Drug Dosage Calculations

How to Solve Drug Dosage ProblemsGeneral Information ----------------------------------------- ----- ------------------ page 2Converting between units --------- page 4Converting between metric units - page 5Calculating Drug Dosages --------- page 6Ratio (Rainbow) MethodProportion MethodFormula MethodDimensional AnalysisUseful Formulas for Calculating Drug Calculation Problems ---------------page 7-9Calculating BSACalculating a child’s dosage from an adult dosageCalculating flow rate in ml/hCalculating flow rate in gtt/minCalculating Heparin dosagesConverting from F to C or C to FHelpful Websites -------------------- page 9Provided by the Academic Center for Excellence1How to Solve Drug Dosage ProblemsReviewed August 2012

General InformationThere are three different types of measurements you will encounter when dealing withmedications: Household, Apothecary, and Metric.TypeNumberSolidsHouseholdWhole numbers andFractions before unit.Ex: 1 ½ TTeaspoons (tsp, t)Drop (gtt)Tablespoons (Tbs,T) Ounce (oz)Pounds (lb)Cup (c)Pint (pt)Quart (qt)GlassGrains (gr)Minum (m)Fluid Dram (dr orDrams (dr or Ʒ)Ʒ)ApothecaryMetricWhole numbers,Fractions, and RomanNumerals after unit.Ex: gr 15 ½ or dr issWhole numbers anddecimals before unit(always put a 0 in frontof the decimal.Ex: 0.15 mLLiquidsGrams (g)Meter (m)Liters (L)Note: When two system-to-system conversion factors exist, consider the unit of the finalanswer. For example, if it is necessary in the drug dosage problem to convert a dosagefrom grains to mg, use the gr 1 60 mg conversion factor.Approximate Conversion FactorsSolid conversionsgr 1 60 mggr 15 1 g2.54 cm 1 in2.2 lb 1 kgFluid conversions1 oz dr 8 or Ʒ 8m 15 1 mL 1 cc4 mL fluid dr 1 Ʒ 115 mL 3 t 1 T30 mL 1 ozExtended conversions1 kg 1000 g 2.2 lbs1 L 1000 mL 33 1/3 oz 200 t 66 2/3 T Ʒ 250Provided by the Academic Center for Excellence2How to Solve Drug Dosage ProblemsReviewed August 2012

Visual Conversions“The Grain Clock”Convert grains to mggr 1 60 mg1 hour 60 mingr ¼ 15 mg¼ hour 15 mingr ¾ 45 mg¾ hour 45 mingr ½ 30 mg½ hour 30 minInches to centimetersUSAWorld1 inch 2.54 cmRoman Numerals½ ss or ss1 I or i or i2 II or ii or ii3 III or iii or iii4 IV or iv (i before v 5-1) or ivProvided by the Academic Center for Excellence5 v or v10 x or x15 xv or xv19 xix [10 (10-1)] or xix20 xx or xx3How to Solve Drug Dosage ProblemsReviewed August 2012

Converting Between UnitsUse of One Conversion Factor:To convert from one unit to another, begin with the unit assigned. Next find a conversionfactor that relates the unit assigned to the unit needed. Then multiply the unit assigned by thefound conversion factor. This calculation results in the new unit.Example: Convert 120 mg to gr .Step one: Think of a conversion factor that relates mg and gr. 60 mg gr 1 (Thiscan be used as either 60 mg/gr 1 or gr 1/60 mg)Step two: set up the multiplication equation.Note: when using the conversionfactor, always place the needed unit on top.120 mg gr 1 gr60 mgStep three: Solve the equation.First cancel mg units,120 mg gr 1 gr60 mg120 gr 1 60 gr 2Then solve the equationTherefore: 120 mg gr 2Use of Multiple Conversion Factors:If a conversion factor for the two units does not exist, then proceed through another unitto obtain the unit needed.Example: Convert 1 T to oz.Step one: Try to find a conversion factor that relates tablespoons to ounces. Lookingat the list, there is not a conversion factor relating tablespoons and ounces.Therefore, two conversion factors are needed: 1 T 15 mL and 30 mL 1 oz.Step two: Set up the equations1 T 15 mL mL1TStep three: Solve the equations.1 T 15 mL 1 T 15 mLmL 1 oz oz30 mL15 mL 1 oz 30 mL 0.5 ozTherefore: 1 T 0.5 ozProvided by the Academic Center for Excellence4How to Solve Drug Dosage ProblemsReviewed August 2012

Converting Between Metric UnitsTo convert between metric units, simply move the decimal place. The easiest way toremember which way to move the decimal as well as the number of places to slide it is themnemonic: “King Henry died by drinking chocolate milk . . merrily.”KingHenrydiedbydrinking chocolate milksymbol khDbdcm†namekilohectorDeca“base” decicentimilliEx.kghgDggramdgcgmg† there are three decimal places between m and mc. This is commonly forgotten!merrilymcmicromcgUsing the “King Henry” method to convert between metric units involves locating thestarting place then sliding the decimal to the desired unit and adding zeros as needed.Example 1: Convert 25.3 g to mgStep one: The given unit is gram, so start at “b”.Step two: The ending place is m, so slide the decimal from “b” to “m”.Step three: King Henry died by drinking chocolate milk . . merrilyk h D b d c m . . mc25.3 25. 3 0 0. 25,300 mgSlide 3 decimal places to the rightTherefore: 25.3 g 25,300 mgExample 2: Convert 300 mcg to mgStep one: The given unit is mc, so start at “mc”.Step two: The ending place is m, so slide the decimal from “mc” to “m”.Step three: King Henry died by drinking chocolate milk . . merrilyk h D b d c m . . mc300 3 0 0. 0.300 mgslide decimal 3 places to left (mc to m)Therefore: 300 mcg 0.300 mgProvided by the Academic Center for Excellence5How to Solve Drug Dosage ProblemsReviewed August 2012

Calculating Drug DosagesWhen performing drug calculations, one of the following four methods should be used:Ratio (Rainbow) Method, Proportion Method, Formula Method, or DimensionalAnalysis. Each of these methods works as well as the others. However, once the studentdecides which method is the most comfortable for them, they should stick with that methodand not switch back and forth between the different methods.Ratio (Rainbow):Step one: Set up ratios.Step two: Multiply means and extremesStep three: Solve for “x” algebraically.Proportion:Step one: Set up proportionsStep two: Cross multiplyStep three: Solve for “x” algebraicallyFormula:D Q answerD (dose ordered) Q (unit quantity) answerHH (on hand)Dimensional Analysis:D Q answerD (dose ordered) Q (unit quantity) answerHH (on hand)Use drug calculations when calculating the quantity of medications needed for a patient andthe strength of medication is already known.Example: If the doctor orders 20 mg of Benadryl, and 10 mg tablets are available, howmany tablets should be given to the patient?Ratio (Rainbow) MethodWe know that 10 mg 1 tablet, and we need 20 mg in an unknown numberof tablets.Step one: Set up ratios.10 mg : 1 tab 20 mg : x tabNotice that on both sides of the equation, mg comes first, then tablets. Thisis very important. It does not matter which unit comes first, as long as unitsare in the same order on both sides of the equal “ ” sign.Step two: Multiply means and extremes10 mg x tab 1 tab 20 mgStep three: Solve for “x” algebraically.x tab 1 tab 20 mgx 2 tablets10 mgProvided by the Academic Center for Excellence6How to Solve Drug Dosage ProblemsReviewed August 2012

Proportion MethodStep one: Set up proportions10 mg 20 mg1 tabx tabStep two: Cross multiply10 mg x tab 20 mg 1 tabStep three: Solve for “x” algebraicallyx tab 20 mg 1 tabx 2 tablets10 mgFormula MethodD Q So: 20 mg 1 tab 2 tabletsH10 mgTherefore: give the patient 2 tablets.Dimensional AnalysisD Q HSo: 20 mg 1 tab 2 tablets10 mgUseful Formulas for Calculating Drug Calculation ProblemsCalculating BSA (m²):Lb x in3131orkg x cm3600 Round to hundredths placeafter taking the square rootExample: If a patient weighs 140 lb and is 62 inches tall, calculate the BSA bysimply plugging the numbers into the formula and solving.140 lb x 62 in3,131140 x 62 8,6808,680 3131 2.77Provided by the Academic Center for Excellence7 2.77 1.66 m² Round to hundredths place Answer is always in m2How to Solve Drug Dosage ProblemsReviewed August 2012

Calculating a child’s dosage using an adult dosage:Child’s BSA1.7 m²x adult dosage child’s dosageExample: The normal adult dosage of a medication is 150 mg. The child weighs 32kg and is 120 cm tall. How much medication should be given to the child?Step one: Find the child’s BSA. To do so, use the formula given above.32 kg x 120 cm 1.0666 1.0666 1.032792 m2 1.03 m23,600 Round to hundredths placeStep two: Use the child’s dosage formula.1.03 m² x 150 mg 90.88 mg1.7 m² Round to hundredths placeCalculating Flow Rate in mL/h:Total mL ordered mL/h (must round to a whole number)Total hours orderedExample: Calculate the flow rate for an IV of 1,820 mL Normal Saline IV to infusein 15 h by controller. Flow rate mL/h1,820 mL 121.33 mL/h 121 mL/h15 h Round to nearest whole numberCalculating Flow Rate in gtt/min:Volume (mL) x drop factor (gtt/mL) Rate (gtt/min)Time (min)(MUST be whole #)Example: The physician orders Lactated Ringer’s IV at 150 mL/h. The drop factoris 15 gtt/mL. Find the flow rate in gtt/min.150 mL x 15 gtt 37.5 38 gtt/min60 min1 mLProvided by the Academic Center for Excellence8How to Solve Drug Dosage ProblemsReviewed August 2012

Calculating Heparin Dosages:Order: D5W Heparin 40,000 U in 1,000 mL D5W to infuse at 40 mL/h. What is thehourly heparin dosage?Find how many Units are in 40 mL.40,000 U x U1,000 mL 40 mLCross multiplyx U 1,000 mL 40,000 U 40 mL40,000 U 40 mL 1,000 mL1,600,000 U1000then divide by 1,000 mL 1600 U/hrConverting from ºF to ºC or ºC to ºF:ºF 1.8 (ºC) 32 Carry to hundredths and round to tenthsºC ºF – 321.8Example: What is 212 ºF in Celsius?ºC ºF – 321.8ºC 212 – 321.8ºC 1801.8ºC 100ººF 66.6 32ºF 98.6ºExample: What is 37 ºC in Fahrenheit?ºF 1.8 (ºC) 32ºF 1.8 (37) 32Helpful WebsitesThere are many helpful drug dosage calculation websites. The following links includepractice problems and solutions. We encourage you to use them to your advantage. After all,the best way to become proficient at solving drug dosage problems is to l.htmhttp://www.testandcalc.com/drugcalc legacy/index.asphttp://www.unc.edu/ u/students/studyaids/drugcalculations/page.php?id 1Provided by the Academic Center for Excellence9How to Solve Drug Dosage ProblemsReviewed August 2012

Useful Formulas for Calculating Drug Calculation Problems Calculating BSA (m²): Lb x in or kg x cm Round to hundredths place 3131 3600 after taking the square root Example: If a patient weighs 140 lb and is 62 inches tall, calculate the BSA by simply plugging the numbers into the formula and solving.