2- Drug Calculations (1 Hour)-1

Considerations for Determining Considerations for Determining Correct Drug DosagesCorrect Drug Dosages

• SexSex

• WeightWeight

• AgeAge

• Physical conditionPhysical condition

• Other drugs that the patient is takingOther drugs that the patient is taking

Persons Responsible for Persons Responsible for Accurate Dosage CalculationsAccurate Dosage Calculations

• The The pharmacistpharmacist who dispenses who dispenses the drugthe drug

• The The prescriberprescriber who orders the who orders the drugdrug

• The The nursenurse who administers the who administers the drug 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 of All units are determined as multiples of 10. 10.

Used worldwide & makes the sharing Used worldwide & makes the sharing ofof


• Basic units of measureBasic units of measure

• For solid = gramFor solid = gram

• For 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 apothecaries or specifically developed for use by apothecaries or pharmacist. 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 of solid as the basic unit of solid measure. measure.

• Uses Roman numerals placed after the unit of Uses Roman numerals placed after the unit of measure to denote amount, for example 15 measure to denote amount, for example 15 grains would be written “gr xv” grains would be written “gr 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 (min)Minim (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 recipe Measuring system found in recipe books.books.

• Uses the Uses the teaspoonteaspoon as the basic unit as the basic unit

of fluid measure and the of fluid measure and the poundpound as as the basic unit of solid measure. the basic unit of solid 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 used for Seldom used by prescriber but may be used for bulk medications that come directly from the bulk medications that come directly from the manufacturer. manufacturer.

Other Systems Other Systems

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

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

the drug in 1 mL of solution. the drug in 1 mL of solution. – The unit is unique for the drug it measures; a The unit is unique for the drug it measures; a

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

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

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

• InternationalInternational unitsunits (IU(IU) are sometimes used to ) are sometimes used to measures certain vitamins or enzymes. These measures certain vitamins or enzymes. These are also unique to each drug & can’t be are also unique to each drug & can’t be converted to another measuring form.converted to another 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 SystemMetric 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 orderedH - what is on hand (available)H - what is on hand (available)Q - unit of measure that contains the available Q - unit of measure that contains the available dose. dose.

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

ExampleExample

Order: Potassium Chloride 20 mEq added to Order: Potassium Chloride 20 mEq added to the IV.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 ccD = 20 mEq H = 40 mEq Q = 10 cc

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 between Ratios indicate a relationship between two numbers with a colon between the two numbers with a colon between the numbers. The colon represents division. numbers. The colon represents division. For example 3:4 = 3/4. For example 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 be For example 3:4 = 6:8. This may also be written as fractions, 3/4=6/8. written as fractions, 3/4=6/8.

Ratio-proportionsRatio-proportions

• Means are the two inner numbers, in this case 4 & 6.Means are the two inner numbers, in this case 4 & 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 product The product of the means (4 X 6) must equal the product

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

determine it, if the other three values are known.. When determine it, if the other three values are known.. When setting up a ratio, the known factor (on hand) is stated setting up a ratio, the known factor (on hand) is stated first, the desired is stated second. H = Dfirst, the desired is stated second. 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 of the cross multiply to obtain the product of the means and extremes 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 prescribedamount of drug prescribed

one tablet or capsule # of tablets or capsules to giveone tablet or capsule # of tablets or capsules to give

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

amount of drug availableamount of drug available = = amount of drug prescribedamount of drug prescribed

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 prescribed per drops/minute = mL of solution prescribed per hour hour x drops delivered per mLx drops delivered per mL

60 minutes/hour60 minutes/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 or T1 T2 T1 - time to infuse (hours 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 less going to infuse for less

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

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

150 months x average adult dose150 months x average adult dose

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 dosechild’s age in years + 12 x average adult dose

Clark’s RuleClark’s Rule

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

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

150 pounds x average adult dose150 pounds x average adult dose

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

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

child’s dose = child’s dose = surface area in square meterssurface area in square meters

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 labeled 16 Available: Trilafon concentrate labeled 16 mg/5 ml.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 q8h2. Ordered: SoluMedrol 100 mg IM q8hAvailable: Vial 1 ml in size labeled 125 mg Available: Vial 1 ml in size labeled 125 mg SoluMedrol/3 mlSoluMedrol/3 ml

How many ml will you administer?How many ml will you administer?What size syringe is best to administer this What size syringe is best to administer this dose? 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 syringe You would need to use a 3 ml syringe. A 5 ml syringe would not give you the decimal point.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 IV 3. The physician orders Lasix 20 mg IV stat for a child weighing 34 lbs. stat for a child weighing 34 lbs.

The pediatric handbook states that 1 mg/kg The pediatric handbook states that 1 mg/kg is a safe initial dose. Should you give this is a safe initial dose. Should you give this dose? 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 The does is too high, you need to call the physician.physician.


• 4. Ordered: Infuse 2 L of Lactated Ringers 4. Ordered: Infuse 2 L of Lactated Ringers solution in 24 hours. The administration solution in 24 hours. The administration set has 12 gtts/ml. How many gtts/min will set has 12 gtts/ml. How many gtts/min will you administer the IV? you 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 other interacting with themselves or with other drugs, with endogenous chemical agents, drugs, with endogenous chemical agents, with components of the diet, or with with components of the diet, or with chemicals used in or resulting from chemicals used in or resulting from diagnostic tests.diagnostic tests.

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2- Drug Calculations (1 Hour)-1