Dimensional Analysis Math Guide

1
Dimensional Analysis Math Guide

• Diana Blum MSN

2

• In any drug calculation problem, for exam
  purposes, if you do not include the proper unit
  in your answer it will be WRONG!
• If you do not show your work in dosage
  calculation on the Exams, your answers will be
  considered wrong !

3

• Remember You may have to perform several
  conversions before you can obtain the answer you
  are seeking

4

• For oral things like tablets, capsules, etc.
  Remember DO/DA
• Dose ordered x desired med (cap, tab, ml)
  amount to be given
• Dose Available
• Weight Based Problems
• When mg/kg/day is ordered, this is not a division
  problem, it is a multiplication problem
• Intravenous fluid must be set for a given rate
• It must be measured as ml/hour, L/hour or
  drops/min.
• To control or adjust the flow rate only drops
  per minute are used.

5

• The formula for working out flow rates is
• Volume (mL) x drop factor gtt (drips) Rate
  (gtt/min) (MUST be whole number)
• Time (min) mL (Volume)

6
Steps

• Determine what you want to know.
• Read the problem
• What is it asking?
• Determine what information you already know.
• Setup the problem using only what you need to
  know.
• Pick a starting point
• pick from what you know and make sure you put it
  in the right place
• Or pick a factor that is given, such as what the
  physician ordered.           Be aware that the
  starting factor will always have at least one
  unit that is not desired.
• This  will need to be changed using a
  cancellation technique
• Keep trying to cancel out units you don't want
  until you end up with only the ones you do
• If you can't get to what you want
• try picking a different starting factor
• Did you Convert everything?

7

• It is time to Solve It Make sure all the units
  other than the answer units cancel out, then you
  are ready to do the math.     a. Simplify the
  numbers through cancellation.
• Same number on top and bottom these should
  cancel out     b. Multiply all the top numbers
  together, then divide into that number all the
  bottom numbers..           Dont Put the decimal
  in the wrong spot.
• Dont add incorrectly
• always double check.     d. Round off the
  calculated answer if possible.
•      e. Add labels to the appropriately rounded
  number to get your answer.
• Always work the problem backwards to check
  accuracy.

8

• You need to start a continuous drip of amiodarone
  at 1 mg per minute (by pump). The standard IV
  mixture is 450 mg in 250 mL.
• Pumps like to be programmed in mL/hr, so mL/hr
  are your answer units.
• 1mg x 60min x 250ml 33.3ml/hr
• 1min 1 hr 450mg
•  Milrinone Lactate (Primacor) has been ordered
  for a patient at 0.4 mcg/kg/min. The patient
  weighs 145 kg. If the pharmacy mixes 20 mg of
  Milrinone in 100 mL of total solution, what would
  be the rate of the infusion?
• First, think what units will be in the answer.
  Since you're using a pump, it's mL/hr.
•  
• 145kg x 0.4mcg x 1mg x 1 00ml x
  60min 17.4ml/hr
• 1kg/1min 1000mcg 20mg
  1hr

9
Practice

• Calculate the drip rate for 100 mLs of IV Fluids
  to be given over a half hour via a giving set
  which delivers 10 drops/ml.
• 2. Calculate the drip rate for 2 liters of IV
  Fluids to be given over 5 hours via a giving set
  which delivers 10 drops/ml.

10

• 3. A client is ordered 20 milligrams of
  Haloperidol decanoate by intramuscular injection.
  50 milligrams in 1 milliliter of liquid for IM
  Injection is available. How many milliliters will
  you administer?
•  
• 4. A client is ordered 200 milligrams of
  Augmentin 600 intravenously. 600 milligrams in 6
  milliliters of liquid for IV Injection is
  available. How many milliliters will you
  administer?

11

• 5. The IV ordered is 1000 mL to infuse at 160
  mL/hour. Calculate the infusion time in hours and
  minutes for this order
•   
• 6. The order is for nitroprusside 50 mg in 250 mL
  D5W to infuse at 3 mcg/kg/min for a patient whose
  weight is 75 kg. Calculate the hourly infusion
  rate in mL/hr.

12

• 7. The order is for dopamine 200 mg/500 mL D5W to
  infuse at 10 mcg/kg/min for a patient whose
  weight is 75 kg. Calculate the hourly flow rate
  in mL/hr.
•  
•  
• 8. The physician orders dopamine (Intropin) 400
  mg in 250 mg D5W TRA 5 mcg/kg/min.For the client
  who weighs 110 lbs, how many
• ml /hr will the pump be set?

13

• 9. Nitroglycerin is infusing at 16 ml/hr. The bag
  has 50 mg NTG in 250 ml D5W. How many mcg/min is
  the client receiving?
•  
• 10.Ms. Bellman is post-op CABGx5. She has an
  order of dobutamine 3 mcg/kg/min. The 250 ml bag
  of D5 indicates 250 mg of Dobutrex. Her weight is
  130 lbs. What is the flow rate?
•  
• 11. Mr. Muruski is being treated for shock. The
  dobutamine infusion is set at 34 ml/hr. The
  medication label indicates Dobutrex 250 mg in 250
  ml D5. His weigh is 190 lbs. What is the dosage
  of dobutamine the client is receiving?

14
Answers

• 33gtts/min
• 67 gtts/min
• 0.4 ml
• 2 ml
• 5. 1000ml x 1 hr 6.25 hours
  then .25hrs x 60min 6 hours and 15 mins
• 160ml
  1 hour
• 6. 3mcg/75kg/60min 13500mcg/hr or 13.5mg/hr
• 250ml x 13.5mg 68mL/hr
• 50mg 1 hr

15

• 7. 10mcg/75kg/60min 45000mcg/min or 45mg/hr
•  
• 500ml x 45mg 112.5 or 112ml/hr
• 200mg 1 hr
• 8. 400 / 250 1.6 mg/ cc 1600 mcg/cc 2)
• Convert lbs to kg. 110 / 2.2 50 3)
• Dose (5) x kg (50) x 60 / concentration (1600) 5
  x 50 x 60 15,000 15, 000 / 1600 9.375
• 9. 50 / 250 0.2 mg/cc 200 mcg/cc
• Rate (16) x Concentration (200) 3200 / 60
  53.33
• 10. 59 kg Concentration is 1000 mcg/ml.
• 11. Wt. 86.36 kg. Concentration 1000 mcg/ml
  (34 x 1000) / (86.6 x 60)