Medication Math - Southern Region EMS Council

CHAPTER

Medication Math 4 ? Jones & Bartlett Learning, LLC

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OBJECTIVES

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1. Identify the basic units of measure for weight, length, and volume. 2. Accurately convert milliliters to cubic centimeters, kilograms to pounds, and milligrams

? Jones & Bartlett Learning, LLtCo grams (and micrograms?). Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBU3.TAIOppNly the four basic formuNlaOs (TsinFgOleRdoSseA, iLnfEusOionRoDf aISmTeaRsIuBreUd TamIOouNnt of fluid in a

set amount of time, drip infusion not based on weight, and drip infusion based on weight) to solve drug problems and determine dosages.

INTRODUCTION

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? Jones & Bartlett Learning, LLC

NOTMofFetdhOiicsRactihoSanApmtLearEthisOctaoRntabDkeeImSaaTwdRaeyIsBitmhUepTlmeIybOsytNemryasotef rminegdoicnaltyioanfemwatbhNasaOincTdforFrempOulaRlcaesS.iTtAhwLeiEtphuOrcpoRonsfieD- ISTRIBUTION

dence to learn and achieve ease in calculating drug dosages.

Anaphylaxis, as presented in the following case, is a life-threatening condition that is

easily treated. However, without a grasp of the concepts of medication math, you cannot

? Jones & BartleptrtoLpeeralyrnadimngin,isLteLr Cthe medication epinephr?ineJ. oAntheosro&ugBh aknrtolweltetdLgeeaofrnthiengco,nLceLpCts NOT FOR SALE OosifoRpnhsDaorIfmSwaTceRoigloIhBgtyUanaTndIdOvdoNolusmineg oanf dmceadliccualtaiotensvoisNluuOmseeTlsesFosfOwdRirtuhgSouAtot LtbhEee aaObdimRlitinyDitsIotSemrTeaRdkIebBacsUoendTvIoeOrn-N

concentration of the drug. As illustrated in the following case, to administer a simple and

common medication such as epinephrine, you will need to make several calculations. To

do this in a potentially life-threatening emergency requires a complete grasp of medication

? Jones & Bartlett Learning, mLLatCh principles.

? Jones & Bartlett Learning, LLC

Y NOT FOR SALE OR DISTRIBUTIOouNand your partner are disNpaOtchTedFtOo aRreSsidAenLcEe oOn aRcaDllIfSorTaRn aIBlleUrgiTc IrOeacNtion. You arrive and are directed to the kitchen, where you find a 6-year-old girl who is sitting in a chair in

obvious respiratory distress. The child's mother tells you she stepped on a bee while running bare-

foot in the backyard. The mother states that the child does not have any known allergies, but she

?

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has and

stridor and a appears quite

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NOT FOYoRurSasAseLssEmeOntRof tDhiIsSsiTtuRatIioBnUisTthIaOt Nthe child is having an anapNhyOlaTcticFrOeaRctioSnAfroLmEaObeRe DISTRIBUTION

sting. You determine that epinephrine should be administered as quickly as possible, and you do

not think waiting to get IV access before administering the epinephrine is prudent. You decide that

the best course of action is to administer IM epinephrine (1 : 1000). You ask the mother how much

the child weighs, and the mother replies 50 pounds. The pediatric dose for IM epinephrine is

? Jones & Bartlett0L.0e1 amrgn/kign(g1,: 1L0L00C). The concentration of the?epJinoepnherinse &(1 :B10a0r0t)leist1t mLge/amrLn. Hinogw,mLaLnyC NOT FOR SALE ORmilDSlieliIvtSeerrasTloRqfuIeeBpsitnUioepnTshIrOminueNs(t1b:e1a0n0s0w) emreudstbbefeoaredmdeinNteisrOmteriTnedinFgtoOhtoRhwis SmchaAinldLy?mEillOilitRersDtoISadTmRinIiBsteUr. TION

1. What is the weight of the child in kilograms?

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The child weighs 50 pounds. To convert to kilograms, 1 kg equals 2.2 pounds.

50 lb = 50 lb = 22.7 kg

2.2 kg lb 22.7 kg

2.2 kg lb? Jones & Bartlett Learning, LLC

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C H A P T E R 4 MEDICATION MATH

65

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NOT

FOR

SALE

OR

DISTRIBUTIO2.NWhIaMt isdothsee

weight-baseNd dOosTe oFfOepRineSphArinLeE(1O: 1R000D) IIMS?TRIBUTION

of epinephrine (1 : 1000) is 0.01 mg/kg

Dose = 0.01mg ? 22.7 kg = 0.01mg ? 22.7 kg = 0.01mg ? 22.7 = 0.23 mg

kg

1

kg

1

Dose = 0.23 mg

? Jones3. &WhBaat irsttlheetvtoLlumeae ronf eipninge,phLriLneC(1 : 1000) that needs to be a?dmJinoisnteeresd &intrBamaurstcluelatrtlyLearning, LLC

NOT FORbSy tAChoeLnsEcyerinnOtgreaR?tioDn IoSf eTpRineIpBhUrinTeI1OmNg/mL

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Milliliters to administer = desired dose ? volume/quantity

dose on hand

1

Milliliters to administer = 0.23 mg ? 1 mL

? Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTMRillIiBliteUrsTtoIOadNminister

=

1 mg 0.23 mg

1 mg

?

1 m1 L? Jones & Bartlett Learning, LLC 1 NOT FOR SALE OR DISTRIBUTION

Milliliters to administer = 0.23 mL

You administer 0.23 mL epinephrine (1 : 1000) intramuscularly. Shortly after administration, the

child's breathing becomes less labored and she is less anxious. You start a peripheral IV, repeat

? Jones & Bartlett Learning, LLyCoChuarpatesrse8s)s.ment, and prepare ?forJtroannseposrt.&(DBruagrtthleeratptyLfoeraarnnapinhygla,xisLiLs cCovered in detail in

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SYSTEMS OF MEASUREMENT

? JoTnheesfirs&t sBysatermtleotftmLeeaasurrneminegn,t LfoLr Cdrugs was the apotheca?ry Jsoysnteems.&InBthaarttsleystttemL,earning, LLC NOTthFe OwReigShtAoLf EdruOgsRwDasISmTeRasuIBreUd TinIOgrNains. Linear measures iNncOluTdeFdOinRchSesA, yLaErdsO, aRndDISTRIBUTION

miles. Volume (i.e., the measurement of fluids and liquids) was measured in minims. The metric system currently is the preferred system for drug measurement and calcula-

tion. It is logical and well organized, based on a basic unit and its multiples or submultiples of 10. It is similar to the U.S. monetary system: one dollar is the basic unit of measurement,

? Jones & BartlewttritLteenaarsn$in1.g00,.LItLcCan be divided into 10 dim?esJ(ownriettsen&asB$a0.r1t0le),twt hLiecharcnaninbge,fuLrLthCer NOT FOR SALE OdivRidDedISinTtoR1I0BpUeTnnIOiesN(written as $0.01). ThNisOanTaloFgOy Ris hSeAlpLfuEl wOhRen DdeItSeTrmRinIBinUg dTrIuOgN

dosages. Just as the apothecary system has basic units of measure for weight, length, and volume,

so does the metric system, as follows: Weight (solids or mass): gram (g)

? Jones & Bartlett Learning, LLC Length: meter (m) ? Jones & Bartlett Learning, LLC NOT FOR SALE OR DISTRIBUTIONVolume (liquid or fluidN):OlitTerF(LO) R SALE OR DISTRIBUTION

In addition, several prefixes are commonly used in medicine to distinguish multiples or smaller parts of these units. The four commonly used in drug calculation are kilo, centi, milli, and micro. They are defined in Table 4-1 along with calculations and examples of equivalents.

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TABLE 4-1

Common Prefixes Used in Medication Calculation

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Examples o?f JoneRsev&ersBe artlett LeMaurlntipinlego,r LPaLrtC

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EquivalentsNOT FO(ARlsoSTAruLe)E OR DoIfSaTBRasIiBc UUnTitION

kilo centi milli micro

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1000 ? basic unit

1 kg = 1000 g

1000 g = 1 kg

Multiple

1/100 of a basic unit 1 cm = 1/100 m 1/100 m = 1 cm Part

1/1000 of a basic unit 1 mg = 1/1000 g 1/1000 g = 1 mg Part

1/1,000,000 of a

1 mcg =

1/1,000,000 g = Part

basic unit

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66

PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL

? Jones & Bartlett Learning, mLLillCiliters (mL). At times, v?olJumoneseosf &solButaiorntsleatrteLalesoarrnepinorgte,dLiLnCcubic centimeters NOT FOR SALE OR DISTRIBU(cTc)I.OMNilliliters and cubic cenNtiOmeTteFrsOreRfeSr tAoLthEe OsaRmeDvIoSluTmReI.BUTION

CONVERSIONS

The ability to convert one unit of measure to another is vital to ensure that the intended

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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 & BartleCthtaLpteear r2n, ilancgk,oLf LexCperience in the performa?ncJeoonf edrsug&caBlcaurlattlieotntsLanedarcnoninvegrs,ioLnLsCis NOT FOR SALE aOcRomDmISonTcRaIuBseUoTf ImOeNdical error, patient injNurOy, TanFdOleRgalSaActLioEn aOgaRinsDt ItSheTpRrIeBhoUspTiItOal N

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, 1L/L10C00 of a liter. The cubic ?cenJtoimneetesr &is aBlsaoratlmetetasLuereamrennitnogf,vLoLluCme, but it is based NOT FOR SALE OR DISTRIBUonTIthOeNcentimeter, which is eNquOalTtoF1O/1R00SoAf aLmEetOerR. BDecIaSuTseR1IcBcUeqTuIOalsN1 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

? Jownoeulsd &beBa acurtbliectcteLnteimarenteirn. gIf,thLeLbCox were filled with 1 mL?ofJwonatersa&t aBteamrptleeratttuLreearning, LLC NOTofF4O? CR, tSheAwLaEteOr wRouDldISeTxaRctIlBy UfilTl tIhOeNbox. Therefore the voNluOmTe iFsOeqRuaSl tAoLthEe OspRaceDISTRIBUTION

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

? Jones & BartlettdLrueg,anront iitns gvo,luLmLeCor the space that it occupies?. Jones & Bartlett Learning, LLC

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NOT FOR SALE OR DISTRIBUTION

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

? Jones & Bartlett Learning, cLaLllCmedical direction for an o?rdJerofnoer ms o&rpBhianer,tlaentdt mLeedaicranl idnirgec, tLioLnCgives the order for NOT FOR SALE OR DISTRIBU3feTmreILnOt(Ncoorn3ccecn)troaftiomnosr.pInhjiencetasNbullOefamTteo.FrMpOhanRinyeSdcrAoumgLseE,smiOnocRrpohnDicneIeSntiTrnaRctliuoIBdnesUdoT,f c2IOommNge/minLs,e4vmerga/lmdiLf,-

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 concen-

tration of 2 mg/mL, the intended order to give 2 mL would have resulted in 4 mg being

? Joadnmeisnis&terBeda.rItflethtet dLreuag rbnoixnwga,sLsLupCplied with 4 mg/mL, the?orJdoernoefs2 &mLBwaorutlldethtavLeearning, LLC

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NOT FOR SALE OR DISTRIBUTION

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1 cm

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1 cm

1 cc = 1 mL

Fig. 4-1 Volume is equal to the space created. The term cc represents cubic centimeter. A cubic

? Jones & Bartlett Learning, cLeLntCimeter is 1 cm wide, 1 cm lon?g, Janodn1ecsm&higBh.aOrntelemtitlliLliteera(rmnL)inisgth,eLeLquCivalent volume of a NOT FOR SALE OR DISTRIBUcuTbIicOcNentimeter. To avoid confuNsioOn,TthFe OterRm mSilAliliLterEisOprReferDreIdSoTveRr cIBc, UorTcuIObicNcentimeter.

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C H A P T E R 4 MEDICATION MATH

67

? Jones & Bartlett Learning, rLesLuClted in the patient gettin?g 8Jomng eosf m&orBpahirntele, totr Ltweiacrenthinegin,tLenLdCed dose. Although NOT FOR SALE OR DISTRIBUmTosItOdNrug boxes are suppliedNwOithTsFtaOndRardSizAedLEconOcRentDraItSioTnsRoIfBmUeTdiIcOatNions, administer-

ing medications on the basis of volume alone (not concentration) is poor practice and not safe.

KILOGRAMS AND POUNDS

? JoTnheense&xt cBoanrvtelresitotnLceomarmnoinnlgy ,usLeLdCto calculate drug dosages?is kJiolongreasms&(kBg)atrotpleotutnLdsearning, LLC

NOT(lbF)O. NRotSe AthLatEthOesRe uDniItSs TreRfeIrBtoUtThIeOpNatient's weight, not thNe OweTigFhtOoRf thSeAdLruEg.OMRanyDISTRIBUTION

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 & BartlettELxeamaprnlei:nIfga, pLaLtieCnt weighs 154 lb, divide?15J4olbnbeys2.&2 lBb/akgrttloetdtetLeermairnneitnhge ,wLeLigCht

NOT FOR SALE iOn RkilDogIrSamTsR. IBUTION

NOT FOR SALE OR DISTRIBUTION

154 lb = weight in kilograms 2.2 lb/kg

First, cross out "like terms" in the problem; in this case, lb.

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Now work the problem:

?15J4olnbes=&weBigahrttilnetktiloLgeraamrns ing, LLC N2.2OlTb /FkgOR SALE OR DISTRIBUTION

154 = 70 kg 2.2 kg

? JoMnIeLsLI&GRBAaMrtSle,tMt LICeRarOnGinRgA, MLLSC, AND GRAMS ? Jones & Bartlett Learning, LLC NOTThFeOneRxtScAonLvEersOioRn isDfIrSomTRmIiBlligUraTmIOs tNo grams and, in reverseN, OfroTmFgOramRsStoAmLiElligOraRmsD. ISTRIBUTION

This process also includes converting milligrams to micrograms (mcg) and micrograms to

milligrams.

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? Jones & Bartlett Learning, LLC

NOT FOR SALE ORR1egmD. eImSbTerR: mIBilliUmTeaIOnsN1/1000 of a basic unit; inNtOhisTcaFseO, gRramSsA. TLhEe eOquRivalDenItSisT1R00IB0 mUgT=ION

To use an everyday example, when changing a dollar into coins (e.g., dimes or pennies),

? Jones & Bartlett Learning, tLhLe Clarger unit (dollar) is c?hanJgoend einsto&anBaeqrtulievatltenLtesaurmniinngs,mLaLlleCr units (dimes or NOT FOR SALE OR DISTRIBUpdoeTnlIlanOriseNs()e..gT.h, e5redfoolrlear,st)obgyetthteNhenOutoTmtabFleOnr uoRmf dbSiemAr eoLsfEothrOepeRsmnnDailelIesSrpTueRnriIdtB,omlUlauTrlt.IiOplyNthe number of

Example 1:

?

Jones

&

Bartlett

5 dollars ? 10 dimes

Learningd, oLllLarC

=

number

of

dime?s

Jones

&

Bartlett

Learning,

LLC

NOT FOR SALE OR DISTRIBUTION

NOT FOR SALE OR DISTRIBUTION

Cross out like terms; in this case, dollar.

5 dollars ? 10 dimes = number of dimes dollar

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? Jones & Bartlett Learning, LLC 5 ? 10 dimesN=O5T0 dFimOeRs SALE OR DISTRIBUTION

Example 2:

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5 dolla?rs J?o10n0epsen&niBesa=rtnluemttbLereoafrpneinnngie,s LLC NOdoTllaFrOR SALE OR DISTRIBUTION

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68

PHARMACOLOGY FOR THE PREHOSPITAL PROFESSIONAL

? Jones & Bartlett Learning, CLrLosCs out like terms; in this c?asJe,odnoellasrs&. Bartlett Learning, LLC

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5 dollaNrsO?T10F0OpeRnnSieAs L=EnuOmRbeDr oIfSpTeRnnIBiesUTION

dollar

Now work the problem:

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NOT FNOoRte SthAatL, EwhOenRcDonISveTrtRinIgBaUpToIOckNet full of change intoNdOolTlarFbOillRs, SsmAaLllEer OunRitsDISTRIBUTION

(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 & BartlesthtouLledabreniinncgre,asLinLgCor decreasing in magnitu?deJ. ones & Bartlett Learning, LLC

NOT FOR SALE ORToDcIoSnTveRrtIBgUramTIsOtoNmilligrams, multiplyNgOramTsFbOy R10S00A. LREemOemRbDerISthTatReIBveUryT1IOg N

contains 1000 mg; this can be written as 1000 mg/g.

Example:

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5

g ? 1000 mg

? Jgones

&= nBumarbtelreotft

mLiellaigrrnamins g,

LLC

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NOT FOR SALE OR DISTRIBUTION

Cross out like terms; in this case, g.

5 g ? 1000 mg = number of milligrams g

? JoNnowesw&orkBtahretlpertotblLeema: rning, LLC

? Jones & Bartlett Learning, LLC

NOT FOR SALE OR DISTR5IB? U10T0I0OmNg = 5000 milligrams NOT FOR SALE OR DISTRIBUTION

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.

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5 g = 50N00OmTgFOR SALE OR DISTRIBUTION

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, TLoLcConvert milligrams (3 zer?os)Jtonmeicsro&grBamasrt(6leztetrLose),asrinmipnlygm, LovLeCthe decimal point NOT FOR SALE OR DISTRIBUthTreIOe mNore places to the righNt,OfoTr aFtOotRal SofA6LzEeroOs.R 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

? Jo10n0espe&nnBiesarbtalcektttoLedaorllnarisn. gT,heLL10C0 actually means 100 c?enJtso. nTheesre&forBeamrtolveettthLeearning, LLC NOTdeFciOmRal pSoAinLt Eto OthRe lDefItSthTeRsIaBmUe TnuIOmNber of places as there NarOe zTerFoOs iRn tSheAeLqEuivOalRentDISTRIBUTION

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 & BartlemttoLviengaronnisnogt,haLtLyCou will understand the re?st Jofotnhee sch&apBtera.rtlett Learning, LLC

NOT FOR SALE OR DISTRIBUTION Practice Problems

NOT FOR SALE OR DISTRIBUTION

Convert grams to milligrams and milligrams to grams:

1. 1 g = ___________ mg

3. 250 mg = ___________ g

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NOT FOR SALE OR DISTRIBU2.T1IO00N0 mg = __________ g NO4T. 4F0O0 RmgS=A_L__E__O__R__D__ISgTRIBUTION

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