Hi. This is Cathy with Level Up RN. In this video, I'll be going over a variety of dosage calculation problems that involve an IV pump. I'll be solving these problems on my whiteboard using three different methods including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations, and our workbook will help you do just that. For more information about our workbook, you can click here. But in a nutshell, our workbook contains all different types of dosage calculation problems that you are likely to encounter in nursing school. And we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
So in this first example, we have an order to infuse one liter of normal saline over six hours by infusion pump. And we need to know what rate in milliliters per hour we should set the pump. And we want to round our answer to the nearest whole number. So we want our rate in milliliters per hour, and the volume we need to infuse is one liter, not milliliters. So the first thing we need to do is convert our one liter to milliliters. So one liter equals 1,000 milliliters. Then we can take that volume, 1,000 milliliters, divide that by the infusion time, which is six hours. And then that is equal to 166.666 ongoing. Because we need to round this to the nearest whole number, this becomes 167 milliliters per hour. So that's the rate that you would program the infusion pump to in order to carry out that order.
All right. Let's work through our second IV pump example. In this example, we have an order for ampicillin 500 milligrams in 50 mls of normal saline that needs to infuse in 30 minutes. At what rate in milliliters per hour should we set the pump at? And we need to round to the nearest whole number. So when we are calculating the rate, all we care about is the volume and the infusion time, so this dose is irrelevant. We don't care about the dose. All we care about is that we have 50 mls, and we need to infuse it over 30 minutes, but we need our rate in milliliters per hour. So we need to first convert 30 minutes into hours. So 30 minutes equals 0.5 hours. So we take 50 milliliters, which is the volume, divide that by 0.5 hours, and then calculate this out, we end up with 100 milliliters per hour. And that is the rate that we would set the pump at. And just checking our rounding now, it says to round to the nearest whole number. We're already rounded, so we're already at a whole number. So that is how you would solve this problem. Again, keep in mind, when you're given dose calculation questions, not all of the numbers and things thrown at you matter for the question being asked. And in this case, we did not care about the 500 milligrams. We only cared about the 50 milliliters and the 30 minutes.
Let's work through our next example problem that involves IV pump breaks. So with this problem, we have an order for potassium chloride 40 mEq IV piggyback to be delivered at a rate of 10 mEq per hour. What we have available to us is potassium chloride 30 mEq in 500 milliliters of normal saline, and we need to round all of our answers to the nearest whole number. And we have two questions to answer. The first question is, how many hours will it take for the ordered dose to be administered? So the ordered dose is 40 mEq, right? And we are ordered to give it at a rate of 10 mEq per hour. So if we multiply this out over one hour, we need to give 10 mEq, this will take four hours. And you might be able to do this part in your head as well. If you know you need to give it at a rate of 10 mEq per hour and you have 40 mEq to give, it will take four hours.
All right. So that was part A. Let's work on part B. Part B is asking us at what rate would we set the IV pump in milliliters per hour to deliver the ordered potassium chloride safely, okay? So we're going to solve part B three different ways. I'm going to solve it with dimensional analysis first, which is the most efficient way to do it, but I'm also going to solve it with ratio proportion as well as the formula method. So let's first solve it with dimensional analysis. So we know we need to give this medication at a rate of 10 mEq per hour, but we are looking for milliliters per hour. So I'm going to take this rate and multiply it by the available concentration. And I'm going to make sure I put milliliters on top and mEq on bottom such that my mEqs will cross off, and I'll be left with milliliters per hour. So if I multiply this out, I end up with 167 milliliters per hour. And that's how you would solve part B of this problem using dimensional analysis.
All right. Let's now solve this same part using ratio and proportion. I'm going to erase my board here to give me some more room. All right. So again, this is part B. Now we're using ratio and proportion. So I want to give this medication at a rate of 10 mEq per hour, but I'm looking for milliliters per hour, so I need to find out how many milliliters it takes to give 10 mEq. So I'm going to set up my ratios. On one side of the equation, I'm going to include my known ratio, which is my medication concentration. So I have 30 mEq in 500 mls of normal saline. And I want to find out for 10 mEq, how many milliliters is that? All right. So I'll do my cross-multiplication now. I end up with 30X equals 500 times 10. And then if I solve for X, so 30X equals 5,000, and then X equals 5,000 divided by 30, this equals 167 milliliters. And this is rounded. So I know that in order to give 10 mEq, it takes 167 milliliters. So my rate in milliliters per hour would be 167 milliliters per hour.
All right. Let's now solve part B using the formula method. So write that up there. So with the formula method, we have desired over half times the vehicle. And again, we are given a rate of 10 mEq per hour. We want to figure out milliliters per hour, so we need to know how many milliliters it takes to give the patient 10 mEq. So what we desire is 10 mEq, and what we have is 30 mEq in 500 mls of normal saline. That is our vehicle. So if we do this math, we end up with 167 milliliters. Again, that amount is going to be administered over an hour, so our rate is 167 milliliters per hour. And that's how we would solve this part with the formula method.
Okay. You guys ready for our next example problem involving IV pumps? With this problem, we have an IV pump that is running at 125 milliliters per hour. How many hours will it take for a 500 milliliter bag of normal saline to infuse? So we can solve this problem with dimensional analysis or ratio and proportion. So using dimensional analysis, we have our 500 milliliter bag, and it's running at 125 milliliters per hour. So if I multiply our volume times the rate, making sure to put my hours on top and my milliliters on bottom such that my milliliters cross off and I'm left with hours, then we end up with four hours. That's how long it would take to infuse. We could also do this with ratio and proportion. So we have a rate of 125 milliliters per hour, and we're wondering for 500 milliliters how long that will take. So if we set up this ratio and then cross-multiply, we end up with 125X equals 1 times 500. So 500X equals 500 divided by 125, X equals 4, so four hours. Get the same answer as you did up here, just two different methods. And that's that problem.
Let's now work through our last IV pump calculation problem. In this problem, we have an order for heparin 10,000 units in 250 milliliters at 40 milliliters per hour. How many units are infused over four hours? Round to the nearest whole number. So this is our drug concentration right here, 10,000 units in 250 mls of solution. And we're not going to freak out about units. We're going to treat them just like we would milligrams or grams. It's just another unit of measure. And then our ordered rate is 40 mls per hour. So we're looking for units. So I'm going to first solve this problem using dimensional analysis, which is probably the most straightforward way to solve the problem. So because I'm looking for units, I'm going to go ahead and write down my available concentration, which is 10,000 units in 250 ml. Then I can multiply this times the rate that the IV pump is running at. And I want to carefully place my unit. So I want to put 40 ml here and one hour here so that my mls cross off. And then per the problem, I am infusing this over four hours, so I'm going to multiply times four hours, and my hours will cross off. And I will be left with units, the number of units that are infused over four hours, which is exactly what I'm looking for. So if I calculate this out, I end up with 6,400 units. And that is already a whole number, so we're good to go as far as rounding.
Now, if we want to solve this with ratio and proportion, we would need to first figure out how many units are in 40 ml. So if we set up our ratios, we have 10-- sorry, not 1,000, 10,000 units. 10,000 units in 250 ml. That's our drug concentration. That's our known ratio. And we are trying to figure out how many units are in 40 ml. So if we cross-multiply here, we have 250X equals 10,000 times 40, so 250X equals 400,000. X equals 400,000 divided by 250, and this equals 1,600 units. So we just figured out that there are 1,600 units in 40 ml. So we are infusing 1,600 units per hour. And the question asked us, how many units are we infusing over four hours? So we just take this times four, and we get 6,400 units. So you can see this kind of took us two different steps. We had to first figure out how many units were in 40 ml, and then figure out how many units were infused over four hours versus this single step with dimensional analysis. This is why I prefer this method, but I always want to show the alternative method for those who use that as well.
