# Master Your Drug Calculations BEFORE You Get to Nursing School

Unit conversions, dosage calculations, percent problems, and IV flow rate problems can all be solved using a simple and safe method called dimensional analysis (DA). If you take a couple of evenings to learn this method, you will save yourself hours of trying to learn a long list of formulas. Nursing Students General Students Knowledge

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## Keys to Success:

• Knowing what is happening in the calculation rather than blindly following a formula.
• Setting up your calculations mathematically correct.

5 g (1000 mg/g) = 5000 mg is correct.

5 g x 1000 = 5000 mg is incorrect.

Unit conversions, dosage calculations, percent problems, and IV flow rate problems can all be solved using a simple and safe method called dimensional analysis (DA). If you take a couple of evenings to learn this method, you will save yourself hours of trying to learn a long list of formulas.

These problems all have the same three parts:

• The Units of the Answer: Think of it as the destination.
• A Given: This is what is given to start the problem and what is changed into the answer.
• One or More Ratios: These are the tools used to change the units of the given into the units of the answer.

Check Out These Examples...

## Unit Conversion: How many mL in 3.5 L.

3.5 L is the given. mL is the unit of the answer. The ratio is 1000 mL/L

3.5 L (1000 mL/L) = 3500 mL

L cancel out and you are left with mL in the answer.

## Dosage Calculation: A patient is ordered 500 mg of a drug which is available in an oral suspension of 250 mg/5 mL. How many mL will you administer?

500 mg is the given. mL is the unit of the answer. The ratio is 250 mg/5 mL

500 mg (5 mL/250 mg) = 10 mL

In this case, we had to flip the ratio upside down, which is permissible.

## Percent Problem: Convert 0.458 to a percent.

0.458 is the given, % is the unit of the answer and 100% is the ratio.

0.458 (100%) = 45.8%

## IV Flow Rate: An IV is running at 30 mL/h with a drop factor of 20 (20 drops/mL), how many drops/min is that?

30 mL/h is the given. Drops/min are the units of the answer. 20 drops/mL and 60 min/h are the ratios.

30 mL/h (1 h/60 min) (20 drops/mL) = 10 drops/min

Unfortunately, there is not enough space here to go into all the details of this method, but you can PM me and I will send you some study material. Also, I am always glad to help with specific calculation questions.

Specializes in Pharmacy, Mathematics, Physics, and Educator.

Let me know if you have any questions. I am retired and pretty much just ski, go to the gym and try to help students where I can. Once you realize that you are only changing the units by multiplying by various forms of 1 (the ratios) to get the units you want, these calculations will be a breeze.

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OMG thank you for the book this is totally awesome material to have! Very helpful

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Thank you so very much!

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I wish you had been around when I was in Nursing school!!!!

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Specializes in Pharmacy, Mathematics, Physics, and Educator.

## The Typical Thought Process of a Student Working an IV Flow Rate Problem using dimensional Analysis

A 59 y.o. male weighing 80 kb has been admitted to the ED and placed on a dopamine infusion at the rate of 45 mL/h. The IV bag contains 400mg of dopamine in 250 mL of D5W (5 g of dextrose/ 100 mL solution).  The IV has been running for 20 minutes. How many mcg/kg of dopamine is the patient receiving each minute?

Student: Oh brother. Someone is trying to be cute by loading this problem up with a lot of crap. What are they asking? mcg/kg/min, OK, that is a rate so the the problem has to start with a rate. The only other rate is 45 mL/h. Glad I read somewhere that mcg/kg/min = mcg/(kg min). I hate those two line things.

Student: That was a fun party last night. Nice of Becky to invite me to her dog's tenth birthday party. Concentrate... I have to change mL to mcg, h to min and add kg to the answer. I will start with something easy.

Student: I probably shouldn't have had that last beer. What is the maximum dose of ibuprofen? Concentrate... There is 400 mg of dopamine in 250 mL. mL will have to go on the bottom to cancel out the mL in 45 mL.

Student: Did I really fill the dog's bowl up with beer? Concentrate... mg to mcg is easy.

Student: He probably didn't drink it. What if he did? What if he got sick? Concentrate... Damn...I do stupid stuff when I drink. I just have to add the kg on the bottom. He weights 80 kg...that is easy.

Student: ml, h, mg all cancel out. Smart of me to highlight the things I want. Looks good. Get out the calculator. 15 mcg/kg/min. I better use the two line thing so I don't confuse the instructor. I better call Becky and make sure her dog is OK.

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I hope Becky's dog is okay, too!'

I love this breakdown, you always make it look so easy!

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Specializes in Pharmacy, Mathematics, Physics, and Educator.

I put together a pdf that goes into a little more detail regarding solving IV Flow Rate problems using dimensional analysis than my book does. I hope you find this helpful.

Solving IV Flow Rate Problems Using Dimensional Analysis.pdf

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Great approach and well explained. Math...formulas..strict old rules....just drove me nuts. This is the "not so math brain"...well...approach. When math confusion/block happens...it can stop a career path ! I made it through Pharm and Chem loving the subject but tense over the math...but years later cried my way through statistics...until I got a wonderful tutor. Three sessions and ...wow...I love statistics ! Even with an engineer father who tried so hard to help me in algebra...I would nod off. It took the right approach and I totally agree with dimensional analysis.

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I cannot state how important this advice is. I was in a program and made it all the way to peds and OB and failed my OB portion by an inch. Pitocin....I froze and couldn't for the life of me remember how to simply convert micro units to units....this caused a potentially fatal error mathematically. And though I knew it was too high, knowing so isn't enough to count. You have to give the correct dose. This lead to my dismissal from my program, so I urge learning this simple arithmetic now and spare yourself the stress of learning it while juggling everything else you will be handling as a nursing student. Back to the beginning for me at a new institution. Hopefully all goes well this time!

?

NNM

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47 minutes ago, NeoNatMom said:

I cannot state how important this advice is. I was in a program and made it all the way to peds and OB and failed my OB portion by an inch. Pitocin....I froze and couldn't for the life of me remember how to simply convert micro units to units....this caused a potentially fatal error mathematically. And though I knew it was too high, knowing so isn't enough to count. You have to give the correct dose. This lead to my dismissal from my program, so I urge learning this simple arithmetic now and spare yourself the stress of learning it while juggling everything else you will be handling as a nursing student. Back to the beginning for me at a new institution. Hopefully all goes well this time!