Originated by Kathy Guyett and Kathy Palumbo Revised by Kathy Palumbo and Eleanor Nixon
INTRODUCTION The role of the nurse often requires the use of mathematical computation. The administration of oral and parenteral medication, as well as intravenous fluid administration, all may require mathematical calculation. Accurate calculation is necessary to safely administer the correct dosage or rate. One approach to calculate dosages is to teach a variety of formulas to fit different situations. The nurse would need to use the correct formula for the situation. An alternative approach is to use the technique of DIMENSIONAL ANALYSIS or LABEL FACTOR METHOD. This technique is used in areas of technology and science, as well as nursing. By learning and applying this formula and a few variations, the nurse will be able to accurately calculate any medication dosage.
OBJECTIVES After completing this module, the student will be able to: 1. Utilize dimensional analysis to accurately calculate oral and parenteral medication dosages for the adult and pediatric patient. 2. Determine safe dosage for pediatric patients. 3. Accurately reconstitute powdered medications. 4. Apply dimensional analysis to dosage calculation problems in various clinical settings.
GCC DOSAGE CALCULATION POLICY Nursing students must demonstrate mastery in dosage calculations in order to progress in the program. Each course has specific expectations and requirements that must be met in order to progress to the next nursing course. These requirements are presented in the next few slides. This information is also found in The Nursing Program Student handbook.
GCC DOSAGE CALCULATION POLICY NUR-110 As a N110 student, the student must pass a dosage calculation exam in class with a grade of 80% or better in order to meet the requirements of the course. A computer program, DOSECALC, must be completed prior to the first dosage calculation exam. A student will have three (3) chances to pass the dosage calculation exam during the course of the semester. These exams will be scheduled at intervals at the discretion of the faculty. Once a student passes the exam with a grade of 80% or better, the requirement is met. If a student cannot achieve a grade of 80% after three (3) exams, the student will fail N110 and will not be allowed to continue in the program.
MEDICATION ADMINISTRATIONEXAM POLICY NUR-120 As a N120 student, the student must pass a medication administration exam in class with a grade of 90% or better in order to meet the requirements of the course. A computer program, DOSECALC/IVCALC, must be completed prior to the first medication administration exam. A student will have three (3) chances to pass the medication administration exam during the course of the semester. These exams will be scheduled at intervals at the discretion of the faculty. Once a student passes the exam with a grade of 90% or better, the requirement is met. If a student cannot achieve a grade of 90% after three (3) exams, the student will fail N120 and will not be allowed to continue in the program.
MEDICATION ADMINISTRATIONEXAM POLICY NUR-131 As a N131 student, the student must pass a medication administration exam in class with a grade of 90% or better in order to meet the requirements of the course. A computer program, DOSECALC/IVCALC, should be reviewed prior to the first medication administration exam. A student will have three (3) chances to pass the medication administration exam during the course of the semester. These exams will be scheduled at intervals at the discretion of the faculty. Once a student passes the exam with a grade of 90% or better, the requirement is met. If a student cannot achieve a grade of 90% after three (3) exams, the student will fail N131 and will not be allowed to continue in the program.
MEDICATION ADMINISTRATIONEXAM POLICY NUR-210 As a N210 student, the student must pass a medication administration exam in class with a grade of 90% or better in order to meet the requirements of the course. DOSECALC/IVCALC, should be reviewed prior to the first medication administration exam. A student will have three (3) chances to pass the medication administration exam during the course of the semester. These exams will be scheduled at intervals at the discretion of the faculty. Once a student passes the exam with a grade of 90% or better, the requirement is met. If a student cannot achieve a grade of 90% after three (3) exams, the student will fail N210, and will not be allowed to continue in the program.
MEDICATION ADMINISTRATIONEXAM POLICY NUR-220 As a N220 student, the student must pass a standardized Medication Administration Exam. Students will be provided with a study guide to prepare for this exam. Students will have three (3) chances to pass the exam. These exams will be scheduled at the discretion of the faculty. Once a student passes the exam, the requirement is met. If a student cannot achieve the established passing criteria after three (3) exams, the student will fail N220, and will not be allowed to continue in the program.
Students will be passing medications as part of the GCC Clinical experience . Students will be expected to recognize when calculations are required and to arrive at the correct answer using dimensional analysis. Please see each course syllabi for more information regarding medication administration.
DIRECTIONS To fully utilize this module, read through EACH section and follow the directions as noted. You can always go back at any time to review a section. You can print out the module but printing it will not give you the answers to the problems. You should have plenty of paper, pens or pencils and a basic calculator (you will be given a calculator for in class testing; you cannot use your own or a graphing calculator). Drinks and snacks optional! If you go through this module all at once, expect it to take an hour or so. 110 students ONLY: You must take an online Dosecalc test to achieve a passing grade of 80% (8 out of 10 questions correct). You can take it as many times as you want. Once passed, you can take more tests for review. There is a finite pool of questions available, however, so the more tests you take, the more questions will be repeated. Please refer to your instructor for more information and how to access the test.
BASIC MATH INFORMATION Before you begin this program, you will need to review some basic math techniques even though you will be allowed to use a calculator (whew!). First of all, remember how to MULTIPLY fractions: To multiply fractions, simply multiply numerator (the top number) times numerator and denominator (the bottom number) by denominator. For example, 1/2 X 3/4= 3/8 (1 x 3=3, 2 x 4=8).
BASIC MATH INFORMATION Second, remember how to DIVIDE fractions: To divide fractions, you must INVERT the second fraction and then multiply as described above. For example, 1/2 divided by 3/4 is 1/2 X 4/3 which is 4/6 or 2/3.
BASIC MATH INFORMATION Third, remember how to CONVERT fractions to decimals and vice versa: In the fraction 1/2, the “/” means divided by. So ½ means one divided by two which is 0.5 To convert decimals to fractions, remember what the place settings mean after the decimal point. The first one is tenths, second hundredths, the third thousandths and so on. So 0.5 is five tenths (5/10) which reduces to ½. In another example, 0.25 is 25 hundredths which is 25/100 which reduces to ¼.
ROUNDING INFORMATION In order to administer accurate dosages, you must ROUND OFF to the nearest appropriate unit. You cannot give tenths of a tablet, for example, so you must round off correctly to give the proper dose. Standard rounding rules call for rounding up if the unit is 0.5 or more, rounding down if the unit is 0.4 or less. When determining dosage administration for tablets, your answer should calculate to either a whole or half tablet or tablets. If your answer does not come out evenly to one of these units, recheck your math, ask another nurse to calculate the dose or call the pharmacy. You can give a half tablet by breaking along the scored line on the tablet and /or cutting with a pill cutter. Capsules cannot be split. If the answer doesnt come out to a whole capsule or capsules, see above.
MORE ROUNDING INFORMATION Liquids, whether given orally or parenterally, are usually rounded to the nearest TENTH of a ml. To determine this, you must know the hundredths place to calculate the correct answer and use standard math rounding rules: 1.25 ml = 1.3 ml 1.2 ml =1.2 ml (the hundredths place is zero) 2.08 ml= 2.1 ml On occasion you may need to round to the hundredths place. If so, calculate to the thousandths place and use standard rounding rules to round to the hundredths place. 1.575= 1.58 3.052= 3. 05 5.788= 5. 79 You will be given specific rounding directions on all exams (including the NCLEX-RN).
REVIEW OF SYSTEMS OFMEASUREMENT : METRIC Traditionally, there are three systems of measurement used in medication administration: the household system, the apothecary system, and the metric system. The metric system is used in prescribing and administering medications and is currently the preferred system. The metric system was developed in the late 1700s and is based on the decimal system. Base units such as grams for weight and liters for volume are modified using prefixes to denote smaller or larger quantities.
REVIEW OF SYSTEMS: HOUSEHOLD The household system is the oldest of the three systems. It was developed from mans earliest attempts to measure mass, distance, and volume. Some common household measurements are cups, pounds, and teaspoons.
REVIEW OF SYSTEMS: APOTHECARY The apothecary system was derived from the measurements used by the first pharmacists or "apothecaries". A quantity of an herb or other medicine was balanced with a "grain" of wheat and labeled a grain. Other measurements in this system are drams and minims. NOTE: The Joint Commission (JACHO) recommends that this system be abandoned as it is unfamiliar to many practitioners and can be confused with metric units.
JCAHO OFFICIAL DO NOT USE LIST Read the next two pages which list “do not use” abbreviations by the Joint Commission for Hospital Accreditation. You will be expected to know the information in this list.
HOUSEHOLD ABBREVIATIONS Drop= gtt Ounce=oz Teaspoon=tsp or t Tablespoon=Tbsp or T Pound=lb Foot=ft
METRIC ABBREVIATIONS Since medical providers order medication in metric units, it is essential that you understand the metric system and conversion between the units. Gram=gm, g Prefixes Liter-L kilo=K Meter=M centi=c milli=m micro=mc
METRIC ABBREVIATIONS You can expect to see: Kg which stands for kilogram mg which stands for milligram cm which stands for centimeter mm which stand for millimeter mL which stands for milliliter (preferred abbreviation) mcg which stands for microgram
CONVERSIONS The form in which a medication is prescribed is not always the form in which it is available. For example, the physician may order Keflex 1 Gram tablets and the pharmacy may provide Keflex 500 mg tablets. Thus a conversion between gm and mg is necessary to give the correct amount of the medication.
LIST OF CONVERSIONSYou MUST know the following in order to calculate different dosage problems on class exams, in lab and in clinical. MEMORIZE THEM!1000 mg (milligram)=1 g or 1 gm (gram)1000 mcg (microgram)=1 mgConversions between the systems include:30 mL=1 oz1 Kg=2.2 lb5 mL=1 tsp
COMPONENTS OF DIMENSIONALANALYSIS Dimensional analysis has 3 components: The first component is the beginning label. The beginning label is the first unit in the equation. This is usually contained in the doctors order. The second component is the ending label or answer label. The ending/answer label is the unit to be administered, such as tablets or milliliters. The final component, the conversion factor, is a sequence of equivalents which can be cancelled, leaving only the ending label. This is not always required depending upon the beginning and ending labels.
BASIC EQUATION The equation can be written like this:beginning label x conversion factor (s) = answer/ending label(BL) x (CFs) = ( AL or EL)
APPLICATION OF DIMENSIONALANALYSIS There are three steps in applying dimensional analysis to dosage calculation problems. The first step is to identify the components of the problem. The first component to identify is the beginning label (BL)which is usually the doctor’s order. Then identify the answer /ending label (EL) and any conversion factors (CF). The second step is to put the components in an equation. The third step is to solve the problem. In the next pages, we will go through this process step by step.
APPLICATION OF DA First, lets identify the components of a problem - the beginning label, the answer/ending label and any conversion factors. At this point, you do not have to set up the problem. You will need scrap paper and pencil. EXAMPLE #1: How many milliliters are there in 8 ounces (oz)? What is the beginning label (BL), the ending label (EL), and the conversion factor (CF)? Write the answers on your scrap paper. Click here for answer #1
APPLICATION: EXAMPLE 2 EXAMPLE #2: How many micrograms are there in 2 milligrams? What is the beginning label (BL), the ending label (EL), and the conversion factor CF)? Write the answers on your scrap paper. Click here for answer to example 2
APPLICATION: EXAMPLE 3 Now lets try a dosage calculation problem. Once again, identify the BL, EL, and CF. EXAMPLE #3: How many 1000 milligram (mg) tablets should be given if the physician orders 500 milligrams (mg)? What is the beginning label (BL), the ending label (EL), and the conversion factor (CF)? Write the answer on your scrap paper. Click here for answer to example 3
SETTING UP THE EQUATION Now that you are able to identify the components of a problem, you will practice setting up the components into an equation format. You do not have to solve for the equation at this point. That will be done in the next section.
SETTING UP THE EQUATION:EQUATION 1 Equation #1: How many milliliters (mL) are there in 8 ounces (oz)? See if you can set up the equation (Note: you will solve the equation in the next section). Remember: BL: 8 oz EL: mL CF: 30 mL = 1 oz Click here for answer to answer to equation 1
SETTING UP THE EQUATION:EQUATION 2 Equation #2: How many micrograms (mcg) are there in 2 milligrams (mg)? See if you can set up the equation (Note: you will solve the equation in the next section). Remember: BL: 2 mg EL: mcg CF: 1000 mcg = 1 mg Click here for answer to equation 2
SETTING UP THE EQUATION:EQUATION 3 Equation #3: How many 1000 milligram (mg) tablets (tab) should be given if the physician orders 500 milligrams (mg)? See if you can set up the equation. Remember: BL: 500 mg EL: tab CF: 1000 mg = 1 tab Click here for the answer to equation #3
SOLVING FOR THE EQUATIONS The final step in solving a dosage calculation problem is to calculate the answer. You should cancel the labels, multiply the numerator (top) and then denominator (bottom) of the fractions and divide the denominator into the numerator for the answer. Before you do any math, MAKE SURE that when you cancel your labels, ONLY the answer /ending label remains. If there is another label remaining that cant be canceled, then you have not set up the problem correctly. Take the equations used in step two and calculate the answers. Click here for the answers to all of the problems: answers
MEDICATION DOSAGE PROBLEMS Now that you have gone through the process step by step, you should be able to calculate actual dosage problems. In this section, a physicians order will appear along with a picture of the medication and box/bottle. These problems will be much like the problems you will see during medication administration. Follow the directions given. You will have a chance to review the problems and you will be given some "clues" to help with the setup. You will need the list of equivalents, calculator, paper and pencil before continuing with this section. If there are some abbreviations that are unfamiliar to you, look in your textbook or medical dictionary. You will benefit by knowing that “po” stands for “by mouth” or “orally”.
MED PROBLEMS: SAMPLE 1 Doctors Order: Cleocin 150 mg po q6h. Problem: How many milliliters will you administer? CLUES: First, copy down the information you will need from the doctors order (the beginning label). Next, look at the problem for the ending label. Check the box for the conversion factor. ( is the unit in which the medication is ordered-mg- the same in which it will be administered- ml ?) Set up the equation, cancel labels and solve. Round to the nearest tenth of a mL Click here for answer sample #1
MED PROBLEMS:SAMPLE 2 Doctors Order: Ibuprofen 600 mg po q4h as needed for pain. Problem: How many tablets should you administer? CLUES: First check the box for the generic name of the drug. Copy down the information you will need from the doctors order (the beginning label). Next, look at the problem for the ending label. Check the box for the conversion factor. Set up the equation, cancel labels and solve. Click here for answer sample #2
MED PROBLEMS: SAMPLE 3 Dolobid 0.5 Gm po q6h as needed for discomfort. Problem: How many tablets should you administer? CLUES: First, copy down the information you will need from the doctors order (the beginning label). Next, look at the problem for the ending label. Check the box for the conversion factor. (box reads 500 mg) When you set up the equation, you will see that you need a second conversion factor to cancel the necessary labels. Use your equivalents for this. Click here for answer sample #3
RECONSTITUTION Reconstitution is the addition of a liquid to a powdered medication to create a form that can be administered to the patient. While most medications are provided in liquid form, some may be distributed as a powder. Since most powders cannot be ingested, and should not be given intravenously (IV) or intramuscularly (IM), reconstitution must be done before administration. The information on the vial will tell you how much and what kind of liquid to add. Dimensional analysis is easily applied to reconstitution problems.
RECONSTITUTION PROBLEM 1 Problem: The doctor orders cefazolin sodium 1 gram IV. The label reads: Add 10 mL of bacteriostatic NaCL to the powdered cefazolin for a concentration of 500 mg per 5 mL. How many mL should the nurse give? The key to solving this type of problem is to ignore extra information that is not necessary to calculate the desired dose. Then apply the steps for dimensional analysis. BL: 1 g EL: mL CF: 1000 mg = 1 g and 500 mg = 5 mL NOTE: The 10 mL of dilutent (liquid) is not necessary to calculate the dose; only the resulting concentration of the medication (500 mg = 5 mL) is necessary. The concentration means that there is 500 mg of medication in every 5 mL of the added liquid. Now setup and solve the equation. Click here for answer to reconstitution 1
RECONSTITUTION PROBLEMS 2 & 3 Setup and solve the following reconstitution problems. 1. The doctor orders penicillin G potassium 1 million units IM. If you reconstitute the medication with 8 mL of sterile water to form a concentration of 500,000 units per mL, how many mL should you give? 2. The order reads: Ancef 225 mg IV. If the instructions call for diluting the powdered medication with 2 mL of sterile water to create a concentration of 125 mg per mL, how many mL should you give? Round to the nearest tenth of a mL. Click here for answers to reconstitution 2 and 3
PEDIATRIC CALCULATIONS Another area in which you can apply dimensional analysis is in calculating pediatric dosages. It is crucial that these types of dosages be calculated correctly since the margin for error in infants and children is very narrow. In other words, an inaccurate dose is more likely to have a harmful, even fatal, effect. In this section two types of problems will be presented: administration problems and safe dose.
PEDIATRIC DOSAGEADMINISTRATION Pediatric dosage administration problems are similar to adult dosage problems. However, when giving very small amounts of liquid oral or parenteral medication to infants or young children, it may be necessary to round to the hundredths place. You would solve to the thousandths place, round to the hundredths place, and then draw up the amount with an oral syringe marked by hundredths of a mL. See if you can setup and solve for this problem: The doctor orders 0.08 mg of Digoxin daily for a 1 year old child. If the label on the bottle reads 50 mcg per mL, how many mL should you give for a single dose? (Round to the nearest tenth of a mL) Click her for answer to pediatric 1
PEDIATRIC SAFE DOSE When a nurse is preparing to administer a medication, one of his/her responsibilities is to know if the dose that has been prescribed is a safe dose. That is, does the dose fall within an established range of safety and effectiveness as noted in pharmacological references? This standard for each drug is based upon an adult 18- 65 years weighing 150 lbs. These ranges are included in all drug references.
PEDIATRIC SAFE DOSE Dosages for the pediatric patient are sometimes based upon age but more often upon drug amount per kilogram of weight per day or per dose. For example, the average safe dose of Keflex for an adult is 250-500 mg. One only has to compare the patients dose to this established range to determine if it is safe. For a child, a safe dose range is 25-100 mg/kg/day. Not only must one multiply the weight by the low and high ends of the range but one must also divide by the number of doses given per day to determine a single safe dose. NOTE: This type of problem WILL NOT be tested in N110 or N120 on class exams.
PEDS SAFE DOSE FORMULA 1 You can use dimensional analysis to determine safe dose. The formula is a variation of the one used for medication administration problems. Use this version of the formula when the drug reference information for usual dosage is in mg/kg/ day (24 hours). The formula is:
PEDS SAFE DOSE FORMULA 2 The other version of the formula for safe dose follows. Use this formula when the drug reference information for usual dosage is in mg/kg/dose. These formulas are different from the administration formula you learned previously. So when faced with a pediatric problem, ask yourself: is it an administration problem (how much should I give) or a safe dose problem (is this a safe dose for the child)?
PEDIATRIC DOSE PROBLEM 1 The physician orders ibuprofen 65 mg po every four hours. If ibuprofen is supplied in liquid form as 100 mg per 5 mL, how many mL should you give for a single dose? (Round to the nearest tenth of a mL) The first step in figuring out this problem is deciding which formula to use. Is this a safe dose problem or an administration problem? Since the problem asks you how much to give, you know it is an administration problem. This is NOT a safe dose problem so use dimensional analysis (beginning label X conversion factor(s) =answer/ending label) to solve for the answer. ROUND TO THE NEAREST TENTH! Click here for answer1
PEDIATRIC DOSE PROBLEM 2 The doctor orders 65 mg of ibuprofen po Q6h prn for a child weighing 14 kg. The Pediatric Dosage Handbook states that the usual dosage is 4- 10 mg/kg/dose. Is the ordered dose safe for this child? First determine the type of problem. This is obviously a safe dose problem. Next, which safe dose formula should you use? Because the medication ordered is on a prn basis and the usual dosage is mg/kg/dose you need to use the second formula. Also note that the usual dosage is a range which means you will have to calculate both the low end of the range and the high end of the range. If the ordered dose falls between the low end of the range and the high end of the range, it is a safe dose. See if you can determine if the ordered dose is safe for the child. Remember to compare your answers to the ordered dose to determine this. Click here for answer to peds example 2
SUMMARY You have now gone through the entire program. If you want more practice, go through the program again. As per the Dosage Calculation policy, you will be tested in every nursing course in this program. A word of advice: DO NOT be tempted to figure out these problems in your head or use another (perhaps more familiar) method of calculation just because you do not have to show your work here. For ALL N110 and N120 in class tests, you will be required to show your work in dimensional analysis. More importantly, when the problems get more difficult in other nursing courses, it will be easier, and your chances of getting the correct answer much better, if you use dimensional analysis. GOOD LUCK!!!
REFERENCES Buchholz, S., and Henke, G. (2006). Med-Math, 5th ed. New York: Lippincott Williams and Wilkins. Daniels, J., and Smith, L. (2005). Clinical Calculations: A Unified Approach. Albany, N.Y.: Delmar Publishers Inc. Hegstad, L., and Hayek, W. (2001). Essential Drug Dosage Calculations, 4th ed. Upper Saddle River, N.J.: Prentice Hall. Kee, J., and Marshall, S. (2000). Clinical Calculations With Applications to General and Specialty Areas, 4th ed. Philadelphia: W.B. Saunders. Taketomo, C., Hodding, J., and Kraus, D. (2006). Pediatric Dosage Handbook, 13th ed. Hudson, Ohio: Lexi-Comp Inc.