1. YES…
YOU
CAN
DO
IT!
DIMENSIONAL ANALYSIS
DOSAGE CALCULATIONS

2. Understand the learning components needed
in order to perform dosage calculations.
Apply dimensional analysis method when
calculating dosages for medication
administration.
OUTCOMES

3.  FORMULA METHOD:
 RATIO AND PROPORTION:
LINEAR: 250 mg : 1 tab :: 1.5 g : x tabs
FRACTIONAL:
OTHER METHODS:
Disadvantages: Must remember the extra step of changing D and H to same unit of
measurement. May have many steps and variables.
250mg
1tab
=
1.5g
xtabs

4. RELAX

5. ADVANTAGES:
Organized and simple structure
Set up in one step so all information is in one problem
Easy to see if set up is incorrect
REQUIRED ELEMENTS:
Need to anticipate what units your answer needs to be in
What your given quantity is and what units need to be converted
Conversion factors – to convert given quantity and units into your
desired answer units
DIMENSIONAL ANALYSIS METHOD

6. What is being ordered?
IN SIMPLER TERMS
What do we have on hand?
Do we need any equivalents, or do we need to convert into
equivalents?
Where are we going, what are we looking for?

7.  Determine the label you want your answer to be in (desired
answer units) and write it on the right side of your equation.
(your book also tells you to put ‘desired answer units’ on the left
side of your page, Mulholland, p.46)
 Put the known values (given quantity and units) of the problem in
fraction form on the left side of your equation. Remember, the
desired answer unit must be in the numerator. (Mulholland, p.47)
 Put in any conversion factors you will need to work towards the
desired label.
 Cancel out all labels that are both in numerator and
denominator.
 Do the math: reduce, multiply the numerators, multiply the
denominators; then divide the numerator by the denominator.
IDEAS TO HELP YOU

8.  Basic math functions / Fractions
Adding, Subtracting, Multiplication, Division
Decimals -
King Henry Doesn't [Usually] Drink Chocolate Milk with a Microscope
The first letters stand for the prefixes, with "Usually" in the middle
standing for the "unit", being meters, grams, or liters. Many memory
phrases omit the "Usually", and consequently students forget where the
basic unit goes, messing up their conversions. Leave the "Usually" in there
so you can keep things straight:
kilo- hecto- deka- [unit] deci- centi- milli- ^- ^- micro-
Must know equivalents / conversions (no apothecary items).
Using Estimation (Mulholland, p.136) and Estimated Dose to
anticipate your answer, then do your DA equation.
THINGS YOU WILL NEED TO KNOW

9. Let’s not make this too complicated: We know that there are
72 hours in 3 days, this is how it would look using D.A. -
SOME THINGS ARE COMMON SENSE
24hr
1day
x
3days
1
= 72hr

10. LET’S START WITH A CONVERSION
40 L = ______ gal
?
gal:
1gal
4L
´
Desired
Answer
Units
Starting
(Conversion)
Factor
40L
1
= gal10
Given
Quantity
and Units
1
10

11. SAME PROBLEM DIFFERENT SETUP
40 L = ______ gal
1gal
4L
=
Desired
Answer
Units
Starting
(Conversion
) Factor
40L
1
´ gal
Given
Quantity
and Units
1
10
10

12. Give Aspirin 0.65 g PO q 4 h prn headache
 Bottle: 325 mg per tablet (1 tablet = 325 mg)
How many tablets will you give per dose?
Conversion factor: 1000 mg = 1 g
What are we looking to give? Tablets
What is dose on hand? 325 mg per tablet
What is the ordered dose? 0.65 g dose
How will we set this up using Dimensional Analysis?
ORDER:

13. What are we looking for?
What is dosage on hand?
What is the conversion factor and what is the order?
WORK IT
Tablet(s)
dose
1tab
325mg
´
0.65g
dose
=
1000mg
1g
´
Mulholland, pg 115-116 for similar problem

14. Cancel out and do the math:
WORK IT
Tablet(s)
dose
1tab
325mg
´
0.65g
dose
´
1000mg
1g
=
650
325
=
2
So, you will give the patient 2 tablets as needed every 4 hrs

15. You have an order for Daypro 1200 mg po bid:
A SIMPLE EXAMPLE
1cap
600mg
´
2
1
cap2
Mulholland, pg 138, problem 5 for similar problem
Desired Answer Units
1200mg
dose
=

16. The order reads Estratab 3125 mcg po daily:
ANOTHER COMPLEX EXAMPLE
tab
1
1.25
´
3125
1
´
1
1000
=
3125
1250
= 2.5
1tab
1.25mg
´
3125mcg
1dose
´
1mg
1000mcg
=
Desired Answer
Units
2.5 tab

17. Order: Azithromycin 12 mg/kg PO daily dose. Patient weighs
22 lbs. Pharmacy sends a 240 mL bottle of Azithromycin
labeled 200mg/5mL. How many mL will you pour for each
dose?
HOW ABOUT A MORE COMPLEX PROBLEM
ml
dose
12mg
kg / dose
´
5ml
200mg
´
1kg
2.2lbs
´
22lbs
1
=
3
Desired Answer UnitsMulholland, pg 160, 147 for similar problems
1
10
1
60ml
20dose
=

18. PRACTICE
Your patient may receive Dilaudid 3 mg IM q3h for pain. At
this hospital Dilaudid is supplied in 1-ml ampules containing
4 mg. How many milliliters will you administer?
m
l
0.75
3
4
=
3mg
1dose
=
1ml
4mg
x

19. Mulholland, J. M. (2011). The nurse, the math, the meds:
Drug Calculations Using Dimensional Analysis. (2nd ed.).
St Louis, MO: Elsevier Mosby.
Moore, S.G. (2011). Nursing math simplified: Math magic. (5th
ed.). Clearwater, FL: H&H Publishing.
Horntvedt, T. (2012). Calculating Dosages Safely: A
dimensional analysis approach. Philadelphia, PA: F.A.
Davis.
RESOURCES