### Overview

- Key Points
- What is the question asking for?
- Drip rate?
- Volume to be infused?
- IV pump rate? (always mL/hr)
- Dose per time?

- Rounding
- Drops – nearest whole drop
- Rate – tenths place

- Use correct units
- Always verify appropriateness

- What is the question asking for?

### Nursing Points

#### Examples

- Order: give 1,000 mL of LR over 12 hours. At what rate should the IV pump be set?
- A patient is receiving 133 mL/hr of Normal Saline. How much NS will the patient receive in 24 hours?
- A nurse is initiating an IV infusion of regular insulin to a patient in DKA. The order is to start the infusion at 8 units per hour. The available bag as 100 units of regular insulin in 50 mL NS. At what rate should the IV pump be set?
- A nurse is preparing to administer Ceftriaxone IV to a patient without a pump using a gravity drip set. The set is calibrated at 10 gtt/mL. The order is to administer 1g Ceftriaxone in 100 mL over 30 minutes. What is the appropriate drip rate?
- A nurse is doing a safety check and notes the IV pump infusing 22.5 mL per hour of Norepinephrine. The bag says 4 mg in 250 mL of D5W. How many mcg/min is this patient receiving?

##### Study Tools

#### Video Transcript

Okay. In this lesson, we’re going to be looking at calculations that involve IV infusions. A couple of key points. Make sure that you know what it is that the problem is asking for. This could be a drip rate, which would be drops per minute. Could be volume to be infused, which you might see abbreviated VTBI, IV pump rates that are always mL per hour. Might be a dose per time. Just make sure that you know what it is that you’re looking for.

A little note on rounding. Remember that drops always need to go to the nearest whole drop. When it comes to a rate, usually mL per hour, we’re typically going to the tenths place. Now, as we’ve said before, make sure that you know the rules at your university. Now, as we’ve said before, make sure that you know the rules at your university or your school as far as what they want for rounding, but I can tell you the NCLEX NCSBN typically is going to the tenths place. Make sure that you end up with the right units. You could be looking for a lot of different things like mcg per minute, mL per hour, mcg per kg per minute. So just make sure that you know what it is that you’re looking for. Then always verify appropriateness. Does it seem too high, too low? Just make sure that it seems like an appropriate dose.

All right. Let’s do a couple examples. The first two I’m going to do both dosage formulas and dimensional analysis and the rest I’m going to do in just dimensional analysis.

The first one, the order is give 1,000 mL of LR over 12 hours. What rate should the IV pump be set? Remember, this is always mL per hour. Our formula is rate equals volume over time. Our steps, identify, convert, solve and verify. We’ve got mL, we’ve got hours. That’s what we’re looking for. We don’t need to do any conversions, so let’s go ahead and set up our formula. Our rate is going to equal our total volume over our total time, which is 12 hours. 1,000 divided by 12 is going to get you 83.33333 repeating. When we round to the nearest tenth, we end up with 83.3 mL per hour.

Now let’s look at this in dimensional analysis. Always start with what you’re looking for. Transfer your units over. What do we know about mL? 1,000 mL in 12 hours. There we go. Same thing. 83.3 mL per hour.

All right. Let’s do another one. Example number two. A patient is receiving 133 mL per hour of normal saline. How much will the patient receive in 24 hours? All right. Remember, rate equals volume over time. This is direct algebra. Let’s just insert these numbers. Our rate is 133 mL per hour equals the volume is what we’re looking for over 24 hours. Straight algebra. Times 24, times 24, these will cancel. Volume equals 133 mL times 24 hours, which is going to get us 3,192 mL in 24 hours. That’s it. That easy.

Now if you want to see what this looks like in dimensional analysis, let’s come back here and say mL equals, because that’s what we’re looking for, what do we know about mL? There are 133 mL given every hour. Transfer your units up. What do we know about hours? We’re looking for 24 hours. Again, 133 times 24. 3,192 mL in 24 hours. If you want to have an extra unit here, you could say mL per day because you know 24 hours is the day. 24 hours in a day. That’s just kind of an extra step. You really don’t need to do that.

All right. Let’s look at the next one. Again, we’re going to work with dimensional analysis from now on. A nurse is initiating an IV infusion of regular insulin to a patient in DKA. The order is to start the infusion at eight units per hour. The available bag has 100 units of regular insulin and 50 mL of NS. At what rate should the IV pump be set? All right. Automatically we know we’re looking for mL per hour. Start with what you’re looking for. mL per hour equals. Transfer your units across. What do we know about mL? We know that for every 50 mL of NS, there are 100 units of regular insulin. Transfer your units up. What do we know about units when we’ve used this piece already? Let’s use this one. Eight units per hour. Cancel units. We’re left with mL per hour, which is exactly where we want to be. Then, you’re going to multiply across the top and divide across the bottom. 50 times eight, divided by 100, divided by one gets you four mL per hour. Does it make sense? Well, we know there’s twice as many units per every mL, eight units an hour being four mLs an hour. Makes sense to me. Doesn’t seem like we’re going to overdose them with insulin.

Okay. Let’s look at the next one. A nurse is preparing to administer Ceftriaxone IV to a patient without a pump using a gravity drip set. The set is calibrated at 10 drops per mL, the order is to administer 1 g of Ceftriaxone in 100 mL over 30 minutes. What is the appropriate drip rate? Now remember, drip rate is always gtt per minute or drops per minute. Again, we start with what we’re looking for. Drops per minute equals. Transfer our top units over. What do we know about drops? Well, right here. We know that we are using a set that is 10 drops for every one mL. All right. Transfer your units up. What do we know about mLs besides the one we already used? Well, we know that there are 100 mL and that 100 mL needs to go over 30 minutes. Okay.

Here’s one little trip up place. You could also have said 100 mL is 1 g. What would that have gotten you? Well, you would then have had to say 1 g in 30 minutes and you would’ve duplicated. It would’ve been okay, but what we know here is we’re looking for this minutes. Whatever gets you to that minutes faster is the way you want to go. Okay? Cancel mL. We’re left with drops per minute. Now we’re going to multiply across the top, divide across the bottom. 10 times 100 divided by one, divided by 30 is going to give you 33.333 repeating, but we’re using drops, right? When we round drops, we round to the nearest whole drop. In this case, 33 drops per minute. Okay?

All right. Let’s do one more. A nurse is doing a safety check and notes that the IV pump is infusing 22.5 mL per hour of Norepinephrine. The bag says four mL in 250 of D5W. How many mcg per minute is this patient receiving? Start with what you’re looking for. mcg per minute. Okay. Transfer your units across. What do we know about mcg? What are we given? Well, nothing. So we convert. 1,000 mcg equals one mg. We know that’s where we’re headed. mg. Okay. What do we know about mg. Transfer units. We know that four mg is in 250 mL of D5W. Cancel mg. Are we where we want to be yet? Nope. So let’s keep going. Transfer your units up. What else do we know about mL? Well, right here we know that we’re going at 22.5 mL per hour. Cancel your mL. Now are we where we want? mcg per hour. Nope. We need to be in minutes. So we do a conversion. One hour, 60 minutes. Cancel your hours. Minutes. mcg. You’re exactly where you want to be.

So now we’re going to multiple across the top, divide across the bottom. 1,000 times four, times 22.5, divided by 250, divided by 60. You’ll notice I skipped a couple of the ones. That is a personal preference. It’s up to you. Sometimes I include them. Sometimes I don’t. Including them in your calculation just helps you to make sure you don’t miss anything. When we do this math, what we end up with is 6 mcg per minute. Again, the final step is always verify. Does this make sense? Is it an appropriate dose? Well, with Norepinephrine, we know we’re typically looking at up to 30 before we get into sepsis protocol, so 6 mcg per minute, that’s a great dose of Norepinephrine.

That’s it for your IV infusion calculations. Now, it’s up to you. You can use the formula rate equals volume over time or you can use dimensional analysis. Either way, just make sure that you’re using the appropriate units, that you’re converting, and you’re getting what the problem’s actually looking for.

All right, guys. Make sure you check out all of the other med math lessons as well. We love you guys. Go out and be your best selves today. As always, happy nursing.