Medication Dosage Calculations

In both my real life nursing school experience and online observations (mostly via Twitter), I see medication dosage calculations are a source of stress for nursing students.  Not surprising...I mean who among us just really loves doing math?  Taking long, convoluted questions that give you a ton of information and coming up with the answer?  I don't know about you, but that's just not my bag, baby.

But dosage calculations and conversions are important...because a doc can order a dosage for your patient that doesn't exist in the pharmacy.  Or the dose is in units per kilogram, and you know your patient's weight in pounds.  So how does that work?  You use your math skillz and figure out the correct dose, because you don't want to over- or under-medicate your patient.  And as we all know, both of those situations can be really, really bad.

In my TNI (Fundamentals) class last semester, we spent a week on dosage calculations.  Our instructor taught us a formula that uses your amount on hand and the dosage required and some other stuff and then you math it all out.  (I had to look it up..it's (desired over have) times (quantity over 1).  Yeah, clear as mud.)  That didn't really work for me and I got frustrated, thinking a stupid MATH quiz was going to take me out of nursing school.  Then I noticed my friend next to me was sailing through the problems, so I asked him for help.  He told me he set it up like equivalency problems done in chemistry class (called dimensional analysis, which I vaguely remember doing in chemistry many years ago...), cancelled out the units, did the math, and voila!  Correct answer with correct units.  Uhhh, what?  Come again?  Let's take a closer look.

Question: The MD orders 125 mcg of Digoxin. Available are 0.25 mg scored tablets. How many tablets will you administer?

And this is how I solved it:

1. My first step was to determine the units I was solving for.  In this one, it was tablets.  So I wrote down "tablets" on the left side.  This tells me that I need to have this particular unit on top in the actual math portion.
2. So in setting up the math, I wrote "tablet" on the top row, and since I knew each tablet was 0.25 mg, I wrote "0.25 mg" on the bottom row below "tablet".
3. Since mg is on the bottom in the first part, I know it has to be on the top at some point so the units will cancel out.  I look at the ordered dose and see that it's in micrograms (mcg)...so I decide to do the conversion from mg to mcg.  The next set of numbers is then "1 mg" on top, "1000 mcg" on the bottom.
4. And then the final part is to put the ordered dose of "125 mcg" on top so the mcg units will cancel.
5. Now you just multiply the numbers across the top, then across the bottom, then do the division.
6. Answer is 0.5 tablets.

How about another one..

Question: The MD orders 1.2 mg/kg Gentamicin. The client weighs 150 pounds. Available is a vial labeled 100 mg/2 mL.  How many mL's will you adminster?

And this is how I solved it:

1. Again, I determined the units I was solving for.  This time it was mL's, so I wrote "mL" on the left.
2. Math time, mL needs to be on top and I know that I have a vial that says 100 mg/2 mL...so I just flip it to get the mL on top.  "2 mL" on top, "100 mg" on bottom.
3. Working the same way to get the units to cancel, I know that the ordered dose is 1.2 mg/kg...so "1.2 mg" on top, "1 kg" on bottom.
4. Now time to convert my patient's weight into kilograms using a known conversion of 1 kg = 2.2# (more on conversions in a bit).  "1 kg" on top, "2.2#" on bottom.
5. And my patient weighs 150#...so to cancel out the #, "150#" is on top.
6. Multiply across the top, then across the bottom, then do division.
7. The answer is 1.6 mL.

I've done calculations solved for simple units such as tablets, mL's, and mg's, but also IV flow rates of mL/hour and gtts/min.  I've also had to solve for time, such as "a new bag is hung at such and such time, at a flow rate of so and so, when will the bag be empty?"  The same principle applies -- figure out the desired unit, make sure the single unit is on top (like the examples I did) or if it's mL/hr, make sure mL is on the top and hr is on the bottom.

As for conversions...these are things you'll just have to memorize.  The ones we're expected to know in our program are: 1 kg = 2.2#; 1 grain = 60 mg; 1 oz = 30 mL; 1 Tbsp = 15 mL; 1 Tbsp = 3 tsp; plus all metric ones -- for example, 1 mg = 1000 mcg; 1 gram = 1000 mg.

Using this method and knowing my conversions, this whole concept of dosage calculations went from "OMG, I'm going to fail!" to "OK, this makes sense, I can do this".  I passed my one quiz on the first attempt last semester, and I passed both quizzes on the first attempt this semester.  This very much not-a-math-major managed to understand and do math...so that counts for a whole lot!  ;-)

Hopefully this information can help a fellow nursing student to not freak out so much about dosage calculations.  Just go with the method that makes the most sense, take your time, double (and triple..and quadruple) check your work, and don't forget your units!  Oh, and rounding rules!  Some of my classmates got their math right, got the units right, but missed the whole question because they didn't follow the rounding rules.  Not sure if they're universal or institution-specific, but I'm sure your instructors will let you know what you need to know.

Good luck!