef 500 mg per tablet EXAMPLE 2: Ordered: On hand: Desired dose Biaxin 0.5 g p.o. q8h Biaxin 250 mg X 6. Ordered: Ampicillin 0.25 g On hand: Ampicillin 125 mg capsules (continues) (Courtesy of Abbott Laboratories) 250 mg : 1 tab : : 500 mg : X tab 250 X 500 X 500 250 2 tablets

74 CHAPTER 8 Drug Dosage Calculations (continued) 7. Ordered: Codeine sulfate gr 3/4 p.o. q4h p.r.n., pain On hand: Codeine sulfate 30 mg per 1 ml 8. Ordered: digoxin elixir 0.25 mg p.o. q.d. On hand: digoxin elixir 50 mcg / ml 9. Ordered: Nitrostat gr 1/400 SL p.r.n., for angina pain On hand: Nitrostat 0.3 mg 10. Ordered: V-Cillin K 0.5 g p.o. q.i.d. On hand: V-Cillin K 250 mg per tablet Calculating the Amount to Administer When calculating the desired ed dose, it is also necessary to calculate the amount to administer to the patient. For example, how many tablets should be given to the patient, or how much volume of solution must be drawn into a ringe or mixed into an intravenous solution bag. To calcu- sylate the amount to administer, the ratio and proportion (already discussed above), or a formula can be used, which all provide the same result. Two important pieces of information, the dosage unit and the dose on hand, come from knowing the dosage strength on a drug label. You have already learned to calculate a third piece of information, the. You can calculate a fourth piece of information, the amount to administer, by using this information. The Proportion Method In this method, it is important to remember that the dosage strength of a drug does not change based on the amount to be administered. If you administer 250 mg of a medication in one capsule, you can give 500 mg in two capsules because the dosage strength remains 250 mg per capsule. EXAMPLE: Use the proportion: 250 mg 500 mg 1 capsule 2 capsules In other words, write this proportion in the general formula as follows: dose on hand dosage unit amount to administer In this example, you need to give a patient 500 mg of medication, but you do not know how many capsules to administer. Using a fraction proportion, write: 250 mg 500 mg 1 capsule X Cross multiply to find the number of capsules to administer. 250 X 1 500 X 500 250 2 capsules STOP AND The Proportion Method REVIEW 1. Ordered: Covera-HS 480 mg p.o. b.i.d. On hand: Covera-HS 240 mg tablets 2. Ordered: Ilosone Liquid (erythromycin) 0.5 g to p.o. q.i.d. On hand: Ilosone 250 mg per 5 ml 3. Ordered: Heparin sodium 850 units by injection On hand: Heparin sodium 1000 units per ml (multidose) 4. Ordered: Naloxone hydrochloride 0.3 mg by injection On hand: Naloxone HCl injection 0.4 mg per ml (multidose) 5. Ordered: Epogen 1400 U by injection On hand: Epogen 2000 units per ml 6. Ordered: Amoxil 250 mg p.o. t.i.d. On hand: Amoxil 250 mg per 5 ml 7. Ordered: Lopid 0.6 g p.o. b.i.d. On hand: Lopid 600 mg tablets 8. Ordered: Clindamycin 0.6 g IV q12h On hand: Cleocin phosphate (Clindamycin injection) 300 mg / 2 ml 9. Ordered: Ritalin 15 mg p.o. q.d. On hand: Ritalin 10 mg tablets

CHAPTER 8 Drug Dosage Calculations 75 10. Ordered: Lorabid 400 mg p.o. b.i.d. On hand: Lorabid 200 mg powder for suspension per 5 ml The Formula Method The formula method can also be used to determine the amount of medication to administer. The pharmacy technician must ensure that the medication information is in the correct place within the formula. This formula can be used for most drug orders and it is useful to remember. The first step in computing medication dosage, regardless of the method used, is to make certain that the strength of the drug ordered and the strength of the drug available are in the same unit of measure. If necessary, conversion to a single unit must be carried out. Once conversion to a single unit has been done, the problem can be set up using the formula: D is the or ordered dosage. H is the dose on hand. Qisthedosage unit or quantity on hand. X is the amount to administer. The answer, or the unknown, most commonly is signified by the letter X and is usually placed on the right side of the formula, preceded by an equal sign. The fraction proportion that was discussed before includes: dose on hand dosage unit D H * Q X If you cross multiply, HA DQ or EXAMPLE 1: Ordered: On hand: X D * Q H amount to administer H Q D X X D * Q H Lasix 10 mg p.o. b.i.d. Lasix 20 mg per tablet 10 mg 20 mg * 1 tablet 10 mg 20 mg * 1 tablet 1 2 * 1 tablet 1 2 tablet The amount to administer is 1/2 tablet. Therefore, you want to give 1/2 tablet of Lasix 20 mg tablets orally twice daily. EXAMPLE 2: Find the amount to administer. Ordered: heparin 6000 U S.C. q12h On hand: heparin 10,000 U / ml vial Desired dose is 6,000 U. The dosage unit (Q) is 1 ml. D * Q H Solve for X: 6000 U * 1 ml 10,000 U 6 U * 1 ml 10 U X S 3 U 0.6 ml 5 X 6000 U * 1 ml 10,000 ml vial X The amount to administer is 0.6 ml. Remember To calculate the amount of medication to administer, use one of the following: The ratio and proportion method The proportion method The formula method Dose on hand Dosage unit STOP AND The Formula Method amount to administer 1. Ordered: nitroglycerin 0.6 mg SL On hand: Nitrostat 0.3 mg tablets REVIEW 2. Ordered: phenobarbital 3/4 gr p.o. On hand: phenobarbital 15 mg tablets 3. Ordered: Ergotrate Maleate 200 mcg by injection On hand: Ergotrate Maleate 0.2 mg per 1 ml 4. Ordered: Cloxacillin 500 mg p.o. t.i.d. On hand: Cloxacillin 125 mg per 5 ml (continues)

76 CHAPTER 8 Drug Dosage Calculations (continued) 5. Ordered: Humulin R Insulin 35 U SC On hand: Humulin R Insulin 100 units per ml 6. Ordered: Decadron 5 mg IM On hand: Decadron 4 mg/ml (multidose vial) 7. Ordered: furosemide 80 mg p.o. now On hand: Lasix (furosemide) 40 mg tablets 8. Ordered: Thorazine 15 mg IM stat On hand: Thorazine 25 mg per ml 9. Ordered: Codeine gr 1/4 q6h p.r.n., severe cough On hand: Codeine 30 mg tablets 10. Ordered: Lorabid oral suspension 150 mg p.o. b.i.d. On hand: Lorabid oral suspension 100 mg per 5 ml TEST YOUR KNOWLEDGE Calculate the and then calculate the amount to administer in the following exercises. 1. Ordered: Valium 3 mg IV stat On hand: Valium 10 mg/2 ml 2. Ordered: Dilantin 25 mg IV q8h On hand: Dilantin 100 mg/2 ml ampule 3. Ordered: ciprofloxacin 500 mg p.o. q12h On hand: ciprofloxacin 250 mg tablets 4. Ordered: Lanoxin 0.125 mg p.o. q.i.d. On hand: Lanox in 0.25 mg tablets 5. Ordered: Diabinese 0.1g p.o. q.d. On hand: Diabinese 100 mg tablets 6. Ordered: sulfisoxazole (Gantrisin) 1g q.d. On hand: sulfisoxazole (Gantrisin) 250 mg per tablet 7. Ordered: mexiletine (Mexitil) 300 mg q8h On hand: mexiletine (Mexitil) 150 mg per tablet 8. Ordered: Prilosec-Dr 20 mg p.o. q.d. On hand: Prilosec-Dr 10 mg capsules Use the labels below to calculate one dose of the following orders. 9. Ordered: Zyloprim 0.25g p.o. b.i.d. On hand: Zyloprim 100 mg scored tablets Label: Amount to administer: 10. Ordered: Vistaril 10 mg p.o. q.i.d. On hand: Vistaril 25 mg per 5 ml Label: Amount to administer: (Label reproduced with permission of Pfizer Inc.)

CHAPTER 8 Drug Dosage Calculations 77 CRITICAL THINKING Use the following label to answer these questions. (Courtesy of Abbott Laboratories) 1. A physician s order reads: Biaxin 150 mg p.o. b.i.d. Calculate the amount to administer. 2. In some cases, the patient may receive 400 mg once a day. Calculate the amount to administer for this dose.