McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved Math for the Pharmacy Technician: Concepts and Calculations Chapter 6: Dosage Calculations Egler Booth

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-2 METHODS OF DOSAGE CALCULATIONS

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-3 Learning Objectives  Identify the information on a medication order and drug label needed to calculate the desired dose.  Convert the dosage ordered to the desired dose. When you have successfully completed Chapter 6, you will have mastered skills to be able to:

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-4 Learning Objectives (con’t)  Calculate the amount to dispense of a drug.  Recognize common errors that occur during dose calculations.  Calculate estimated days supply.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-5 Introduction  This chapter will bring all of the previous information together to calculate the amount of medication to dispense to a patient.  You will use: Basic math Information from the physician’s order Drug labels Method of converting quantities from one unit of measurement to another

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-6 Dosages and Doses To calculate medication dosages you must know: Desired Dose:  The amount of the drug to be dispensed at a single time.  Its unit of measurement must be the same as the dosage unit.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-7 Dosages and Doses (con’t) Dosage ordered:  The total amount of drug the physician has ordered, along with the frequency.  Its unit of measurement may not be the same as that of the dosage unit.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-8 Dosages and Doses (con’t)  The amount of drug contained within a dosage unit of medication. Dose on hand:  If a medication has 250 mg of drug per tablet, the dose on hand is 250 mg.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-9 Dosages and Doses (con’t)  The unit of measurement for the desired dose must be the same as the unit of measurement of the dose on hand before the amount to dispensed can be calculated.  This is calculated by converting the dose ordered into the same unit of measurement as the dose on hand; once converted it becomes the desired dose.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-10 Calculating the Desired Dose  Before calculating the amount to be dispensed, you must first determine the desired dose.  The dosage ordered is not always written in the same units that are found on the drug label.  You must convert the dosage ordered into a desired dose having the same units as the dose on hand.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-11 Calculating the Desired Dose (con’t)  Three methods to calculate desired dose: Fraction proportion Ratio proportion Dimensional analysis  Each gives the same result  Use the method that you like  Once you identify your favorite method, follow the color coding of that method in the book

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-12 Fraction Proportion Method Procedure Checklist Write the conversion factor with the units that you are converting to in the numerator and the units you are converting from in the denominator. 2.Write a fraction with the unknown,”?,” in the numerator and the number that you need to convert in the denominator.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-13 Fraction Proportion Method (con’t) 3. Set the two fractions up as a proportion. 4. Cancel units. 5. Cross multiply, then solve for the unknown value.Example: The dosage ordered is 0.2 mg once a day. The dosage strength is 100 mcg/tablet. Find the desired dose. Desired Dose = 200 mcg

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-14 CAUTION!  In a fraction proportion, units from the fraction can be canceled only when they are the same portion of the fraction. Units in the denominator of one fraction cannot be canceled with units found in the numerator of the other. Always include the units when performing calculations.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-15 Ratio Proportion Method Procedure Checklist Write the conversion factor as a ratio A : B so that A has the units of the value that you are converting (the dosage ordered) and B has the unit of value of the dose on hand. 2.Write a second C : D so that C is the missing value (desired dose) and D is the number that is being converted (the dosage ordered).

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-16 Ratio Proportion Method (con’t) 3. Write the proportion in the form A : B :: C : D. Note: When using the ratio proportion method to calculate the desired dose, C indicates the unknown value (desired dose). 4. Cancel units. 5. Solve the proportion by multiplying means and extremes.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-17 Ratio Proportion Method (con’t) Example Practice by determining the desired dose. The desired dose is 325 mg. The order reads: ASA gr v PO daily. The drug label indicates 325 mg tablets. Find the desired dose.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-18 CAUTION!  In a ratio proportion, units can be canceled only when they are found in the same part of each of the ratios. Always include the units when performing calculations.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-19 Dimensional Analysis Procedure Checklist Determine the units of measure for the answer and place it as the unknown on one side of the equation. 2.On the other side of the equation, write a conversion factor with the units of measure for the answer on top and the units you are converting from on the bottom.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-20 Dimensional Analysis (con’t) 3. Multiply the conversion factor by the number that is being converted over one. 4. Cancel units on the right side of the equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation. 5. Solve the equation.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-21 Dimensional Analysis (con’t) Example Find the desired dose for the following: Ordered: Levsinex timecaps ER 1500 mcg once daily On hand: Levsinex timecaps mg Desired dose = 1.5 mg

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-22 CAUTION!  In dimensional analysis, units can be canceled only when they are found in both the numerator and the denominator of the fraction. Always include the units when performing calculations.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-23 Review and Practice Desired dose: 250 mg Determine the desired dose. Ordered: Penicillin VK 0.25 g On hand: Penicillin VK 500 mg

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-24 Calculating the Amount to Dispense Once you have determined the desired dose, you still must calculate the amount to dispense.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-25 Calculating the Amount to Dispense (con’t) To calculate the amount of medication to dispense (A), the following information must be known: The desired dose (D) or the amount of drug to be given at a single time. This is the dosage ordered converted to the same units as the dose on hand, if necessary.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-26 Calculating the Amount to Dispense (con’t) The dosage strength or the dose on hand (H) per the dosage unit (Q). The dose on hand (H) is the amount of drug contained in a dosage unit. The dosage unit (Q) is the unit by which you will measure the medication-tablets, capsules, milliliters, teaspoons, etc. (Find this on the medication label).

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-27 Calculating the Amount to Dispense (con’t) Procedure 6-4 Calculating the Amount to Dispense by Fraction Proportion: 1. Set up the proportion as follows: dosage unit amount to dispense dose on hand desired dose 2. Cancel units 3. Cross multiply, then solve for the unknown value

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-28 Calculating the Amount to Dispense (con’t) Example:  Ordered: 250 mg IM  Dosage strength available: 0.5 g/mL  Find the amount to dispense Amount to dispense = 0.5 mL

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-29 Procedure 6-5 Calculating the Amount to Dispense by Ratio Proportion: 1.The proportion will be set up as follows: dosage unit : dose on hand :: amount to dispense : desired dose Or Q : H :: A : D 2. Cancel units 3. Multiply the means and extremes then solve for the missing value Calculating the Amount to Dispense (con’t)

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-30 Calculating the Amount to Dispense (con’t) Example:  Ordered is Famvir 500 mg PO q 8h  On hand: Famvir 250 mg tabs  Find the amount to dispense Amount to dispense = 2 tablets

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-31 Calculating the Amount to Dispense (con’t) Procedure 6-6 Calculating the Amount to Dispense by Dimensional Analysis: With dimensional analysis you will not need to calculate the desired dose and amount to dispense separately. You will place your unknown (amount to dispense) on one side of the equation then multiply a series of factors on the right side of the equation. Canceling units will help you determine the equation has been set up correctly.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-32 Calculating the Amount to Dispense (con’t) Procedure 6-6 Calculating the Amount to Dispense by Dimensional Analysis (con’t): 1.Determine the units of measure for the answer and place it as the unknown on one side of the equation. 2.On the right side of the equation, write a conversion factor with the units of measurement for the desired dose on top and the unit of measurement for the dose on hand.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-33 Calculating the Amount to Dispense (con’t) Procedure 6-6 Calculating the Amount to Dispense by Dimensional Analysis (con’t): 3.Multiply the conversion factor by a second factor: the dosage unit over the dose on hand. 4.Multiply by a third factor: dose ordered over the number one. 5.Cancel units on the right side of the equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation. 6.Solve the equation.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-34 Calculating the Amount to Dispense (con’t) Example:  The order reads: Prozac Liquid 40 mg daily  On hand: Prozac 20 mg/5 mL  Find the amount to dispense Amount to dispense = 10 mL

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-35 Calculating the Amount to Dispense (con’t) Procedure 6-7 Calculating Amount to Dispense Using the Formula Method: 1. Determine the desired dose. Determine the dose on hand (H) and dosage unit (Q). 2. Fill in the formula D for the desired dose H for the dose on hand Q for the dosage unit in the formula A for the unknown or the amount to dispense

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-36 Calculating the Amount to Dispense (con’t) Procedure 6-7 Calculating Amount to Dispense Using the Formula Method (cont.): 3. Cancel the units. 4. Solve for the unknown.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-37 Calculating the Amount to Dispense (con’t) Example:  The dosage ordered is 500 mg PO q 8 h  On hand: Famvir 250 mg/tabs  Find the amount to dispense Amount to dispense = 2 tablets

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-38 Estimated Days Supply  As a pharmacy technician you may need to determine the estimated days supply of a prescription, which is how long the medication will last the patient if taken correctly.

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-39 Estimated Days Supply (con’t)  To determine estimated days supply you will multiply amount of medication to dispense by days needed over the number of dosage units per day. Amount to dispense 

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-40 Review and Practice The amount of the drug to be dispensed at a single time is called the: a.dosage ordered b.dosage unit c.desired dose d.dosage strength Answer: c. desired dose

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-41 Review and Practice True or False If a medication has 300 mg of drug per tablet, the dose on hand is 300 mg. Answer: True

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-42 Review and Practice The MAR reads Glucotrol 10 mg PO qd. The desired dose is ____ mg. Answer: 10 mg

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-43 Review and Practice Calculate the amount to dispense.  Ordered: Prednisone 10 mg PO qid  On hand: Prednisone 5 mg tablets Answer (Using ratio proportion) 5 mg : 1 tablet : : 10 mg : ? tablet 1 x 10 = 5 x ? ? = 2 Amount to dispense: 2 tablets

McGraw-Hill ©2010 by the McGraw-Hill Companies, Inc All Rights Reserved 6-44 Methods of Dosage Calculations THE END Performing dosage calculations is a large part of the pharmacy technician’s daily responsibilities. It is important to always use any resources available to you when performing dosage calculations.