DIMENSIONAL ANALYSIS
AKA: FACTOR-LABEL METHOD
OBJECTIVES
• To increase knowledge of Dimensional Analysis (DA)
for calculating medication dosages
• Demonstrate the application and usage of
Dimensional Analysis (DA) during medication
dosage calculation and medication administration
SAFETY SUPPORT FOR DA?
• The Quality and Safety Education for Nurses (QSEN)
project goal is to minimize the risk of harm to
patients through individual performance (Cronenwett
et al., 2007)
• Teacher knowledge makes a substantial
contribution to student achievement (Ball & Bass, 2003)
• A standardized approach to medication
calculation can provide a solution to more than 1 in
6 medication errors (Lesar, Briceland, & Stein, 1997)
ADVANTAGES OF USING DA FOR
MEDICATION CALCULATIONS
• DA is a consistent approach without memorizing
formulas
• One step equations: no need for multiple equations
• No formulas needed
• Can be used for all problems and medications calculations
• Promotes critical thinking
• Use for simple or complex problems
• Supports problem solving and critical thinking
• Evidence supports the use of DA
EVIDENCE FOR DA
• Performance of the dimensional analysis method
group as compared with the formula/ratio-andproportion method group, indicated that the DA
group performed statistically significantly higher
(Serembus, 2000).
• DA used in chemistry, physics, and engineering
• “While mistakes can still be made using any
technique, DA does the best job of minimizing
them. The only fault lies in the name. Perhaps the
Math-Weenie No-Brainer Technique would be
appropriate” (Lee, 2006) .
CONVERSIONS AND ABBREVIATIONS
TO REMEMBER
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1,000 mcg = 1 mg gtt = drop
mcg = microgram
1,000 mg = 1 g
IM = intramuscular
mg = milligram
1,000 g = 1 kg
IV = intravenous
g = gram
1, 000 ml = 1 L
IVP = intravenous push ml = milliliter
2.2 lbs = 1 kg
BID = twice a day
L = liter
1 oz = 30 ml
TID = three times a day oz = ounce
gr1 = 60mg or 65 mg
IVPB = intravenous piggyback
1 tsp = 5 ml
PO = oral (by mouth)
gr = grain
1 Tbsp = 15 ml
tsp = teaspoon
Tbsp = tablespoon
DIMENSIONAL ANALYSIS
Five Steps for Dimensional Analysis
1.
2.
3.
4.
5.
Identify the unit of measure desired in the calculation.
Write the label for the answer on the right side of the
equation.
Place the available information from the problem in
fraction form on the left side of the equation. The
abbreviation or unit matching the desired unit on the
left side, must be placed in the numerator.
Enter conversion factors as fractions to work toward the
desired label. (Equals over equals)
Cancel all labels that are in both the numerator and
the denominator.
Do the math: multiply the numerators; multiply the
denominators: then divide the numerator by the
CALCULATION FOR PEDIATRIC
MEDICATIONS
• Safe dosage needs to be completed prior to
administering pediatric medications. The following
steps should be taken to do this:
• Pediatric medications are most commonly
calculated based on body weight. The first step is
to determine your patient’s weight in kg (most
formulas are based on kg).
• Safe dosage ranges are expressed in one of two
ways:
• mg/kg/day in specific divided doses (2 step procedure)
• mg/kg/dose (1 step procedure)
• Now you can calculate the patient’s safe dosage.
SAMPLE PROBLEM #1
• A 280 pound man weighs how many
kg?
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1.
=
kg
2. 1kg/2.2lb
X 280lb = 280kglb/2.2lb
3. 1kg/2.2lb X 280lb = 280kg/2.2
4. Answer = 127.2kg
Answer sounds logical
SAMPLE PROBLEM #2
• Order: Lasix (furosemide) 40mg PO
daily
• Available: tablets labeled 20mg
• How many tablets will the nurse
administer?
SAMPLE PROBLEM #3
• Administer D5LR at 75 ml/h. The drop
factor is 10 gtt/ml.
• Calculate the flow rate in gtt/min.
SAMPLE PROBLEM #4
• Administer 1000 ml D5W in 6 hr. The
drop factor is 15 gtts/ml.
• Calculate the flow rate in gtts/min.
SAMPLE PROBLEM #5
• Infuse 200ml of NSS in 2 hr. The drop
factor is 20gtt/ml.
• Calculate the flow rate in gtt/min.
SAMPLE PROBLEM #6
• Order: Gentamicin (garamycin) 55 mg
IM q8h.
• Available: Gentamicin (garamycin) 80
mg per 2 ml.
• How many ml will the nurse administer
for one dose?
• How many ml will the nurse administer
for one day?
SAMPLE PROBLEM #7
• Ampicillin 750 mg IV q4h.
• Available: 2000mg per 5ml.
• How many ml will the nurse administer
for one dose?
• How many ml will the nurse administer
for one day?
SAMPLE PROBLEM #8
• An IV of 500ml. NSS is to infuse at
60ml/hr. How long will the infusion
take?
• If the IV was started at 2000
(chronological time; military time),
when would the infusion be complete
(state in chronological time; military
time).
SAMPLE PROBLEM #9
• Order: Gentamcin 50 mg IVPB q8h for
a child weighing 40 lb.
• The recommended dosage for a child
is 6 to 7.5 mg/kg/day divided q8h.
• Is the dosage ordered safe?
SAMPLE PROBLEM #10
• Order: Phenobarbital 10 mg PO q12h is
ordered for a child weighing 9 lb.
• The recommended maintenance dose
is 3 to 5mg/kg/day q 12h.
• Is the dosage ordered safe?
RESOURCES
• Ball, D.L., & Bass, H. (2003). Toward a practice-based theory of
mathematical knowledge for teaching. In Canadian
mathematics education study group. Proceedings of the 2007
annual meeting of the Canadian mathematics education study
group. Reston, VA: National Council of Teachers of Mathematics.
• Cronenwett, L., et al., (2007). Quality and safety education for
nurses. Nursing Outlook, 55 (3)122-131.
• Lee, R.E. (2006). Medication math for the nursing student.
Retrieved 6/12/2006 from:
http://alysion.org/dimention/analysis.htm
• Lesar, T., Briceland, L., & Stein, D. (1997). Factors related to errors in
medication prescribing. Journal of the American Medical
Association , 277, 312-317.
• Serembus, J. (2000). Medication calculation ability of
baccalaureate nursing students as a function of method of
instruction. Widener University (doctoral dissertation).