Pharmacy Calculations

University of Kentucky / NetLearning CBL 1 of 39

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Pharmacy Calculations

Authors:

Philip Trapskin, PharmD

Rebecca Reagan, RPh

Kimberley Hite, MS, PharmD

John Armitstead, MS, RPh, FASHP

Service Area: Pharmacy Services

Phone: (859) 257-8414

Email: [email protected]

Date Developed

Or Revised: April, 2005

Curriculum: Pharmacy

Target Audience: Pharmacists and Pharmacy Technicians


Supplies needed for this CBL

• Please have a calculator, pencil and paper available to complete this CBL.


Objectives

Basic Mathematics

Units of Measure

Ratios and Proportions

Intravenous flow (drip) rate calculations

Common Abbreviations

Menu


Objectives

•Review basic mathematics•Review units of measure•Review ratios and proportions•Review concentration and dilution•Review intravenous flow (drip) rate calculations•Provide sample problems and solutions


Basic Mathematics

•Numerals– A numeral is a word or a sign, or a group of

words or signs that expresses a number.• Arabic (0, 1, 2, 3, 4...)• Roman (I, X, L, D, C, M …)

•Numbers– A number is a total quantity or amount that is

made of one or more numerals.


Basic Mathematics cont. (Kinds of Numbers)

•Whole Numbers (10, 220, 5, 19)•Fractions

– Parts of whole numbers (1/4, 2/7, 11/13)

•Decimal Numbers– Another means of writing fractions

(1/2 =0.5, 1&3/4 = 1.75)

Numerator

Denominator


Basic Mathematics cont. (Kinds of Numbers)

•WARNING: Writing decimals incorrectly can lead to medication errors.

– Trailing zeros• Write 5 not 5.0

– Naked decimal points• Write 0.5 not .5

•Periods are sometimes difficult to see leading to a 10 fold error.


Basic Mathematics cont. (Problem Set #1)

•Convert the following fractions to decimal numbers:

a. 1/2 b. 3/4 c. 1 d. 2/5

e. 1/3 f. 5/8 g. 50/100 h. 12/48

i. 11/2 j. 2 2/3 k. 5 1/4 l. 3 4/5


Basic Mathematics cont. (Problem Set #1)

•Answers for problem set #1:

a. 0.5 b. 0.75 c. 1 d. 0.4

e. 0.33 f. 0.625 g. 0.5 h. 0.25

i. 5.5 j. 2.67 k. 5.25 l. 3.8


Basic Mathematics cont. (Percentages)

•Percentage means “by the hundred” or “in a hundred.” Percents (%) are just fractions, but fractions with a set denominator of 100.

– Example: “50%” means “50 in a hundred” or “50/100” or “1/2”.

•Converting percentages to fractions– Write the number preceding the percent sign over 100

and simplify the resulting fraction– Example: 25%=25/100=1/4



• Converting fractions to percentages

1. Write the fraction in decimal form. (3/4=0.75)

2.Write the decimal over one. (0.75/1)

3.Multiply the numerator and denominator by 100. (0.75/1 = 75/100)

4.Because you already know the “divided by a hundred” is the same as percent you can write 75/100 as 75%.



• Concentration expressed as percentage– Percent weight-in-weight (w/w) is the grams of

drug in 100 grams of the product.– Percent weight-in-volume (w/v) is the grams of

drug in 100ml of the product.– Percent volume-in-volume (v/v) is the milliliters of

drug in 100ml of the product.• These will be discussed further later in the CBL.


Units of Measure (Metric System)

• The metric system is based on the decimal system, in which everything is measured in multiples or fractions of 10.

• Standard measures

– Meter; Length

– Gram; Weight

– Liter; Volume

• Prefixes

– kilo-; 1000

– milli-; 1/1000 = 0.001

– micro-; 1/1000000 = 0.000001


Units of Measure cont. (Metric System)

• Volume is the amount of space occupied by a three-dimensional object as measured in cubic units (as milliliters or liters)– L = Liter– ml = milliliter– 1 Liter = 1000 milliliters– 3.5L = 3500ml


Units of Measure cont. (Metric System)

• Mass is a property of physical objects which measures the amount of matter in an object.

kg = kilograms

g = gram

mg = milligram

mcg = microgram

ng = nanogram

1 kilogram = 1000 grams

1 gram = 1000 milligrams

1 milligram = 1000 micrograms

1 microgram = 1000 nanograms

Example 0.004kg = 4g = 4000mg = 4,000,000mcg


Units of Measure cont. (Other Systems)

• Avoirdupois – used in measuring bulk medications (pounds, ounces, grains)

• Apothecary – developed after the Avoirdupois system to enable fine weighing of medications (pounds, ounces, drams, scruples, grains, gallons, pints, fluid ounces, fluid drams, minims)

• Household – commonly used to measure liquids with home utensils (teaspoons, tablespoons, cups, pints, quarts)


Units of Measure cont. (Equivalencies)

• Equivalencies among systems– 1 inch = 2.54 cm– 1 kg = 2.2 pounds (lb)– 1 fluid ounce (fl oz) = 29.57(30) milliliters (ml)– 1 pint (pt) = 473.167 (480) milliliters (ml)– 1 teaspoonful (tsp) = 5 milliliters (ml)– 1 tablespoonful (TBS) = 15 milliliters (ml)– 1 ounce (oz) = 28.35 grams (g)– 1 pound (lb) = 453.59 (454) grams (g)


Units of Measure cont. (Problem set #2)

• Fill in the blanks:

a.1 liter (L) = ________ml

b.1000 g = __________kg

c.1 g = _____________mg

d.1000 mcg =_________mg

e.1 TBS = ____________tsp

f. 1 TBS =_____________ml

g. 2 fl oz =_____________ml

h.70 kg = ______________pounds (lb)


Units of Measure cont. (Problem set #2)

• Fill in the blanks:

a.1 liter (L) = 1000 ml

b.1000 g = 1 kg

c.1 g = 1000 mg

d.1000 mcg = 1 mg

e.1 TBS = 3 tsp

f. 1 TBS = 15 ml

g. 2 fl oz = 60 ml

h.70 kg = 154 pounds (lb)


Ratios and Proportions

• A ratio states a relationship between two quantities.– Example: 5 g of dextrose in 100 ml of water (Dextrose 5% in

Water often abbreviated as D5W)

• A proportion is two equal rations.– Example: 5 g of dextrose in 100 ml of water equals 50 g of

dextrose in 1000 ml of water 5 g 50 g

100ml 1000ml

– If you know three of the four terms you can calculate the fourth. =


Ratios and Proportions cont.

• A vial of drug contains 40mg/2ml. How many milliliters (ml) are required to obtain 300mg of drug?

1. 40mg = 300mg 2. (40mg)(X)= (2ml)(300mg)2ml X

3. X = (2ml)(300mg) 4. X=15ml(40mg)

5. TIP – Make sure your units cancel


Concentration and Dilution

• Terminology– 5% dextrose in water is the same as D5W.– 0.9% sodium chloride (NaCl) is the same as

normal saline (NS).– Half-normal saline is half the strength of

normal saline (0.9% NaCl), or 0.45% NaCl. This may also be referred to as 1/2NS


Concentration and Dilution cont.

• Reminder– Percent weight-in-weight (w/w) is the grams

of drug in 100 grams of the product.– Percent weight-in-volume (w/v) is the grams

of drug in 100ml of the product.– Percent volume-in-volume (v/v) is the

milliliters of drug in 100ml of the product.



• Example 1:– 0.9% sodium chloride (w/v) = 0.9 g of sodium chloride

in 100 ml of solution.• Example 2:

– 5% dextrose in water (w/v) = 5 g of dextrose in 100 ml of solution.

• Example 3:– 23.4% sodium chloride (w/v) = 23.4 g of sodium

chloride in 100 ml of solution.



• Example 4:– How many grams of dextrose are in 1 L of D5W?– Know ratio: D5W means 5g

100ml– Unknown ratio: X

1000ml – Write the proportion and solve for X:

X 5g X = 50 g

1000ml 100ml

=



Solving concentration and dilution problems

1. Calculate the number of grams in 100 ml of solution. That is your “known” ratio.

2. Then calculate the number of grams in the volume requested in the problem by setting up a proportion.

3. Check to make sure your units are in the same order.

4. Make sure that the units that are across from each other are the same.

5. Convert your answer to the requested units.


Concentration and Dilution cont. (Problem Set #3)

1. In 100 ml of D5W/0.45% NaCl solution:

a.How many grams of NaCl are there?

b.How many grams of dextrose are there?

2. How many grams of dextrose are in 1 L of a 10% dextrose solution?

3. How many grams of NaCl are in 1 L of 1/2NS?

4. How many mg of neomycin are in 50 ml of a 1% neomycin solution?

5. How many grams of amino acids are in 250 ml of a 10% amino acid solution?



Solutions

1. a. 0.45g

b. 5g

2. 100g

3. 4.5 g

4. 500 mg

5. 25 g



1. An order calls for 5 million units of aqueous penicillin. How many milliliters are needed if the concentration is 500,000 units/ml?

2. How many milliliters are needed fro 15 million units of penicillin if the concentration is 1 million units per milliliter?

3. Pediatric chloramphenicol comes in a 100mg/ml concentration. How many mg are present in 5 ml of solution?

4. How many milliliters of a 250mg/ml chloramphenicol solution are needed for a 4 g dose?



5. Oxacillin come in a 500mg/1.5ml solution. How many milliliters will be required for a 1.5 g dose?

6. How many grams of ampicillin are in 6 ml of a 500mg/1.5ml solution?

7. How many milliliters contain 3 g of cephalothin if the concentration of the solution is 1g/4.5 ml?

8. How many grams of magnesium sulfate are in 2 ml of a 50% magnesium sulfate solution?

9. How many milliliters of a 50% dextrose solution are needed for a 10 g dextrose dose?

10. How many grams of dextrose are in 50 ml NS solution?



Solutions:

1. 10 ml

2. 15 ml

3. 500 mg

4. 16 ml

5. 4.5 ml

6. 2 g

7. 13.5 ml

8. 1 g

9. 20 ml

10. zero


Intravenous (IV) flow (drip) rate calculations

• Using flow rates you can calculate the volume of fluid or amount of drug a patient will be receiving over a certain period of time.• Calculation of IV flow (drip) rates is necessary to ensure that patients are receiving the amount of medication the physician ordered.• At UKCMC pharmacy technicians perform drip rounds to verify drip rate doses for patient safety, enhance patient care, and minimize drug waste.


Intravenous (IV) flow (drip) rate calculations cont.

• Example:

– An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 1000units/hr, what is the correct rate of the infusion (in ml/hr)?

1. Concentration of IV = 4. IV rate =

2. Concentration of IV = 5. IV rate =

3. Concentration of IV = 100units/ml of heparin 6. IV rate = 10 ml/hr

(1000 units/hr)(100 units/ml)

Dose desiredConcentration of IV

Total amount of drugTotal volume

25,000 units of heparin250ml of D5W



• Practice problem set #5

1. An order is written for 2 g of lidocaine in 250 ml of D5W to infuse at 120mg/hr. What is the correct infusion in (ml/hr)?

2. An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 17ml/hr. How many units of heparin will the patient receive in 12 hours?



• Practice problem set #5 solutions

1. An order is written for 2 g of lidocaine in 250 ml of D5W to infuse at 120mg/hr. What is the correct infusion in (ml/hr)? 15ml/hr

2. An order is written for 25,000 units of heparin in 250 ml of D5W to infuse at 17ml/hr. How many units of heparin will the patient receive in 12 hours? 20,400 units


Common Abbreviations

D5W – 5% dextrose in water

D10W – 10% dextrose in water

NSS or NS – 0.9% sodium chloride (normal saline)

1/2NS – 0.45% sodium chloride (half normal saline)

1/4NS or 0.2NS – 0.225% sodium chloride (quarter normal saline)

LR – Lactated Ringer’s

D5LR – 5% dextrose in Lactated Ringer’s


Common Abbreviations cont.

D5NS – 5% dextrose in 0.9% sodium chloride

CL or Cl – Chloride

Na – Sodium

Mg – Magnesium

K – Potassium

SO4 or SO4 – Sulfate

mEq – milliequivalent

mmol - millimole


Summary

For more information on this topic or to request additional training please contact:

Kimberley Hite, MS, PharmD [email protected]

• Please proceed to the test and complete all the questions.

• The passing score for this module is 25 correct answers.

• Successful completion of this exam is required to demonstrate pharmacy calculations competency.


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Pharmacy Calculations