# Medication Math OBJECTIVES INTRODUCTION. Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION

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3 66 PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL Jones & Bartlett Learning, milliliters LLC (ml). At times, volumes Jones of & solutions Bartlett are Learning, also reported LLC in cubic centimeters (cc). Milliliters and cubic centimeters refer to the same volume. CONVERSIONS The ability to convert one unit of measure to another is vital to ensure that the intended Jones dose of & medication Bartlett is Learning, administered LLC to the patient. Failure to understand Jones and & Bartlett use unit conversions may lead to overdosing the patient inadvertently or providing the patient with a Learning, LLC less than optimal dose. Most IV medications are supplied as solutions expressed as a concentrations (e.g., milligrams per milliliter [mg/ml]). Medications are dosed as a mass (e.g., milligrams), and drug doses are often determined based on a patient s weight (e.g., pounds or kilograms) or body surface area (square meters). As mentioned in Jones & Bartlett Chapter Learning, 2, lack of LLC experience in the performance Jones of drug & calculations Bartlett Learning, and conversions LLCis a common cause of medical error, patient injury, and legal action against the prehospital professional. MILLILITERS AND CUBIC CENTIMETERS The milliliter is a measurement of volume (liquids or fluids in this case) and is equal to Jones & Bartlett Learning, 1/1000 LLC of a liter. The cubic centimeter Jones & is also Bartlett a measurement Learning, of volume, LLC but it is based on the centimeter, which is equal NOT to FOR 1/100 SALE of a meter. OR Because DISTRIBUTION 1 cc equals 1 ml, the terms are often used interchangeably. For example, you may receive an order to administer 2 ml of morphine sulfate. The same order may be given as 2 cc of morphine sulfate. These two doses are considered equivalent. If a box measured 1 cm 1 cm 1 cm in dimension, the volume of the box Jones would & be Bartlett a cubic centimeter. Learning, If the LLC box were filled with 1 ml of Jones water at & a Bartlett temperature Learning, LLC NOT of FOR 4 C, the SALE water OR would DISTRIBUTION exactly fill the box. Therefore the volume NOT is FOR equal SALE to the OR space DISTRIBUTION that was created (Fig. 4-1). Remember: 1 cc 1 ml, but 1 ml does not equal 1 mg. Gram refers to the weight of a powdered drug, not its volume or the space that it occupies. Never take medication orders in dosages of volume. For example, you are transporting a 43-year-old man with a severe open femur fracture incurred after he fell off a roof. You call medical direction for an order for morphine, and medical direction gives the order for 3 ml (or 3 cc) of morphine sulfate. Many drugs, morphine included, come in several different concentrations. Injectable NOT morphine FOR SALE comes in OR concentrations DISTRIBUTION of 2 mg/ml, 4 mg/ml, 5 mg/ml, 8 mg/ml, and 10 mg/ml. For instance, if medical direction thought that the advanced life support (ALS) drug box was stocked with morphine sulfate with a concentration of 2 mg/ml, the intended order to give 2 ml would have resulted in 4 mg being administered. If the drug box was supplied with 4 mg/ml, the order of 2 ml would have 1 cm NOT FOR 1 cmsale OR DISTRIBUTION 1 cm 1 cc 1 ml Fig. 4-1 Volume is equal to the space created. The term cc represents cubic centimeter. A cubic centimeter is 1 cm wide, 1 cm long, Jones and 1 cm & high. Bartlett One milliliter Learning, (ml) is the LLC equivalent volume of a cubic centimeter. To avoid confusion, the term milliliter is preferred over cc, or cubic centimeter...

4 CHAPTER 4 MEDICATION MATH 67 Jones & Bartlett Learning, resulted LLC in the patient getting 8 Jones mg of morphine, & Bartlett or Learning, twice the intended LLC dose. Although most drug boxes are supplied with standardized concentrations of medications, administering medications on the basis of volume alone (not concentration) is poor practice and not safe. KILOGRAMS AND POUNDS Jones The next & conversion Bartlett Learning, commonly used LLCto calculate drug dosages is kilograms Jones &(kg) Bartlett to pounds Learning, LLC NOT (lb). FOR Note SALE that these OR units DISTRIBUTION refer to the patient s weight, not the NOT weight FOR of the SALE drug. OR Many DISTRIBUTION drug dosages, particularly those administered to pediatric patients, are based on the patient s weight in kilograms to ensure safety from overdose. The equivalent to remember is 1 kg 2.2 lb. Therefore, to convert weight in pounds to weight in kilograms, divide the number of pounds by 2.2. Jones & Bartlett Example: Learning, If a patient LLC weighs 154 lb, divide 154 Jones lb by 2.2 & lb/kg Bartlett to determine Learning, the weight LLC NOT FOR SALE in OR kilograms. DISTRIBUTION 154 lb weight in kilograms 2.2 lb/kg First, cross out like terms in the problem; in this case, lb. 154 lb Jones & weight Bartlett in kilograms Learning, LLC 2.2 lb /kg Now work the problem: kg 2.2 kg Jones MILLIGRAMS, & Bartlett MICROGRAMS, Learning, LLCAND GRAMS NOT The FOR next SALE conversion OR is DISTRIBUTION from milligrams to grams and, in reverse, NOT from FOR grams SALE to milligrams. OR DISTRIBUTION This process also includes converting milligrams to micrograms (mcg) and micrograms to milligrams. Remember: milli means 1/1000 of a basic unit; in this case, grams. The equivalent is 1000 mg 1 g. To use an everyday example, when changing a dollar into coins (e.g., dimes or pennies), Jones & Bartlett Learning, the LLClarger unit (dollar) is changed Jones into & an Bartlett equivalent Learning, sum smaller LLC units (dimes or pennies). Therefore, to get the total number of the smaller unit, multiply the number of dollars (e.g., 5 dollars) by the number of dimes or pennies per dollar. Example 1: 5 dollars 10 dimes Jones & Bartlett Learning, number of dimes dollar LLC Cross out like terms; in this case, dollar. 5 dollars 10 dimes number of dimes dollar Jones & Bartlett Now Learning, work the problem: LLC 5 10 dimes 50 dimes Example 2: 5 dollars Jones 100 pennies & Bartlett number Learning, of penniesllc NOT dollar FOR SALE OR DISTRIBUTION..

5 68 PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL Jones & Bartlett Learning, Cross LLC out like terms; in this case, Jones dollars. & Bartlett Learning, LLC 5 dollars NOT 100 FOR pennies SALE OR DISTRIBUTION number of pennies dollar Now work the problem: pennies 500 pennies NOT FOR Note SALE that, when OR converting DISTRIBUTION a pocket full of change into NOT dollar FOR bills, SALE smaller OR units DISTRIBUTION (coins) are being changed into larger units (dollars). The result will be fewer larger units (dollars) than smaller units (coins). So, when converting between units, ask yourself, Am I changing small units for larger units, or large units for smaller units? This question also applies in practice; you should have an initial sense of whether the numbers and units Jones & Bartlett should Learning, be increasing LLCor decreasing in magnitude. NOT FOR SALE OR To DISTRIBUTION convert grams to milligrams, multiply NOT grams FOR by SALE Remember OR DISTRIBUTION that every 1 g contains 1000 mg; this can be written as 1000 mg/g. Example: 5 g 1000 mg Jones number of milligrams g & Bartlett Learning, LLC Cross out like terms; in this case, g. 5 g 1000 mg number of milligrams g Jones Now work & Bartlett the problem: Learning, LLC mg 5000 milligrams This can be quickly accomplished by moving the decimal point to the right the same number of spaces as there are zeros in the number. For example, because 1000 mg has 3 zeros, move the decimal point three decimal places to the right. 5 g 5000 mg The same process can be used to convert milligrams (mg) to micrograms (mcg). milli means 1000, or add 3 zeros micro means 1,000,000, or add 6 zeros Jones & Bartlett Learning, To LLC convert milligrams (3 zeros) Jones to micrograms & Bartlett (6 zeros), Learning, simply move LLCthe decimal point three more places to the right, NOT for a FOR total SALE of 6 zeros. OR DISTRIBUTION 5000 mg 5,000,000 mcg To convert milligrams to grams (smaller to larger), divide the number of grams by 1000, or simply move the decimal point three places to the left. This is the same as changing Jones 100 pennies & Bartlett back to Learning, dollars. The LLC 100 actually means 100 cents. Jones Therefore & Bartlett move the Learning, LLC NOT decimal FOR point SALE to OR the left DISTRIBUTION the same number of places as there NOT are zeros FOR in the SALE equivalent OR DISTRIBUTION of \$1.00 (100 pennies; therefore 2 zeroes, 2 spaces): 100 pennies (cents) 1.00 dollar Following are some practice problems. Be sure to master the art of conversion before Jones & Bartlett moving Learning, on so that LLC you will understand the rest Jones of the chapter. & Bartlett Learning, LLC Practice Problems Convert grams to milligrams and milligrams to grams: 1. 1 g mg mg g mg g NOT FOR mg SALE OR DISTRIBUTION g..

6 CHAPTER 4 MEDICATION MATH 69 Jones & Bartlett Learning, 5. LLC 500 mg g Jones g & Bartlett Learning, mg LLC g mg 9. 2 g mg g mg mg g NOT Convert FOR SALE milligrams OR to DISTRIBUTION micrograms and micrograms to milligrams: 1. 1 mg mcg ,000 mcg mg mcg mg mg mcg NOT FOR SALE 3. OR 250 DISTRIBUTION mcg mg mg NOT FOR SALE mcg OR DISTRIBUTION mg mcg mcg mg mg mcg ,000 mcg mg Answers Convert grams to milligrams and milligrams to grams: 1. 1 g 1000 mg g 750 mg mg 1 g g 1250 mg mg 0.25 g g 10,000 mg Jones & mg Bartlett 0.4 g Learning, 9. 2 g 2000 LLCmg NOT 5. FOR 500 mg SALE 0.5 OR g DISTRIBUTION mg 2.5 g Convert milligrams to micrograms and micrograms to milligrams: 1. 1 mg 1000 mcg ,000 mcg 800 mg mcg 0.5 mg mg 800,000 mcg Jones & Bartlett Learning, mcg 0.25 LLC mg mg 200,000 Jones mcg & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTION mg 400,000 mcg mcg NOT 1 mg FOR SALE OR DISTRIBUTION mg 200 mcg ,000 mcg 200 mg Box 4-1 summarizes basic conversions that are useful in drug calculations. BOX 4-1 BASIC CONVERSIONS 1 g 1000 mg 1 mg 1000 mcg 1 L 1000 ml or 1000 cc 1 kg 2.2 lb Jones 2.5 cm & Bartlett 1 in Learning, LLC NOT FOR Remember: SALE 1 mg OR does not DISTRIBUTION equal 1 ml or 1 cc. DRUG PREPARATIONS AND CONCENTRATIONS NOT FOR SALE OR Regarding DISTRIBUTION drug dosage calculations, understanding NOT that FOR drugs SALE are supplied OR DISTRIBUTION in various concentrations with differing preparations is important. The same drug can come in various concentrations, and dosages must be calculated according to the particular preparation. For example, atropine sulfate, a medication commonly used to increase a slow heart rate, comes packaged in two ways in prefilled syringes: 0.5 mg/10 ml and 1 mg/10 ml. The second preparation is twice as Jones concentrated & Bartlett as the first Learning, and therefore LLCrequires a dose of only half the amount. Another NOT drug, FOR dopamine, SALE which OR is DISTRIBUTION used by prehospital professionals..

7 70 PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL Jones & Bartlett Learning, in LLC certain situations in the field to Jones raise blood & Bartlett pressure, Learning, comes three LLC different concentrations: 0.8 mg/ml, 1.6 mg/ml, and 3.2 mg/ml. FORMULAS Formulas are used to solve drug problems or determine dosages for patients. They should Jones be used & in Bartlett conjunction Learning, with the LLC basic conversions explained previously. Jones & Four Bartlett basic formulas can be used to solve all prehospital pharmacology math problems: Learning, LLC Formula 1 Single dose (e.g., bolus of lidocaine or IM injection of Benadryl): desired dose volume/quantity X dose on hand Jones 1 & Bartlett Learning, LLC NOT FOR SALE Formula OR DISTRIBUTION 2 To infuse a measured amount of fluid in a set amount of time (e.g., fluid challenge): total volume drops/ml of IV set drops/min time in minutes Jones & Bartlett Learning, Formula LLC 3 Drip (infusion) not based on NOT weight FOR (e.g., SALE lidocaine OR drip): DISTRIBUTION dose desired drops/ml of IV set drops/min dose on hand 1 Formula 4 Jones Drip (infusion) & Bartlett based Learning, on weight (e.g., LLCdopamine drip): NOT FOR SALE OR dose DISTRIBUTION desired wt ( lb) dose desired kg 22. lb kg dose desired wt ( lb) kg 22. lb kg dose desired drops/ml of IV set Jones & drops/min Bartlett Learning, LLC dose on hand 1 APPLICATION OF FORMULA 1 The first of the four formulas listed in the previous section is used to calculate the amount of a drug to give a patient in a single dose on the basis of the desired dose (DD), or the amount ordered by medical direction; the dose on hand (DH) or the amount of the weight Jones & Bartlett Learning, of LLC the drug (grams, milligrams, Jones micrograms); & Bartlett and the Learning, volume (V) or LLC quantity (Q), or the amount of solution in which NOT the drug FOR is dissolved. SALE OR DISTRIBUTION A 64-year-old woman is enjoying a round of golf when she suddenly steps in a hornets nest and is stung multiple times. Because she is allergic to bee stings, she quickly heads back to the clubhouse and asks for help. A paramedic unit is dispatched. On arrival, the patient is in mild distress, with large hives appearing on her face and neck. Because of her age and the relatively mild signs and symptoms at this point, the paramedics avoid epinephrine and choose to administer diphenhydramine (Benadryl) 25 mg IM. Their prefilled syringe reads 50 mg/ml. How many milliliters should they administer? Jones & Bartlett Step Learning, 1: Choose the LLC proper formula. desired dose volume NOT ( quantity FOR SALE ) OR DISTRIBUTION dose on hand 1 Step 2: Fill in known values. 25 mg 1 ml Jones & Bartlett Learning, LLC 50 mg..

11 74 PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL Jones & Bartlett Learning, Formula LLC 3 Answers 1. 1 mg 1000 mcg, so the DH (drug concentration) is 1000 mcg/250 ml 4 mcg/ml. DD: 4 mcg min 60 gtt ml 4 mcg min 60 gtt ml 4 min 60 gtt DH: 4 mcg ml 4 mcg ml gtt min 60 gtt min Jones & Bartlett Learning, 4 LLC NOT FOR 2. 1 g SALE 1000 OR mg, so DISTRIBUTION the DH is 1000 mg/250 ml 4 mg/ml. DD: 3 mg min 60 gtt ml 3 mg min 60 gtt ml 3 min 60 gtt DH: 4 mg ml 4 mg ml Jones & Bartlett Learning, LLC gtt min 45 gtt min 4 NOT FOR SALE OR 3. DISTRIBUTION 1 mg 1000 mcg, so the DH is 1000 mcg/500 NOT FOR ml 2 SALE mcg/ml. OR DISTRIBUTION DD: 2 mcg min 60 gtt ml 2 mcg min 60 gtt ml 2 min 60 gtt DH: 2 mcg ml 2 mcg ml gtt min Jones 60 gtt & minbartlett Learning, LLC 2 APPLICATION OF FORMULA 4 Formula 4 is used to calculate the amount of a drug to give a patient by drip (infusion) when the dosage is based on weight.... You are transporting an elderly woman with a history of multiple cardiac events to the hospital. En route, her blood pressure begins to drop even though her cardiac rhythm shows only sinus tachycardia at a rate of 120 beats/min. You contact medical direction and are told to begin a dopamine infusion at 2 mcg/kg/min and to titrate it until her blood pressure is approximately 90 mm Hg systolic. Prepare the infusion by adding 800 mg of dopamine to a 500-mL bag of normal saline. The patient weighs 110 pounds. In this last formula, one more step in the process must be calculated to determine what the desired dose is on the basis of the patient s weight in kilograms. Remember that 1 kg Jones & Bartlett Learning, LLC 2.2 pounds. Step 1: Choose the proper formula. DD lb DD lb DD kg 22. lb kg kg 22. lb kg Jones & Bartlett Learning, DD drops/ml LLCof IV set drops per minute DH 1 Step 2: Determine the patient s weight in kilograms by dividing the weight in pounds by lb 110 lb 50 kg 22. lb kg Jones 22. lb kg & Bartlett Learning, LLC Step 3: Multiply the weight in kilograms by DD/kilograms and cross out like terms to determine the DD, with weight adjustment. If this patient weighs 50 kg, and the DD is 2 mcg/kg per minute: 50 kg 2 mcg 50 kg 2 mcg 50 2 mcg Jones & Bartlett Learning, 100 mcg LLCmin kg min NOT kg FOR minsale OR mindistribution..

12 CHAPTER 4 MEDICATION MATH 75 Jones & Bartlett Learning, Step LLC4: Prepare the infusion and Jones calculate & the Bartlett DH (drug Learning, concentration). LLC 800 mg 800,000 NOT mcg FOR to be SALE added OR to 500 DISTRIBUTION ml normal saline 800, 000 mcg 1600 mcg ml 500 ml Step 5: Determine the drip rate with a microdrip IV infusion set that delivers 60 gtt/ml. 100 mcg/min 60 gtt/ml gtt/min 1600 mcg/ml Step 6: Cross out like terms and multiply across. 100 mcg /min 60 gtt/ ml gtt/min 1600 mcg / ml Note: The zeros can be crossed out if only one above and one below the line are crossed out at a time, as in this example: 100 mcg /min 60 gtt/ ml gtt/min Jones 1600 mcg & / Bartlett ml Learning, LLC If the problem is rewritten by NOT leaving FOR out everything SALE OR that DISTRIBUTION has been crossed out, it becomes much simpler: 10 min 6 gtt 375. gtt min ( round off to 4 gtt min) 16 PRACTICAL APPLICATION PROBLEMS Answers to the problems in this section are found in Appendix E. V entricular Fibrillation You are assisting in the resuscitation of a 49-year-old man who is unresponsive and apneic. The cardiac monitor shows ventricular Jones fibrillation, & Bartlett and the paramedic Learning, charge LLC has directed you to prepare and give the medications. NOT Cardiopulmonary FOR SALE resuscitation OR DISTRIBUTION (CPR) is being performed, defibrillation has been appropriately accomplished, the patient has been successfully intubated and is being bagged with 100% oxygen, and an IV has been established The first medication to administer is epinephrine 1:10,000 1 mg IV push. Your Jones & prefilled Bartlett syringe Learning, reads epinephrine LLC 1:10,000 1 mg/10 ml. Jones How many & Bartlett milliliters Learning, LLC NOT FOR should SALE you OR administer? DISTRIBUTION... Five minutes later you are asked to repeat the above dose of epinephrine, but you discover that your IV has infiltrated. The paramedic directs you to administer twice the dose through the endotracheal tube. The patient has good lung sounds bilaterally with bagging......

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