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Dimensional Analysis as a Nurse?

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by MikeyJ MikeyJ, RN (Member)

MikeyJ is a RN and specializes in Peds, PICU, Home health, Dialysis.

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In NS they teach us to use dimensional analysis when faced with med math. I am curious if practicing nurses actually use dimensional analysis everytime they are doing a calculation, or does it just become second nature?

Ex: The order is to administer 4 g of an antibiotic mixed in 100 mL to run over 40 minutes. The tubing label reads 15 gtts = 1 ml. What is the drip rate of the infusion per minute?

I know the answer is 38 gtts/min -- however, in the hospital do nurses actually whip out the pen and paper and do dimensional analysis, or what? Just curious! :)

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llg has 40 years experience as a PhD, RN and specializes in Nursing Professional Development.

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Most experienced nurses actually get out a pen and paper (or paper towel) and do the calculations as necessary.

However, in my extensive experience teaching new graduates in orientation programs, I find that most who try to use dimensional analysis to solve real-life clinical problems struggle. The ones who have the easiest time with the types of problems that occur in actual situations are those that break the problem down into steps -- and then use basic algebra with ratios/proportions to solve the various steps of the problem.

Those people who rely on dimensional analysis often "freeze up" when faced with a situation that requires multiple stages or layers of problem-solving. They look to make 1 equation in which they will place all the variables, when what is actually needed is a series of equations to address each stage of the problem's solution.

Dimensional analysis works fine for certain types of problems (the type they emphasize in school). But real life isn't so neat and tidy. For the messy complexity of some types of real-life problems, you need to truly understand the quantities involved and the logic of the different aspects of the problem. Many students who rely on dimensional analysis to get themselves through school never learn the internal logic of the mathematical situations and therefore struggle when they are faced with a situation that doesn't match their "template" and they have to improvise.

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21,306 Visitors; 6,487 Posts

Many facilities use pumps to regulate rate, but we still have to do a lot of math because the doc might order how much of a drug per body weight to give, but we have to actually figure out the dosage. Or the order often reads for a fraction of what is supplied, so you need to calculate the amount of solution to give. Nurses have different methods of doing the math, depending on what formula each is more comfortable with. I love dimensional analysis for drug calcs, but my partner used a different formula.

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puggymae specializes in OB, NP, Nurse Educator.

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It depends - I use order/available for some calculations; for those that require more steps I use dimensional analysis.

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My calcs are mostly with a pen scratched on a scrap of paper; I have been known to do it on an alcohol pad!

Have used arithmetic, DA, whatever gets me my answer quickest at the time I need it. Oh, and a calculator if one is very handy (and it never seems to be, hence the aforementioned pen and paper).

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Daytonite has 40 years experience as a BSN, RN and specializes in med/surg, telemetry, IV therapy, mgmt.

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sistermike. . .no, i don't use dimensional analysis for figuring out dosages at work with one exception, drips like dopamine.

i came from a time when there were no iv pumps and we had to titrate all our ivs drips. after you've calculated hundreds of them you can do these in your head because it's the same set up every time. i would just quickly calculate what the hourly rate would be (in this case 40 minutes is 2/3 of an hour, so it would be 150 ml in an hour) and divide that by 4 (the result of 15 drops/60 minutes which is a conversion short cut for iv drip rates that i learned in school). i would get the same answer as you did.

for most other things the "dose desired divided by the dose on hand times the amount on hand" works very quickly for me. eventually i saw how it worked for iv problems too. i also carried a small calculator after they came out on the market. i would pull a piece of paper toweling and write the figures down if i wasn't sure i was setting a problem up correctly. the more problems you do, the better you get at doing them. that's a fact. eventually, you begin to see the relationships between all these numbers.

dimensional analysis is a good tool to start with. there's really not much thinking involved in using it. it's a very mechanical, unemotional and manipulative tool. that's all it is. primarily you want to keep relationships together and express them as a ratio (fraction) when you set up a dm equation. so, if each of the fractions in the equation you create have a relationship to each other and represent one entity, a marriage, an identity, "one thing" then it doesn't matter which term is in the numerator or denominator. 100 ml/1 hour is always going to be the same as 1 hour/100 ml in a dm equation. what is important is how you are using it to get rid of other labels on other fractions in the equation. it still represents your flow rate in constructing the problem. conversion factors are always equivalents of each other, i.e. 1000 mg = 1 gram, so 1000 mg/1 gram is always the same as 1 gram/1000 mg no matter which is on the top or bottom. as long as they are both kept together in the same fraction, they are "1". basic concept in math is identities and the number 1: "any number multiplied by the number 1 results in that same number". using conversion factors is a tricked out way of manipulating that rule. with dm you can safely include two or more conversion factors in your dm equation as necessary to get to the final measurement you are looking for. with dm you want to manipulate all the ratios (fractions) in the string of them that you are creating and flip them so that certain terms end up either in the numerator or denominator. keep in mind that if "drops per minute" is to be how your final answer is expressed, that this is actually a ratio, or a fraction, with "drops" in the numerator and "minute" in the denominator. the actual working of the math becomes a secondary concern and the numbers are just along for the ride.

the one very important thing that you do have to be cautious of in working problems by dm is when they start to get more complicated and you are working with complex "dose desired divided by dose on hand" problems. this happens with problems where you have mg/kg/hour. the "dose desired divided by dose on hand" part becomes an entity in and of itself within your dm equation. often this entity can become two very distinct fractions that must maintain their numerator/denominator relationship. you can still flip them, but if you flip one of the fractions, you have to also flip the other fractions or the whole relationship has just been dramatically altered and your final answer is not going to be correct.

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kubivern specializes in CNS, PMHNP, EMS, ER, Instructor.

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In nursing school I was taught the "dose desired" and "dose on hand" methods, but I have always used the dimensional analysis method to perform nursing calculations. I also used the dimensional analysis method in chemistry, physics, and other scientific calculations - it works.

However, it is also the way I was taught years ago (prior to nursing), so I am sure that is a deciding factor. Of course if all else fails, I can pull out my PDA and look at my nursing software that does all the calculations for me!

The most important factor is practice the way you want to do it!

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21,306 Visitors; 6,487 Posts

At the start of each clinical rotation we had to pass a drug calc test. One instructor had me scared to death.....I had always had problems with calcs but for the first time I failed a test. She was going to give me one more chance. I went back to the school in tears, begging another instructor to tutor me. She showed me how to do calcs using DA, which I remembered from chemistry, and it clicked right away. I have never miscalculated a dosage or drip rate using DA.

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MikeyJ is a RN and specializes in Peds, PICU, Home health, Dialysis.

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I love dimensional analysis, and a few of the older nurses I've spoken with did not learn it and find it a little lengthy.

And in regards to one of the previous posters who said that DA doesn't work for more indepth calculations -- I'm curious as to where DA doesn't work well? I purchased a med calc book (not used by my school but rather just for my own information) and I flipped to one of the last chapters that focused on calculation problems commonly found in the ICU. I used DA and quickly came up with the right answer.

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2,325 Visitors; 316 Posts

I love DA in school. I've never had to use it passing meds yet. I know most nurses where I've done clinical don't use it.

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mixyRN specializes in Ortho/Neuro, Med-Surg, ICU.

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I have a math degree and I prefer to use DA for med calculations, however, my school won't give credit for it on exams. Only ratio proportion method or formula method. I actually think it's comical but whatever... the instructors are nurses not mathematicians or scientists. :)

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MikeyJ is a RN and specializes in Peds, PICU, Home health, Dialysis.

9,217 Visitors; 1,124 Posts

I have a math degree and I prefer to use DA for med calculations, however, my school won't give credit for it on exams. Only ratio proportion method or formula method. I actually think it's comical but whatever... the instructors are nurses not mathematicians or scientists. :)

Wow, how odd. I can see schools showing students both ways and allowing them to choose which works best for them. But that is odd that a school doesn't allow their students to use DA. If it works, and it is easy, why not let students use it?

At our school we are required to do all of our math requirements online, so they don't care what method you use.. although they recommend DA.

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