# The Center for Nursing Excellence Calculations of Drug Dosages and Solutions

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1 The Center for Nursing Excellence Calculations of Drug Dosages and Solutions Directions: This learning has been compiled to assist nurses who will be taking the Medication and Drug Calculation Test. You will need to achieve 88% on this test prior to administering medications at Brigham and Women s Hospital (BWH). You will be able to use a calculator. Learning Objectives: 1. Identify BWH approved abbreviations* 2. Calculate drug dosages utilizing the metric system. 3. Determine the amount of the drug needed to administer the amount of drug ordered. 4. Identify the principles of conversion and use a conversion table. 5. Calculate the infusion rate of an IV solution. 6. Identify common drug scenarios. *All abbreviations are found online in the BWH Hospital Policy Manual.

2 ABBREVIATIONS of COMMONLY USED IN MEDICATION ORDERS (See Comprehensive List online in the BWH Hospital Policy Manual) a.c. before meals N/V/D nausea, vomiting, diarrhea ad lib as desired oz ounce gm gram pc after meals IM intramuscular p.r. by rectum IV intravenous p.r.n. whenever necessary L liter stat immediately mcg micrograms sc subcutaneous ml milliliter NKA no known allergies NKDA no known drug allergies 2

3 CONVERSION EQUIVALENTS 1 kg = 2.2 pounds 30 ml = 1 oz To convert kg to lbs: multiply (x) kg by kg x 2.2 = 132 lbs Note: DO NOT round off these values To convert lbs to Kg: divide (:) lbs by lbs : 2.2 = kg Note: DO NOT round off these values To convert ounces to milliliters: multiply(x) ounces by 30 8 oz x 30 = 240 ml To convert milliliters to ounces: divide (:) milliliters by ml : 30 = 12 oz 1000 ml = 1 liter 1 gm = 1000 milligrams To convert grams to milligrams: multiply (x) grams by (grams) x 1000 = 200 mg To convert milligrams to grams: divide (:) milligrams by (mg) : 1000 = 2.5 grams 1 mg = 1000 micrograms To convert milligrams to micrograms: multiply (x) milligrams by (mg) x 1000 = micrograms To convert micrograms to milligrams: divide (:) micrograms by (micrograms) : 1000 = 20 mg TIME CONVERSION To convert US standard to international time: AM: omit colon and AM example: 8:45AM = 0845 PM: omit colon and PM add 1200 example: 7:50 PM= = 1950 To convert international time to US standard: AM: insert colon and AM example: 0207=2:07AM PM: subtract 1200, insert colon and PM example: 2125 = = 9:25 PM 3

4 SOLVING DRUG DOSAGE PROBLEMS 1. Dosage problems that you encounter in the hospital may be set up in the form of a simple equation in which you must determine the value of x. D = Desired the dosage you wish to give. H = Have the dosage strength available. Q = Quantity of the preparation. x = unknown. The amount one must give to obtain the desired dosage. D x Q = x H Example: The physician orders Digoxin mg. The drug label reads Digoxin 0.25 mg. How much would you give the patient? D = 0.125mg x 1 tablet = H = 0.25 mg x 1 = 0.5 tablet Problems may also be solved using the proportion method. In proportion the product of the means equals the product of the extremes. It is very important to set up the equation properly and to remember that the means are in the inner numbers and the extremes are the outer numbers. In the example above the problem would be set up in this manner. a. Set up what you KNOW then what is UNKNOWN 0.25 mg : 1 tab :: mg : x tab b. Multiply means and extremes 1 x = and 0.25 x x tab = 0.25x c. Solve for x by dividing (:) : 0.25 = 0.5 d. Answer 0.5 tab 4

5 CALCULATONS OF FRACTIONAL DOSAGE Medications are manufactured in various forms; solid drug forms such as tablets and capsules and liquid forms such as aqueous solutions (syrups), aqueous suspensions (mixtures and emulsions), and alcohol solutions (elixirs, tinctures and extracts). When computing the correct dosage of a medication, one must determine the amount of the drug form needed to administer the volume of drug ordered. 1. Colace is available in 100 mg capsules. The basic vehicle for Colace is one capsule, each of which carries 100 mg of the drug. The amount of drug is usually obvious when the solid forms of capsules or tablets are the vehicles. However, some people have difficulty perceiving that the liquid vehicle measure of ml should be treated in the same fashion as the solid drug vehicles. Example: Morphine is available in 30 ml vials, with each ml of volume containing 1 mg of morphine. If a physician orders 2 mg to be administered, the correct amount to be given is 2 mls (SEE SOLVING DRUG DOSAGE PROBLEMS page 4). 2. In multiple-dose vials, the powder to be dissolved often adds to the final total volume of the liquid in the vial. When this is the case, the label indicates the amount of solution to use to dissolve the powder volume factor. Example: If a vial contains 1 gm of Cefazolin powder and you are to give 500 mg IM, you must first dissolve the powder in sterile water. This label states Dissolve powder in 2.5 ml. Total volume will equal 3 ml. This vial should then contain 1000mg/3L. You will need to administer 1.5 ml. MEDICATIONS REVIEW The test includes but is not limited to the following drugs. You are encouraged to review them. Dilantin Insulin Coumadin Heparin Digoxin 5

6 CALCULATION OF INTRAVENOUS FLOW RATE When electronic device is not used 1. The eye of the dropper greatly influences the actual number of drops required to move 1 ml of fluid into the drip chamber. The label on the tubing box will indicate the dropper capacity of the specific tubing used. The calibration of IV tubing in gtt/mls is known as the drop factor. Common macrodrop factors are 10 gtt/ml, 15gtt/mL, 20gtt/mL and the common microdrop factor is 60gtt/mL. 2. Determine drip capacity by choosing the microdrop chamber or macrodrip chamber. If you are infusing under 60 ml/hr, then choose a micro or mini drip set which delivers 60gtt/mL. 3. To calculate the gtt of IV solution that should be administered per minute, you need to calculate the amount of fluid to be delivered per hour, the number of drops to be administered per hour and then the drops per minute. To calculate the ml that should be delivered in 1- hour, divide the total fluid volume ordered by the number of hours over which the fluid is to be infused. Formula states: gtt/min = amount of solution (ml) multiply by drop factor then divide by infusion time in minutes You are to administer 1000 ml NS in 5 hours using a 10 gtt/ml drop factor. How many ml/hr are needed? 1000mL : 5hrs = 200mL/hr How many gtt/minute? 200 ml/hr x 10 gtt/ml = 2000 drops/hr 2000drops/hr : 60 min = drops/min If decimal answer is <0.50: Round DOWN If decimal answer is >0.51: Round UP Otherwise it will be incorrect. You CANNOT measure or count one third of a drop! You are to administer 2000 ml D5W in 10 hours using a 15 gtt/min drop factor. How many ml/hr are needed? 2000mL : 10 hrs How many drops per minute are needed? 2000 ml : 10 hr = 200 ml/hr 200 ml/hr x 15 gtt/ml = 3000 drops/hr 3000 drops/hr : 60 min = 50 drops/min 6

7 COMMON DRUG SITUATIONS 1. Drugs are also ordered for patients based on dose per kg. per minute. These drugs include Nipride, Dopamine and Dubutamine, among others. Example: Dr. orders Dopamine 2 mcg/kg/min. The solution available is 400 mg in 250 ml D5W. The patient weights 150 lbs. How many micrograms do you administer per minute? a) Convert the patient s weight to kg. 150 lbs : by 2.2 = kg b) Determine dose per minute. 2 mcg x kg = mcg/min 2. The common heparin drip mix at Brigham and Women s Hospital is units in 250 ml D5W. Therefore, 100 units are equal to 1 ml. Example: Dr. orders 1400 units per hour IV. How many ml s are administered? a) Set up known and unknown: units : 250 ml :: 1400 units : x ml b) Multiply means and extremes: 250 x 1400 = and x x ml = 25000x c) Solve for X: : = 14 d) Answer: 14 mls 3. When administering a mixture of short acting (Regular) and long acting insulin, the short acting (clear) insulin is always withdrawn from the vial first. Remember Clear then Cloudy. Only Regular insulin may be administered IV. Insulin drips expire in 24 hours. Verify ALL insulin doses with a 2 nd nurse. 4. Amphotericin IV, a systemic antifungal, is only compatible in D5W. premedication with acetaminophen and diphenhydramine is common. An infusion may produce rigors, shaking chills, which can be controlled with meperidine IVB. Blood should not be administered concurrently. 5. Dilantin must be administered only in Normal Saline through a 0.22 micron filter. 7

8 6. Amiorodone, used for ventricular and supraventricular dysrrhythmias, must be given diluted and in a glass bottle, through a dedicated central line. 7. Maximum acetaminophen dose per day 4000 mg. Watch combination drugs such as Percocet, which contains oxycodone with acetaminophen. 8. Intravenous Gamma Globulin is not compatible with ANY other drug. It is recommended that it NOT be administered within 2 hours after receiving a blood product. Patient s weight must be known in kilograms. Patient should receive premedications of acetaminophen and diphenhydramine 30 minutes prior to infusion. Use appropriate filter with corresponding brand of Immune Globulin. Frequent vital signs are required. FOLLOW DRUG ADMINISTRATION GUIDELINES CLOSELY! IMPORTANT NOTE: All medication policies can be accessed in the Clinical Practice Manual and the Drug Administration Guidelines (DAG). Calculating Percentages in Relationship to Time Example: How long will it take 925 ml to infuse if it is running at 75 ml/hr? Divide 925 by 75 = Caution: that is NOT the final answer. It is incorrect to leave it at that. You must calculate what percentage.33 is of one hour. Multiply.33 (the percentage) by 60 (minutes).33 x 60 = 19.8 then divide by : 100 = or 20 minutes So, final answer is 12 hours and 20 minutes. 8

9 PRACTICE PROBLEMS Follow directions in each section below. You may answer problems directly in space provided you may use a calculator. Double check all of your work. 1. Identify the following abbreviations. a) IM d) ml b) IV e) a.c. c) stat f) mg. 2. Complete the following equivalents. a) 10 cc = ml d) 500 mg = gm b) 0.2 gm = mg e) 1 kg. = lbs c) 30 ml = oz f) 0.5 liter = ml 3. Order states: Pentobarbital 150 mg IM X 1 now. Drug available is Pentobarbital 150 mg per 1 ml. How many milliliters would you give? 4. Order states: Tetracycline 0.5 gm p.o. twice a day. Drug available is 250 mg per tablet. How many tablets would you give in 24 hours? 5. Order states: Morphine Sulfate 5 mg IVB q2h. Drug is available in 15 mg/ml multi-dose vial. How many milliliters would you give per dose? 9

10 6. Order states: NS 50 ml / hr x 24 hours. No infusion pumps are available. Using a microdrip chamber (60 drops per ml), how many drops per minute will the patient receive? How many milliliters in 12 hours? 7. Order states: Heparin 2500 units subcutaneous daily. Drug is available in 10,000 Units per ml. How many milliliters would you give? What needle gauge would you use? 8. Order states: Regular insulin U Units subcutaneous and NPH U Units subcutaneous each morning. How many total Units do you administer? Which do you withdraw first? Which syringe is better suited for this patient? A. B. 9. Order states: NS IV 3 liters over 24 hours. How much will the patient have received in 11 hours? What would a pump be set at? 10

11 10. Order states: Dopamine 400 mg in 250 ml D5W administer 5 mcg/kg/min IV. How many ml/hr will you administer? 11. Order above unable to compute without patient s weight. You weight the patient and find she is 192 lbs. How many mcg/hr will you administer? 12. Order states: Half strength Jevity at 60 cc/hr via NG tube. How many ml s of Jevity will you need for the next 4 hours? 11

12 ANSWERS TO PRACTICE QUESTIONS 1. Abbreviations a) Intra-muscular d) milliliters b) Intra-venous e) before meals c) Immediately f) milligrams 2. Equivalents a) 10 ml d) 0.5 grams b) 200 mg e) 2.2 lbs c) 1 oz f) 500 ml 3. 1 ml 4. 4 tablets mls drops per minute. 600 mls in 12 hours mls. 25G needle units. Regular Insulin, clear. B) 100 units syringe ml in 11 hours. 125 ml 12

13 10. Insufficient information 11. Patient s wt kg /min mcg/hr ml Jevity and 120 ml of water 13

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