This document outlines the dimensional analysis method for calculating medication dosages and the policies for dosage calculation exams at GCC Nursing Program. It provides examples of identifying the beginning label, ending label, and conversion factors in dosage problems. It also explains setting up the basic dimensional analysis equation. The document emphasizes accurately calculating dosages is essential for patient safety and outlines the requirements and policies for passing dosage calculation exams throughout the nursing courses.

1. Originated by Kathy Guyett and Kathy Palumbo
Revised by Kathy Palumbo and Eleanor Nixon

2. INTRODUCTION
 The role of the nurse often requires the use of mathematical computation. The
administration of oral and parenteral medication, as well as intravenous fluid
administration, all may require mathematical calculation. Accurate calculation
is necessary to safely administer the correct dosage or rate.
 One approach to calculate dosages is to teach a variety of formulas to fit
different situations. The nurse would need to use the correct formula for the
situation.
 An alternative approach is to use the technique of DIMENSIONAL ANALYSIS
or LABEL FACTOR METHOD. This technique is used in areas of technology
and science, as well as nursing.
 By learning and applying this formula and a few variations, the nurse will be
able to accurately calculate any medication dosage.

3. OBJECTIVES
 After completing this module, the student will be able
to:
 1. Utilize dimensional analysis to accurately calculate
oral and parenteral medication dosages for the adult
and pediatric patient.
 2. Determine safe dosage for pediatric patients.
 3. Accurately reconstitute powdered medications.
 4. Apply dimensional analysis to dosage calculation
problems in various clinical settings.

4. GCC DOSAGE CALCULATION POLICY
 Nursing students must demonstrate mastery in dosage
calculations in order to progress in the program. Each
course has specific expectations and requirements that
must be met in order to progress to the next nursing
course. These requirements are presented in the next
few slides. This information is also found in The
Nursing Program Student handbook.

5. GCC DOSAGE CALCULATION POLICY
 NUR-110
 As a N110 student, the student must pass a dosage calculation exam
in class with a grade of 80% or better in order to meet the
requirements of the course.
 A computer program, DOSECALC, must be completed prior to the
first dosage calculation exam. A student will have three (3) chances
to pass the dosage calculation exam during the course of the
semester. These exams will be scheduled at intervals at the
discretion of the faculty.
 Once a student passes the exam with a grade of 80% or better, the
requirement is met.
 If a student cannot achieve a grade of 80% after three (3) exams, the
student will fail N110 and will not be allowed to continue in the
program.

6. MEDICATION ADMINISTRATION
EXAM POLICY
 NUR-120
 As a N120 student, the student must pass a medication
administration exam in class with a grade of 90% or better in order
to meet the requirements of the course.
 A computer program, DOSECALC/IVCALC, must be completed
prior to the first medication administration exam. A student will
have three (3) chances to pass the medication administration exam
during the course of the semester. These exams will be scheduled
at intervals at the discretion of the faculty.
 Once a student passes the exam with a grade of 90% or better, the
requirement is met.
 If a student cannot achieve a grade of 90% after three (3) exams, the
student will fail N120 and will not be allowed to continue in the
program.

7. MEDICATION ADMINISTRATION
EXAM POLICY
 NUR-131
 As a N131 student, the student must pass a medication administration
exam in class with a grade of 90% or better in order to meet the
requirements of the course.
 A computer program, DOSECALC/IVCALC, should be reviewed
prior to the first medication administration exam. A student will
have three (3) chances to pass the medication administration exam
during the course of the semester. These exams will be scheduled
at intervals at the discretion of the faculty.
 Once a student passes the exam with a grade of 90% or better, the
requirement is met.
 If a student cannot achieve a grade of 90% after three (3) exams, the
student will fail N131 and will not be allowed to continue in the
program.

8. MEDICATION ADMINISTRATION
EXAM POLICY
 NUR-210
 As a N210 student, the student must pass a medication
administration exam in class with a grade of 90% or better in order to
meet the requirements of the course.
 DOSECALC/IVCALC, should be reviewed prior to the first
medication administration exam. A student will have three (3)
chances to pass the medication administration exam during the
course of the semester. These exams will be scheduled at intervals
at the discretion of the faculty.
 Once a student passes the exam with a grade of 90% or better, the
requirement is met.
 If a student cannot achieve a grade of 90% after three (3) exams, the
student will fail N210, and will not be allowed to continue in the
program.

9. MEDICATION ADMINISTRATION
EXAM POLICY
 NUR-220
 As a N220 student, the student must pass a standardized
Medication Administration Exam.
 Students will be provided with a study guide to prepare for
this exam.
 Students will have three (3) chances to pass the exam. These
exams will be scheduled at the discretion of the faculty.
 Once a student passes the exam, the requirement is met.
 If a student cannot achieve the established passing criteria
after three (3) exams, the student will fail N220, and will not
be allowed to continue in the program.

10.  Students will be passing medications as part of the GCC
Clinical experience . Students will be expected to recognize
when calculations are required and to arrive at the correct
answer using dimensional analysis.
 Please see each course syllabi for more information
regarding medication administration.

11. DIRECTIONS
 To fully utilize this module, read through EACH section and follow the
directions as noted. You can always go back at any time to review a section. You
can print out the module but printing it will not give you the answers to the
problems.
 You should have plenty of paper, pens or pencils and a basic calculator (you will
be given a calculator for in class testing; you cannot use your own or a graphing
calculator). Drinks and snacks optional!
 If you go through this module all at once, expect it to take an hour or so.
 110 students ONLY: You must take an online Dosecalc test to achieve a passing
grade of 80% (8 out of 10 questions correct). You can take it as many times as
you want. Once passed, you can take more tests for review. There is a finite pool
of questions available, however, so the more tests you take, the more questions
will be repeated. Please refer to your instructor for more information and how
to access the test.

12. BASIC MATH INFORMATION
 Before you begin this program, you will need to review
some basic math techniques even though you will be
allowed to use a calculator (whew!).
 First of all, remember how to MULTIPLY fractions:
 To multiply fractions, simply multiply numerator (the
top number) times numerator and denominator (the
bottom number) by denominator. For example, 1/2 X
3/4= 3/8 (1 x 3=3, 2 x 4=8).

13. BASIC MATH INFORMATION
 Second, remember how to DIVIDE fractions:
 To divide fractions, you must INVERT the second
fraction and then multiply as described above. For
example, 1/2 divided by 3/4 is 1/2 X 4/3 which is 4/6 or
2/3.

14. BASIC MATH INFORMATION
 Third, remember how to CONVERT fractions to
decimals and vice versa:
 In the fraction 1/2, the “/” means divided by. So ½
means one divided by two which is 0.5
 To convert decimals to fractions, remember what the
place settings mean after the decimal point. The
first one is tenths, second hundredths, the third
thousandths and so on. So 0.5 is five tenths (5/10)
which reduces to ½. In another example, 0.25 is 25
hundredths which is 25/100 which reduces to ¼.

15. ROUNDING INFORMATION
 In order to administer accurate dosages, you must ROUND OFF
to the nearest appropriate unit. You cannot give tenths of a
tablet, for example, so you must round off correctly to give the
proper dose.
 Standard rounding rules call for rounding up if the unit is 0.5 or
more, rounding down if the unit is 0.4 or less.
 When determining dosage administration for tablets, your
answer should calculate to either a whole or half tablet or tablets.
If your answer does not come out evenly to one of these units,
recheck your math, ask another nurse to calculate the dose or
call the pharmacy. You can give a half tablet by breaking along
the scored line on the tablet and /or cutting with a pill cutter.
 Capsules cannot be split. If the answer doesn't come out to a
whole capsule or capsules, see above.

16. MORE ROUNDING INFORMATION
 Liquids, whether given orally or parenterally, are usually rounded to the
nearest TENTH of a ml. To determine this, you must know the
hundredths place to calculate the correct answer and use
standard math rounding rules:
 1.25 ml = 1.3 ml
 1.2 ml =1.2 ml (the hundredths place is zero)
 2.08 ml= 2.1 ml
 On occasion you may need to round to the hundredths place. If so,
calculate to the thousandths place and use standard rounding rules to
round to the hundredths place.
 1.575= 1.58
 3.052= 3. 05
 5.788= 5. 79
 You will be given specific rounding directions on all exams (including
the NCLEX-RN).

17. REVIEW OF SYSTEMS OF
MEASUREMENT : METRIC
 Traditionally, there are three systems of measurement used
in medication administration: the household system, the
apothecary system, and the metric system.
 The metric system is used in prescribing and administering
medications and is currently the preferred system.
 The metric system was developed in the late 1700's and is
based on the decimal system. Base units such as grams for
weight and liters for volume are modified using prefixes to
denote smaller or larger quantities.

18. REVIEW OF SYSTEMS: HOUSEHOLD
 The household system is the oldest of the three systems. It
was developed from man's earliest attempts to measure
mass, distance, and volume. Some common household
measurements are cups, pounds, and teaspoons.

19. REVIEW OF SYSTEMS:
APOTHECARY
 The apothecary system was derived from the
measurements used by the first pharmacists or
"apothecaries". A quantity of an herb or other
medicine was balanced with a "grain" of wheat and
labeled a grain. Other measurements in this system
are drams and minims.
 NOTE: The Joint Commission (JACHO)
recommends that this system be abandoned as it
is unfamiliar to many practitioners and can be
confused with metric units.

20. JCAHO OFFICIAL DO NOT USE LIST
 Read the next two pages which list “do not use”
abbreviations by the Joint Commission for Hospital
Accreditation. You will be expected to know the
information in this list.

21. DO NOT USE LIST

22. DO NOT USE LIST

23. HOUSEHOLD ABBREVIATIONS
 Drop= gtt
 Ounce=oz
 Teaspoon=tsp or t
 Tablespoon=Tbsp or T
 Pound=lb
 Foot=ft

24. METRIC ABBREVIATIONS
 Since medical providers order medication in metric units,
it is essential that you understand the metric system and
conversion between the units.
 Gram=gm, g Prefixes
 Liter-L kilo=K
 Meter=M centi=c
milli=m
micro=mc

25. METRIC ABBREVIATIONS
 You can expect to see:
 Kg which stands for kilogram
 mg which stands for milligram
 cm which stands for centimeter
 mm which stand for millimeter
 mL which stands for milliliter (preferred abbreviation)
 mcg which stands for microgram

26. CONVERSIONS
The form in which a medication is prescribed is not
always the form in which it is available. For example,
the physician may order Keflex 1 Gram tablets and the
pharmacy may provide Keflex 500 mg tablets. Thus a
conversion between gm and mg is necessary to give
the correct amount of the medication.

27. LIST OF CONVERSIONS
You MUST know the following in order to calculate
different dosage problems on class exams, in lab and in
clinical. MEMORIZE THEM!
1000 mg (milligram)=1 g or 1 gm (gram)
1000 mcg (microgram)=1 mg
Conversions between the systems include:
30 mL=1 oz
1 Kg=2.2 lb
5 mL=1 tsp

28. COMPONENTS OF DIMENSIONAL
ANALYSIS
 Dimensional analysis has 3 components:
 The first component is the beginning label. The beginning
label is the first unit in the equation. This is usually
contained in the doctor's order.
 The second component is the ending label or answer label.
The ending/answer label is the unit to be administered,
such as tablets or milliliters.
 The final component, the conversion factor, is a sequence
of equivalents which can be cancelled, leaving only the
ending label. This is not always required depending upon
the beginning and ending labels.

29. BASIC EQUATION
 The equation can be written like this:
beginning label x conversion factor (s) = answer/ending label
(BL) x (CFs) = ( AL or EL)

30. APPLICATION OF DIMENSIONAL
ANALYSIS
 There are three steps in applying dimensional analysis to
dosage calculation problems.
 The first step is to identify the components of the
problem. The first component to identify is the beginning
label (BL)which is usually the doctor’s order. Then identify
the answer /ending label (EL) and any conversion factors
(CF).
 The second step is to put the components in an equation.
 The third step is to solve the problem.
 In the next pages, we will go through this process step by
step.

31. APPLICATION OF DA
 First, let's identify the components of a problem - the
beginning label, the answer/ending label and any
conversion factors.
 At this point, you do not have to set up the problem.
You will need scrap paper and pencil.
 EXAMPLE #1: How many milliliters are there in 8
ounces (oz)? What is the beginning label (BL), the
ending label (EL), and the conversion factor (CF)?
 Write the answers on your scrap paper.
 Click here for answer #1

32. APPLICATION: EXAMPLE 2
 EXAMPLE #2: How many micrograms are there in 2
milligrams? What is the beginning label (BL), the
ending label (EL), and the conversion factor CF)?
 Write the answers on your scrap paper. Click here for
answer to example 2

33. APPLICATION: EXAMPLE 3
 Now let's try a dosage calculation problem. Once
again, identify the BL, EL, and CF.
 EXAMPLE #3: How many 1000 milligram (mg) tablets
should be given if the physician orders 500 milligrams
(mg)? What is the beginning label (BL), the ending
label (EL), and the conversion factor (CF)?
 Write the answer on your scrap paper. Click here for
answer to example 3

34. SETTING UP THE EQUATION
 Now that you are able to identify the components of a
problem, you will practice setting up the components
into an equation format. You do not have to solve for
the equation at this point. That will be done in the
next section.

35. SETTING UP THE EQUATION:
EQUATION 1
 Equation #1: How many milliliters (mL) are there in 8
ounces (oz)? See if you can set up the equation (Note:
you will solve the equation in the next section).
 Remember:
 BL: 8 oz
 EL: mL
 CF: 30 mL = 1 oz
 Click here for answer to answer to equation 1

36. SETTING UP THE EQUATION:
EQUATION 2
 Equation #2: How many micrograms (mcg) are there
in 2 milligrams (mg)? See if you can set up the
equation (Note: you will solve the equation in the next
section).
 Remember:
 BL: 2 mg
 EL: mcg
 CF: 1000 mcg = 1 mg
 Click here for answer to equation 2

37. SETTING UP THE EQUATION:
EQUATION 3
 Equation #3: How many 1000 milligram (mg) tablets
(tab) should be given if the physician orders 500
milligrams (mg)? See if you can set up the equation.
 Remember:
 BL: 500 mg
 EL: tab
 CF: 1000 mg = 1 tab
 Click here for the answer to equation #3

38. SOLVING FOR THE EQUATIONS
 The final step in solving a dosage calculation problem is to
calculate the answer. You should cancel the labels, multiply
the numerator (top) and then denominator (bottom) of the
fractions and divide the denominator into the numerator
for the answer. Before you do any math, MAKE SURE that
when you cancel your labels, ONLY the answer /ending
label remains. If there is another label remaining that can't
be canceled, then you have not set up the problem
correctly.
 Take the equations used in step two and calculate the
answers.
 Click here for the answers to all of the problems: answers

39. MEDICATION DOSAGE PROBLEMS
 Now that you have gone through the process step by step, you
should be able to calculate actual dosage problems. In this
section, a physician's order will appear along with a picture of
the medication and box/bottle. These problems will be much
like the problems you will see during medication administration.
 Follow the directions given. You will have a chance to review the
problems and you will be given some "clues" to help with the
setup.
 You will need the list of equivalents, calculator, paper and pencil
before continuing with this section.
 If there are some abbreviations that are unfamiliar to you,
look in your textbook or medical dictionary. You will
benefit by knowing that “po” stands for “by mouth” or
“orally”.

40. MED PROBLEMS: SAMPLE 1
 Doctor's Order: Cleocin 150 mg po q6h.
 Problem: How many milliliters will you administer?
 CLUES:
 First, copy down the information you will need from the doctor's order
(the beginning label).
 Next, look at the problem for the ending label.
 Check the box for the conversion factor. ( is the unit in which the
medication is ordered-mg- the same in which it will be administered-
ml ?)
 Set up the equation, cancel labels and solve.
 Round to the nearest tenth of a mL
 Click here for answer sample #1

41. MED PROBLEMS:SAMPLE 2
 Doctor's Order: Ibuprofen 600 mg po q4h as needed for pain.
 Problem: How many tablets should you administer?
 CLUES:
 First check the box for the generic name of the drug.
 Copy down the information you will need from the doctor's order (the
beginning label).
 Next, look at the problem for the ending label.
 Check the box for the conversion factor.
 Set up the equation, cancel labels and solve.
 Click here for answer sample #2

42. MED PROBLEMS: SAMPLE 3
 Dolobid 0.5 Gm po q6h as needed for discomfort.
 Problem: How many tablets should you administer?
 CLUES:
 First, copy down the information you will need from the
 doctor's order (the beginning label).
 Next, look at the problem for the ending label.
 Check the box for the conversion factor. (box reads 500 mg)
 When you set up the equation, you will see that you need a second conversion
factor to cancel the necessary labels. Use your equivalents for this.
 Click here for answer sample #3

43. RECONSTITUTION
 Reconstitution is the addition of a liquid to a
powdered medication to create a form that can be
administered to the patient. While most medications
are provided in liquid form, some may be distributed
as a powder. Since most powders cannot be ingested,
and should not be given intravenously (IV) or
intramuscularly (IM), reconstitution must be done
before administration. The information on the vial will
tell you how much and what kind of liquid to add.
 Dimensional analysis is easily applied to reconstitution
problems.

44. RECONSTITUTION PROBLEM 1
 Problem: The doctor orders cefazolin sodium 1 gram IV. The label
reads: Add 10 mL of bacteriostatic NaCL to the powdered cefazolin for a
concentration of 500 mg per 5 mL. How many mL should the nurse
give?
 The key to solving this type of problem is to ignore extra information
that is not necessary to calculate the desired dose. Then apply the
steps for dimensional analysis.
 BL: 1 g
 EL: mL
 CF: 1000 mg = 1 g and 500 mg = 5 mL
 NOTE: The 10 mL of dilutent (liquid) is not necessary to calculate the
dose; only the resulting concentration of the medication (500 mg = 5
mL) is necessary. The concentration means that there is 500 mg of
medication in every 5 mL of the added liquid.
 Now setup and solve the equation. Click here for answer to
reconstitution 1

45. RECONSTITUTION PROBLEMS 2 & 3
 Setup and solve the following reconstitution problems.
 1. The doctor orders penicillin G potassium 1 million
units IM. If you reconstitute the medication with 8 mL
of sterile water to form a concentration of 500,000
units per mL, how many mL should you give?
 2. The order reads: Ancef 225 mg IV. If the instructions
call for diluting the powdered medication with 2 mL of
sterile water to create a concentration of 125 mg per
mL, how many mL should you give? Round to the
nearest tenth of a mL.
 Click here for answers to reconstitution 2 and 3

46. PEDIATRIC CALCULATIONS
 Another area in which you can apply dimensional
analysis is in calculating pediatric dosages. It is crucial
that these types of dosages be calculated correctly
since the margin for error in infants and children is
very narrow. In other words, an inaccurate dose is
more likely to have a harmful, even fatal, effect. In this
section two types of problems will be presented:
administration problems and safe dose.

47. PEDIATRIC DOSAGE
ADMINISTRATION
 Pediatric dosage administration problems are similar to
adult dosage problems. However, when giving very small
amounts of liquid oral or parenteral medication to infants
or young children, it may be necessary to round to the
hundredths place. You would solve to the thousandths
place, round to the hundredths place, and then draw up the
amount with an oral syringe marked by hundredths of a
mL. See if you can setup and solve for this problem:
 The doctor orders 0.08 mg of Digoxin daily for a 1 year old
child. If the label on the bottle reads 50 mcg per mL, how
many mL should you give for a single dose? (Round to the
nearest tenth of a mL)
 Click her for answer to pediatric 1

48. PEDIATRIC SAFE DOSE
 When a nurse is preparing to administer a medication,
one of his/her responsibilities is to know if the dose
that has been prescribed is a safe dose. That is, does
the dose fall within an established range of safety and
effectiveness as noted in pharmacological references?
This standard for each drug is based upon an adult 18-
65 years weighing 150 lbs. These ranges are included in
all drug references.

49. PEDIATRIC SAFE DOSE
 Dosages for the pediatric patient are sometimes based
upon age but more often upon drug amount per
kilogram of weight per day or per dose. For example,
the average safe dose of Keflex for an adult is 250-500
mg. One only has to compare the patient's dose to this
established range to determine if it is safe. For a child,
a safe dose range is 25-100 mg/kg/day. Not only must
one multiply the weight by the low and high ends of
the range but one must also divide by the number of
doses given per day to determine a single safe dose.
 NOTE: This type of problem WILL NOT be tested in
N110 or N120 on class exams.

50. PEDS SAFE DOSE FORMULA 1
 You can use dimensional analysis to determine safe
dose. The formula is a variation of the one used for
medication administration problems. Use this version
of the formula when the drug reference information
for usual dosage is in mg/kg/ day (24 hours). The
formula is:


51. PEDS SAFE DOSE FORMULA 2
 The other version of the formula for safe dose follows. Use
this formula when the drug reference information for usual
dosage is in mg/kg/dose.
 These formulas are different from the administration
formula you learned previously. So when faced with a
pediatric problem, ask yourself: is it an
administration problem (how much should I give) or a
safe dose problem (is this a safe dose for the child)?


52. PEDIATRIC DOSE PROBLEM 1
 The physician orders ibuprofen 65 mg po every four hours.
If ibuprofen is supplied in liquid form as 100 mg per 5 mL,
how many mL should you give for a single dose? (Round to
the nearest tenth of a mL)
 The first step in figuring out this problem is deciding
which formula to use. Is this a safe dose problem or an
administration problem? Since the problem asks you how
much to give, you know it is an administration problem.
This is NOT a safe dose problem so use dimensional
analysis (beginning label X conversion factor(s)
=answer/ending label) to solve for the answer.
 ROUND TO THE NEAREST TENTH!
 Click here for answer1

53. PEDIATRIC DOSE PROBLEM 2
 The doctor orders 65 mg of ibuprofen po Q6h prn for a child weighing
14 kg. The Pediatric Dosage Handbook states that the usual dosage is 4-
10 mg/kg/dose. Is the ordered dose safe for this child?
 First determine the type of problem. This is obviously a safe dose
problem.
 Next, which safe dose formula should you use? Because the medication
ordered is on a prn basis and the usual dosage is mg/kg/dose you need
to use the second formula.
 Also note that the usual dosage is a range which means you will have to
calculate both the low end of the range and the high end of the range.
If the ordered dose falls between the low end of the range and the high
end of the range, it is a safe dose.
 See if you can determine if the ordered dose is safe for the child.
Remember to compare your answers to the ordered dose to determine
this.
 Click here for answer to peds example 2

54. SUMMARY
 You have now gone through the entire program. If you want
more practice, go through the program again. As per the
Dosage Calculation policy, you will be tested in every
nursing course in this program.
 A word of advice: DO NOT be tempted to figure out
these problems in your head or use another (perhaps more
familiar) method of calculation just because you do not
have to show your work here. For ALL N110 and N120 in
class tests, you will be required to show your work in
dimensional analysis. More importantly, when the
problems get more difficult in other nursing courses, it will
be easier, and your chances of getting the correct answer
much better, if you use dimensional analysis.
 GOOD LUCK!!!

55. REFERENCES
 Buchholz, S., and Henke, G. (2006). Med-Math, 5th ed.
New York: Lippincott Williams and Wilkins.
 Daniels, J., and Smith, L. (2005). Clinical Calculations: A
Unified Approach. Albany, N.Y.: Delmar Publishers Inc.
 Hegstad, L., and Hayek, W. (2001). Essential Drug Dosage
Calculations, 4th ed. Upper Saddle River, N.J.: Prentice
Hall.
 Kee, J., and Marshall, S. (2000). Clinical Calculations With
Applications to General and Specialty Areas, 4th ed.
Philadelphia: W.B. Saunders.
 Taketomo, C., Hodding, J., and Kraus, D. (2006). Pediatric
Dosage Handbook, 13th ed. Hudson, Ohio: Lexi-Comp Inc.