**Overview**

Dimensional analysis is one of the most commonly used techniques, it is easy to comprehend making it easier to work out mathematical problems for drug calculations.

**Nursing Points**

#### General

- 1. Heparin
- 12/units/kg/hr

- 2. Vasopressors
- Levophed 1mcg/kg/min
- Dopamine 10mcg/kg/min

- 3. Amiodarone
- 1mg/min then 0.5mg/min

- 4. Antibiotics
- Zosyn 3.375 g IV in 50 mL of NS over 30 minutes Q 8 Hours
- Ancef 500mg IV in 100 mL of NS over 30 minutes

- 5. Normal Saline
- 1 Liter of NS over 8 hours
- 1/2 NS in 500mL over 4 hours

##### Study Tools

#### Video Transcript

Hey guys, in this lesson we’re going to do some interactive drip calculations and work out some math problems and we’re going to be using the dimensional analysis method. So let’s go ahead and get started. So the first one I want to talk about is Heparin.

So our order for heparin is 12 units per kg per hour. So let’s go ahead and work that one out now because we know that this is an infusion I need to set up my problem up as milliliters per hour because that’s the only way to fix the pump. So when a problem starts out with milliliters per hour, I always need to put milliliters first in my next little section. So in order to do that, I need to know what’s available. Usually heparin comes in a 500 ml bag and it contains 25,000 units of heparin in it. So I’m going to put 500 milliliters over 25,000 units.

In dimensional analysis rules in order to cancel something out, whatever is down here is going to be up here. So I have 12 units per kg and let’s say my patient weighs 70 kilos so I put that over an hour. So if I cancel things out, I cancel units, I cancel kilograms and I’m left with milliliters per hour. So if I multiply 500 times 12 times 70 it’s going to give me a really big number, but I’m going to have 420,000 divided by 25,000 and it’s going to give me 16.8 mls per hour. All right, simple.

Let’s do another one. So this next one I want to work out is going to be Levephed. Our order for Levophed on this particular one is going to be one microgram per kilogram per minute. So again, because this is an infusion, we’re going to start our problem with milliliters per hour. I need to know what to put here. It’s milliliters. So in order to do that, I need to know the concentration of the medication that I’m going to use. So usually levophed, comes in a 250 ml bag and it contains four milligrams. So I’m going to put 250 mls over 4 milligrams.

Well, I know that I need to start with milligrams, but I need to convert it over to mcgs because my order is in mcgs. So I’m going to have to do some conversions. So one milligram over one that was in mcg, and now I can put my mcg up here over kilograms. Uh, let’s say this patient weighs 80 kilos so that is over a minute, but I’m solving this problem an hour, so I need to convert that over.

Okay,

so now let me make sure I can cancel everything out. Milligrams and milligrams cancel out mcg and mcg cancel out kilos and kilos cancel out. And that’s supposed to be a minute, minute and minute cancels out. So I am left with hour and milliliters, which is perfect. It’s what I wanted. So I multiply 250 times, one times one times 80 times 16, I end up with a big number. And then I need to multiply four times a thousand and I end up with a smaller number of 4,000. And when I divide this out, I get 300 milliliters per hour. If you need to rewind this little section to do this problem over and over again, please do that. My best advice is if it’s milliliters per hour, your first segment is going to start with mls and whatever’s here you have to put up here so it cancels out. Let’s do another one. This one is going to be Amiodarone and it’s going to be at one milligram a minute.

So again, it’s an infusion. So we’re going to start with milliliters per hour. I need to know what is available because I’m going to start with mls. Since mls is here, I have to start with mls there. So I need to know what’s available. So in this particular case with Amiodarone, I have 1.8 milligrams per every ml. And depending on the bag, some bags may contain 250 milliliters. Others may contain a hundred mls. It just depends. Um, but the concentration is usually that. So we’re going to do one ml and it has 1.8 milligrams. My order is one milligram a minute.

Well I need to change that to hours. So 60 minutes over one hour and let’s go back and cancel things. Milligrams and milligrams, minutes and minutes. And I am left with mls and hours, which is what I’m trying to solve for. So one times one times 60 equals 60 over 1.8. When you divide that out, it gives me 33.3 mls. All right, let’s do a couple more. A lot of students always get antibiotics confused. Keep this simple. If I have an order for Zysyn 3.375 grams in 50 mls of normal saline over 30 minutes. So again, this is an infusion. What am I solving for? Ml per hour. Well, what do I know? I know I have a 50 ml bag and I need to run that over 30 minutes.

So this one is very, very simple. So 30 minutes. So here, I need to convert it over to hours because if I cancel this out, I have mls and hours left. So 50 times 60 equals 3000 and I divide that by 30 because 30 times one is 30 and I get 100 mils per hour. This is where a lot of people get confused. They want to add this in here and there’s absolutely no need to, if I were to have my problem set up with 50 milliliters over 3.375 grams, well from what I’ve told you about dimensional analysis, whatever is down here, I have to start up here. I have no other grams, so I would not be able to cancel this out. So with antibiotics, there’s no need to add the dosage in there. Just how long to run it for.

Okay, so keep these very simple and let’s go ahead and do another one. These are a little bit more simpler. So let’s say we have normal saline, one liter over eight hours. So it’s an infusion, so milliliters per hour. And I know that one leader is at a thousand mls over eight hours. That’s it. And then I’m going to divide and it’s going to be 125 milliliters per hour. That’s all. There’s nothing else to add in the problem. So keep these simple.

Okay, so a little recap. Most math problems that nursing schools teach nowadays are with dimensional analysis. It’s an easier method of instruction to do, math problems with medications because it’s a step by step process, whatever is here, if that’s your problem and this is milliliters here you start with milligrams will usually milligrams will go up there. If you have kilograms here will kilograms will go up here so that it cancels each other.

That’s what makes it a step by step process that it’s easier to eliminate what you don’t need. And it’s very important when you do this type of medication, problems that you know the concentration of the medication because then you know exactly what to plug in, especially right here, right here. So always know the concentration of the medication so that you set your pumps up correctly. And never just rely on the pumps. Pumps are machines. They can fail. Always double check your math.

So I hope that this lesson has helped you guys with some simple and quick and easy dimensional analysis problems and how to set them up. If you need any additional resources, make sure you check out our pharmacology section and in our med administration for any additional help. So as always, make sure you guys go out and be your best selves today and happy nursing.