Pharmacy calculations

University of Kentucky / NetLearning CBL 1 of 39
All materials on this template are Copyright © 2004 University of Kentucky Chandler Medical Center Learning Center unless
otherwise noted. All rights reserved. Certain graphic images, text elements and logos are derived from The University of Kentucky
and NetLearning and are used by permission.
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: khite2@email.uky.edu
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 desired
Concentration of IV
Total amount of drug
Total volume
25,000 units of heparin
250ml 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
khite2@email.uky.edu
• 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.

We hope this Computer Based Learning course has been both informative and helpful.
Feel free to review the screens of this course until you are confident about your knowledge of
the material presented.
Click the Take Test button on the left side of the screen when you are ready to complete the
requirements for this course.
Exit
Choose the My Records button to view your transcript.
Select Exit to close the Student Interface.

Pharmacy calculations

More Related Content

What's hot

Similar to Pharmacy calculations

Pharmacy calculations