2- Drug Calculations (1 Hour)

Considerations for Determining Considerations for Determining Correct Drug DosagesCorrect Drug Dosages

SexSex WeightWeight AgeAge Physical conditionPhysical condition Other drugs that the patient is Other drugs that the patient is

takingtaking

Persons Responsible for Persons Responsible for Accurate Dosage CalculationsAccurate Dosage Calculations

The The pharmacistpharmacist who who dispenses the drugdispenses the drug

The The prescriberprescriber who orders who orders the drugthe drug

The The nursenurse who administers who administers the drug the drug

Types of Systems Used in Drug Types of Systems Used in Drug MeasurementMeasurement

Metric systemMetric system Apothecary systemApothecary system Household systemHousehold system Avoirdupois systemAvoirdupois system

Metric SystemMetric System

Most widely used system of measure.Most widely used system of measure. Based on the decimal system, Based on the decimal system, All units are determined as multiples All units are determined as multiples

of 10. of 10. Used worldwide & makes the sharing Used worldwide & makes the sharing

ofof


Basic units of measureBasic units of measure

For solid = gramFor solid = gramFor liquid = literFor liquid = liter


Solid measure: Solid measure: Gram (g) Gram (g) 1 milligram (mg) = 0.001 g 1 microgram (mcg) = 0.000001 g 1 kilogram (kg) = 1000 g

Liquid measure: Liquid measure: Liter (L)Liter (L) 1 milliliter (mL) = 0.001 L 1 mL = 1 cubic centimeter = 1 cc

Apothecary SystemApothecary System Is a very old system of measure that was Is a very old system of measure that was

specifically developed for use by specifically developed for use by apothecaries or pharmacist. apothecaries or pharmacist.

Uses the Uses the minimminim as the basic unit of liquid as the basic unit of liquid measure, and the measure, and the graingrain as the basic unit as the basic unit of solid measure. of solid measure.

Uses Roman numerals placed after the Uses Roman numerals placed after the unit of measure to denote amount, for unit of measure to denote amount, for example 15 grains would be written “gr example 15 grains would be written “gr xv” xv”

Apothecary SystemApothecary System

Solid measure: Solid measure: Grain (gr)Grain (gr) 60 gr = 1 dram (dr) 8 dr = 1 ounce (oz)

Liquid measure: Liquid measure: Minim Minim (min)(min) 60 minim = 1 fluidram (f dr) 8 f dr = 1 fluidounce (f oz)

Household SystemHousehold System

Pts need to be advised that flatware Pts need to be advised that flatware teaspoons & drinking cups vary teaspoons & drinking cups vary tremendously in the volume that they tremendously in the volume that they contain. contain.

Important to clarify that the measures Important to clarify that the measures indicated in the instructions of liquid indicated in the instructions of liquid medication refer to a standardized medication refer to a standardized measuring device. measuring device.

Household SystemHousehold System

Solid measure: Solid measure: Pound (lb)Pound (lb) 1 lb = 16 ounces (oz)

Liquid measure: Liquid measure: Pint (pt)Pint (pt) 2 pt = 1 quart (qt) 4 qt = 1 gallon (gal) 16 oz = 1 pt = 2 cups (c) 32 tablespoons (tbsp) = 1 pt 3 teaspoons (tsp) = 1 tbsp 60 drops (gtt) = 1 tsp

Household System Household System

Measuring system found in Measuring system found in recipe books.recipe books.

Uses the Uses the teaspoonteaspoon as the basic as the basic

unit of fluid measure and the unit of fluid measure and the poundpound as the basic unit of solid as the basic unit of solid measure. measure.

Avoirdupois SystemAvoirdupois System

Uses Uses ouncesounces & & grainsgrains but they measure but they measure differently than those of the apothecary & differently than those of the apothecary & household systems. household systems.

Seldom used by prescriber but may be Seldom used by prescriber but may be used for bulk medications that come used for bulk medications that come directly from the manufacturer. directly from the manufacturer.

Other Systems Other Systems

Some drugs are measured in units Some drugs are measured in units reflecting the chemical activity or reflecting the chemical activity or biological equivalence. biological equivalence.

One of these measures is the One of these measures is the unitunit (U). (U). A A unitunit usually reflects the biological usually reflects the biological

activity of the drug in 1 mL of solution. activity of the drug in 1 mL of solution. The unit is unique for the drug it The unit is unique for the drug it

measures; a unit of heparin would not measures; a unit of heparin would not be comparable to a unit of insulin. be comparable to a unit of insulin.

MilliequivalentsMilliequivalents ( (mEq)mEq) are used to are used to measure electrolytes (example K, Na,). measure electrolytes (example K, Na,). Milliequivalent refers to the ionic activity of the Milliequivalent refers to the ionic activity of the

drug in question; the order is usually written drug in question; the order is usually written for a number of milliequivalents instead of a for a number of milliequivalents instead of a volume of drug.volume of drug.

InternationalInternational unitsunits (IU(IU) are sometimes ) are sometimes

used to measures certain vitamins or used to measures certain vitamins or enzymes. These are also unique to each enzymes. These are also unique to each drug & can’t be converted to another drug & can’t be converted to another measuring form.measuring form.

Conversion among Metric, Conversion among Metric, Apothecary & Household SystemApothecary & Household System

Metric system Apothecary System

Household System

Solid measure

1 kg 2.2 lb

454 g 1.0 lb

1 g= 1000 mg 15 gr (gr xv)

60 mg 1 gr (gr i)

30 mg ½ gr (gr ss)

Liquid measure

1 L – 1000 mL About 1 qt

Conversion among Metric, Conversion among Metric, Apothecary & Household SystemApothecary & Household System

Metric system Apothecary System

Household System

240 ml 8 f oz ( 8 oz viii) 1 c

30 ml 1 f oz ( f oz i) 2 tbsp

15-16 ml 4 f dr ( f dr iv) 1 tbps= 3 tsp

8 mL 2 f dr ( f dr ii) 2 tsp

4-5 mL 1 f dr ( f dr i) 1 tsp= 60 gtts

1 mL 15-16 min ( min xv or min xvi)

0.06 mL 1 min (min i)

Methods of CalculationsMethods of CalculationsFormula method:Formula method: D/H x Q = D/H x Q = XX D - dosage desired or orderedD - dosage desired or ordered

H - what is on hand (available)H - what is on hand (available)Q - unit of measure that contains the Q - unit of measure that contains the available dose. available dose.

When using solid products (tablets, capsules) When using solid products (tablets, capsules) Q is always 1 and can be eliminated. Q varies Q is always 1 and can be eliminated. Q varies when using liquid measures.when using liquid measures.XX - the unknown dosage you need to - the unknown dosage you need to administeradminister

ExampleExample

Order: Potassium Chloride 20 mEq Order: Potassium Chloride 20 mEq added to the IV.added to the IV.

Available: 40 mEq per 10cc.Available: 40 mEq per 10cc.

How much potassium will you add?How much potassium will you add?

D = 20 mEq H = 40 mEq Q = 10 D = 20 mEq H = 40 mEq Q = 10 cccc

20 mEq 20 mEq X 10 cc = X 10 cc = XX

40 mEq40 mEq

0.5 X 10 = 0.5 X 10 = XX = 5 cc = 5 cc

Methods of CalculationsMethods of Calculations

Ratio-proportionsRatio-proportions Ratios indicate a relationship Ratios indicate a relationship

between two numbers with a colon between two numbers with a colon between the numbers. The colon between the numbers. The colon represents division. For example 3:4 = represents division. For example 3:4 = 3/4. 3/4.

Proportions are equations containing Proportions are equations containing ratios of equal value. ratios of equal value. For example 3:4 = 6:8. This may also For example 3:4 = 6:8. This may also be written as fractions, 3/4=6/8. be written as fractions, 3/4=6/8.

Ratio-proportionsRatio-proportions Means are the two inner numbers, in this case 4 & Means are the two inner numbers, in this case 4 &

6.6.Extremes are the two outer numbers, 3 and 8.Extremes are the two outer numbers, 3 and 8.

3 : 4 = 6 : 83 : 4 = 6 : 8 The product of the means (4 X 6) must equal the The product of the means (4 X 6) must equal the

product of the extremes (3 X 8). product of the extremes (3 X 8). Therefore when you do not know one value (Therefore when you do not know one value (xx), you ), you

can determine it, if the other three values are can determine it, if the other three values are known.. When setting up a ratio, the known factor known.. When setting up a ratio, the known factor (on hand) is stated first, the desired is stated (on hand) is stated first, the desired is stated second. H = Dsecond. H = D x x

3 : 4 = 3 : 4 = xx : 8 multiply the means and : 8 multiply the means and 44xx = 3 X 8 the extremes = 3 X 8 the extremes44xx = 24 = 24 xx= 24 ¸ 4 = 6= 24 ¸ 4 = 6

Fractional FormulaFractional Formula

3 3 = = xx

4 8 4 8 44xx = 3 X 8 = 24 = 3 X 8 = 24 x x = 24 ÷ 4 = = 24 ÷ 4 = 66

cross multiply to obtain the product cross multiply to obtain the product of the means and extremes of the means and extremes

ExampleExample

Ordered: 600,000 units of penicillin po q6hOrdered: 600,000 units of penicillin po q6h Available: 400,000 units per scored tablet Available: 400,000 units per scored tablet How many tablets will you administer? How many tablets will you administer?

400,000 units : 1 tablet = 600,000 units : 400,000 units : 1 tablet = 600,000 units : x x 600,000 = 400,000600,000 = 400,000xx (multiply means (multiply means 600,000600,000 = = xx = 1.5 tablets & extremes) = 1.5 tablets & extremes)400,000 400,000

OR set it up as a fractionOR set it up as a fraction 400,000400,000 = = 600,000600,000

1 1 xx 400,000400,000xx = 600,000 = 600,000 xx = = 600,000600,000 = 1.5 tablets = 1.5 tablets

400,000 400,000

Ratio for Converting Drug Ratio for Converting Drug Dosages (Tablets)Dosages (Tablets)

amount of drug availableamount of drug available = = amount of drug amount of drug prescribedprescribed

one tablet or capsule # of tablets or capsules to one tablet or capsule # of tablets or capsules to givegive

Ratio for Converting Drug Ratio for Converting Drug Dosages (Liquids)Dosages (Liquids)

amount of drug availableamount of drug available = = amount of drug amount of drug prescribedprescribed

volume available volume to administervolume available volume to administer

Ratio to Determine Amount of Drops Ratio to Determine Amount of Drops of Fluid to Administer per Minuteof Fluid to Administer per Minute

drops/minute = mL of solution drops/minute = mL of solution prescribed per hour prescribed per hour x drops delivered x drops delivered per mLper mL 60 60 minutes/hourminutes/hour

Formula for calculating IV flow rateFormula for calculating IV flow rate

V1V1 X X V2V2 = gtt/min V1 - volume to infuse = gtt/min V1 - volume to infuseT1 T2 T1 - time to infuse (hours T1 T2 T1 - time to infuse (hours or or minutes) minutes) V2 - drop factor V2 - drop factor T2 - time in minutes - this T2 - time in minutes - this

number is always number is always 60 (minutes/hour) 60 (minutes/hour)

unless you are unless you are going to infuse for going to infuse for lessless

than 60 minutes than 60 minutes

Medical prescription: 250 ml 5% D/W to infusion over 10 hours. Drip factor is 60.

Total fluid = 250 mL(cc)Drip factor = 60 gtts/minInfusion time in minutes = 600 min

Fried’s Rule for a Child Younger Fried’s Rule for a Child Younger Than 1 YearThan 1 Year

This rule assumes that an adult dose This rule assumes that an adult dose would be appropriate for a child who is would be appropriate for a child who is 12.5 years (150 months) old12.5 years (150 months) old

child’s dose (age <1 year) = child’s dose (age <1 year) = infant’s age (in infant’s age (in months)months)

150 months x average adult 150 months x average adult dosedose

Young’s Rule for Children 1 – 12 Young’s Rule for Children 1 – 12 Years OldYears Old

child’s dose (age 1–12 years) = child’s dose (age 1–12 years) =

child’s age in yearschild’s age in years child’s age in years + 12 x average adult child’s age in years + 12 x average adult

dosedose

Clark’s RuleClark’s Rule

Uses the child’s weight to calculate Uses the child’s weight to calculate the appropriate dose and assumes the appropriate dose and assumes that the adult dose is based on a 150-that the adult dose is based on a 150-lb personlb person

child’s dose = child’s dose = weight of child in poundsweight of child in pounds

150 pounds x average adult 150 pounds x average adult dosedose

Using Child’s Surface Area to Using Child’s Surface Area to Determine DosageDetermine Dosage

Determine the child’s surface area Determine the child’s surface area with the use of a nomogram (the with the use of a nomogram (the height and weight of the child are height and weight of the child are taken into consideration in this chart) taken into consideration in this chart)

child’s dose = child’s dose = surface area in square surface area in square metersmeters

1.73 x average adult dose1.73 x average adult dose

Sample NomogramSample Nomogram

Basic Drug Calculation Practice Basic Drug Calculation Practice ProblemsProblems

1. Ordered: Trilafon 24 mg po bid.1. Ordered: Trilafon 24 mg po bid.Available: Trilafon concentrate Available: Trilafon concentrate labeled 16 mg/5 ml.labeled 16 mg/5 ml.How many ml will you administer? How many ml will you administer?

AnswerAnswer

Ratio-proportions: Ratio-proportions: 24 mg : 24 mg : xx = 16 mg : 5 ml = 16 mg : 5 ml

16 16 xx = 24 X 5 = 120 = 24 X 5 = 120xx = 120 ¸ 16 = 120 ¸ 16 xx = 7.5 ml = 7.5 ml

Formula method:Formula method: D/H X Q = D/H X Q = XX 2424 X 5 = X 5 = XX

16161.5 X 5 = 7.5 ml1.5 X 5 = 7.5 ml


2. Ordered: SoluMedrol 100 mg IM 2. Ordered: SoluMedrol 100 mg IM q8hq8hAvailable: Vial 1 ml in size labeled Available: Vial 1 ml in size labeled 125 mg SoluMedrol/3 ml125 mg SoluMedrol/3 ml

How many ml will you administer?How many ml will you administer?What size syringe is best to What size syringe is best to administer this dose? administer this dose?

AnswerAnswer Ratio-proportion method:Ratio-proportion method: 100 mg : x = 125 mg : 3 ml100 mg : x = 125 mg : 3 ml

125 x = 300125 x = 300x = 300 ¸ 125x = 300 ¸ 125x = 2.4 mlx = 2.4 ml

You would need to use a 3 ml syringe. A 5 ml You would need to use a 3 ml syringe. A 5 ml syringe would not give you the decimal point.syringe would not give you the decimal point.

Formula method:Formula method: D/H X Q = D/H X Q = XX 100 ¸ 125 X 3 ml = 100 ¸ 125 X 3 ml = xx

0.8 X 3 =0.8 X 3 = x x2.4 ml = 2.4 ml = xx


3. The physician orders Lasix 20 mg 3. The physician orders Lasix 20 mg IV stat for a child weighing 34 lbs. IV stat for a child weighing 34 lbs.

The pediatric handbook states that 1 The pediatric handbook states that 1 mg/kg is a safe initial dose. Should mg/kg is a safe initial dose. Should you give this dose? you give this dose?

AnswerAnswer

34 lbs. X 1kg/2.2 lbs = 15.5 kg34 lbs. X 1kg/2.2 lbs = 15.5 kg

15.5 kg X 1 mg/kg = 15.5 mg 15.5 kg X 1 mg/kg = 15.5 mg

The does is too high, you need to call The does is too high, you need to call the physician.the physician.


4. Ordered: Infuse 2 L of Lactated 4. Ordered: Infuse 2 L of Lactated Ringers solution in 24 hours. The Ringers solution in 24 hours. The administration set has 12 gtts/ml. administration set has 12 gtts/ml. How many gtts/min will you How many gtts/min will you administer the IV? administer the IV?

AnswerAnswer

2000 ml2000 ml X X 12 gtts/ml12 gtts/ml = = xx 24 hr 60 min/hr 24 hr 60 min/hr

2400024000 = = xx14401440

16.7 gtts/min or 17 gtts/min = 16.7 gtts/min or 17 gtts/min = xx

Definition of Drug InteractionDefinition of Drug Interaction

The pharmacological result, either The pharmacological result, either desirable or undesirable, of drugs desirable or undesirable, of drugs interacting with themselves or with interacting with themselves or with other drugs, with endogenous other drugs, with endogenous chemical agents, with components of chemical agents, with components of the diet, or with chemicals used in or the diet, or with chemicals used in or resulting from diagnostic tests.resulting from diagnostic tests.

2- Drug Calculations (1 Hour)

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