Dosage Calculations Using Dimensional Analysis

Shiraz University of Medical Sciences , Aliasghar Hospital

M.A Salehi, BSN, MSc.

Outcomes:Understand the learning components needed for nurses success in performing dosage calculations.

Utilize dimensional analysis to calculate dosage.

Potential resources for teaching dimensional analysis in the ward(e.g MW3).

Ways to calculate dosage:Formula Method

VH

DAmount to Give

Challenge: Must remember the extra step

of changing D and H to same unit of

measurement. Also may have extra

variables such as body weight, times per

day, etc.

Ways to calculate dosage:Ratio and Proportion

Linear Ratio and Proportion

Fractional Ratio and Proportion

500mg : 1 tab :: 1 g : x tabs

Product of the means equals the product of the

extremes.

xtabs

g

tab

mg 1

1

500

The products of cross

multiplication in a proportion

are always equal

Dimensional AnalysisDimensional Analysis involves setting up a series of fractions.

All information is in one problem

Nurses do not have to remember multiple steps

Nurses ask four simple questions to set up their dimensional analysis problem.

Necessities for Nurses Success in Dosage Calculations

Review of basic math functions –fractions and decimals

Adding

Subtracting

Multiplication

Division

Nurses must memorize equivalents

The 4 main questionsWhat is the order?

What is on hand?

Do you need any equivalents?

Where are you going? (or what are you being asked to give?)

Start with conversions

240 mg = ______ grains

240

1

mg

Start with conversions

240 mg = ______ grains

240

1

1

60

mg grain

mg grains

1

4

4

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

What is the order?

dose

mg

1

40

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

What is on hand?

dose

mg

1

40

mg

ml

80

10

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

Do you need any equivalents?

dose

mg

1

40

mg

ml

80

10

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

Where are you going? (or what are you being asked to give?)

mlmg

ml

dose

mg________

80

10

1

40

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

Begin by cross canceling labels

mlmg

ml

dose

mg________

80

10

1

40

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

Labels left should be “what you are looking for”

mlmg

ml

dose

mg________

80

10

1

40

Order: Lasix 40 mg PO dailyDose on Hand: 80 mg/10 ml

Do the math

mlmg

ml

dose

mg________

80

10

1

40

1

2

55

1

What about problems with different units of measurement?

Order: digoxin elixir 0.05 mg PO daily

Label: Digoxin 50 mcg per ml

How many milliliters will you give?

dose

mg

1

05.0

mcg

ml

50

1

mg

mcg

1

1000ml

1

20

1

Complex Problems

Order: Augmentin 12.5mg/kg PO every 12 hours. Child

weighs 22 lbs. Mr.Kargar sends a 75 ml bottle of

Augmentin labeled 125mg/5ml. How many milliliters will

you pour from the bottle?

dosekg

mg

/

5.12

mg

ml

125

5

lbs

kg

2.2

1

.1

22

pt

lbs ml

5275

1375

1

22

2.2

1

125

5

1

5.12

5

What about IV problems?Order: 250ml 5% D/W IV in 2.5 hours.

Tubing package reads 15 gtts/ml.

How many gtts/min will you adjust the IV?

hrs

ml

5.2

250

ml

gtts

1

15

.min60

1hr

min___

gtts

25150

3750

60

1

1

15

5.2

250

25

Physicians order Daypro 1200 mg bid.

mg

cap

dose

mg

600

1

1

1200

1

2

cap2

Order: Estratab 1250mcg daily

mcg

mg

mg

tab

dose

mcg

1000

1

25.1

1

1

1250tab

11250

1250

1000

1

25.1

1

1

1250

1

The order reads: Administer 1000cc of D5NS over 10 hrs.The drop factor on your tubing is 15 gtts/cc.

How many gtts/min?

hours

cc

10

1000

cc

gtts

1

15

min60

1hourgtts/min

1

4

1

25

25

or

25600

15000

60

1

1

15

10

1000

Practice Problems

Your patient may receive Dilaudid 3 mg IM q3h for pain. Dilaudid is supplied in 1-ml ampules containing 4 mg. How many milliliters will you administer?

3

1

mg

dose

1

4

ml

mg ml¾= 0.75

Dr. Zamani orders heparin 2500U subq. You have heparin, 5000U per ml. How many ml will you administer?

2500

1

u

dose

1

5000

ml

u ml

1

2

1

2

Your patient needs morphine 1/6 gr. SQ stat for chest pain. You have a 20 ml syring prepared by Miss. Shahryari and labeled 15mg/ml. How many milliliters will you give?

1 6

1

/ gr

dose

1

15

ml

mg

60

1

mg

gr ml

1 6 60

15

60 6

15

10

150 67

/ /.

x

0.67

A patient with tachycardia has an order for Brevibloc to be started at 50 mcg/kg/min. The concentration is Brevibloc 5 g in 500ml of D5W. The patient weighs 176 pounds. How many ml/h should the IV pump be programmed for?

50mcg

kg / min

500

5

ml

g ml/hr

176

1

lbs

pt

.

.

1

2 2

kg

lbs.

1

1000

mg

mcg

1

1000

g

mg

60

1

min

hour

50

1

500

5

176

1

1

2 2

1

1000

1

1000

60

1

.

1

2

1

251

401

80

1

2

1

12

24

24

Resources for teaching Dimensional Analysis

IV Calculations site

http://www.geocities.com/Heartland/Valley/3049/iv/clcltns.html

Math tutorials

http://www.utep.edu/nurs4710/tutorials/

IV drip rate problems and dosage calculation problems

http://www.dalesplace.net/iv.htm