Dimensional analysis for dosage calculations


I’m in nursing school. I can do the fractional method just fine, but dimensional analysis is just not something I can wrap my head around. I’m not the “plug this number in here, there, etc.” person. I know the metric conversions.

I just have no idea how to set up the dimensional analysis equation.

How do you guys know what the second fraction is, how to write it, etc.?

It makes zero sense to me unless I’m watching a video, but I want to be able to do this on my own.

Thanks in advance.

In: 1

I always started by writing what I need to end up with. For example, ml/dose. Then I’d set up my first equation to start with ml. Then you just need each equation after that to cancel out the previous one until the only units you’re left with are ml/dose. So after ml/dose you could follow with 20mg/5ml then 4mg/dose. Hope that kind of makes sense, it’s difficult to explain without writing it out.

What do get if you divide 2 by 2? You get 1. What if you divide 3 by 3? You get 1. What if you divide x by x? You get 1.

What if you multiplied 2 by 1? You get 2. Etc. Multiply any thing by 1 and the thing doesn’t change.

2.2 lbs = 1 kg. That equals sign means they are the same thing (they’re both “x”). If I was holding 2.2 lbs of bananas, then I could say that I was holding 1 kg of bananas. The bananas don’t change, just how I describe them. If I divided 2.2 lbs by 1 kg, I would get 1. If I divided 1 kg by 2.2 lbs, I would still get 1.

“Per” is another way to say “divided by”. 2mg per kg is the same as saying 2mg divided by 1kg.

Dimensional analysis is just dividing everything by itself to get 1, and then multiplying by 1. The goal is to end up with units you need.

EX: A 150 lb patient needs 2mg/kg of medication. We need to convert first to kg, then to mg. I’m going to multiply 150lbs by 1 to get kg, then by a different 1 to get mg. The first 1 I will use is 1kg/2.2lbs. I use this 1 instead of 2.2lbs/1kg because it puts the lbs on opposite sides of the dividing line. This way they make their own little 1, and disappear (cancel out). The next 1 I multiply with is 2mg/1kg. Once I have written down the original number and the two 1s I’m multiplying by, I just multiply all the top numbers together (150lbs *1kg *2mg), then the bottom numbers (2.2lbs *1kg) then divide the top by the bottom (300lbskgmg/2.2lbskg) cancelling out the units that appear in both (300mg/2.2). 136.4mg of medication.

This would be easier to see if you wrote it all out so instead of a / for divide, you had a horizontal line.

That’s dimensional analysis in a nutshell.

For more, I recommend [Khan Academy](https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:rate-conversion/v/dimensional-analysis-units-algebraically)