### Overview

- It’s basic algebra!

### Nursing Points

#### General

- Three Main Formulas
- Dosages
- Dose = Want/Have x In

- Infusions
- Rate = Volume/Time

- Drip Rate
- Drip Rate = Volume/Time x Drip Factor

- Dosages
- Four Steps
- Identify
- What is the order?
- What do I have available?
- What am I looking for?
- What formula should you use?

- Convert
- Units should match what you’re looking for
- Weight-based conversions
- You MUST know your conversions

- Solve
- Use the appropriate formula
- May need more than one

- Verify
- Round appropriately
- Appropriate units in your answer
- Does it make sense?

- Identify

#### Examples

- Provider orders 650 mg Acetaminophen PO x 1 dose. You have 325 mg tablets on hand. How many tablets should be given?
- 2 tabs

- Give 1,000 mL NS over 8 hours. What rate should you set the pump?
- 125 mL/hr

- You are administering 120 mL over 30 minutes with a drip set that has a drip factor of 15 drops per mL. What is the drip rate?
- 60 gtt/min

- Provider orders 60 mEq of KCl IV to be given over 4 hours. The bag contains 100 mEq in 1 L of NS. What is the rate you should set on the pump?
- 150 mL/hr

##### Study Tools

#### Video Transcript

In this lesson we’re going to start with the basics of med calculations and give you a good foundation moving forward.

Guys – first and foremost, we want to tell you that med math does NOT have to be your arch nemesis! I know it’s something that a lot of people struggle with and we promise we are here to help! I’m not going to lie, I’m a big nerd and I actually love this stuff! What I’m going to do for you is show you the three main formulas you need to know – that’s right – only THREE! Then, I’m going to give you a simple 4-step process for all of your calculations. The purpose of this lesson is to establish a foundation and the process. We also have a whole lesson on dimensional analysis if that’s a method you prefer. Then we have individual lessons for different types of calculations with lots of examples, so make sure you check those out.

Okay – let’s get started. There are only THREE main formulas you need to know. There are some rare times you may need something different, but for 95% of what you’re going to need, these three will cover it. The big thing to know here is that this is all just basic algebra. I know sometimes we see the word problems and we get intimidated by the medication math aspect of it – but it’s not complex calculus – we’re just solving for X – basic algebra. The three main formulas are for dosages – so like how many tabs to give, how many milligrams, etc., infusions – so rates, volumes, times, etc., and drip rates – which is how many drops per minute. Let’s look at each one.

Your first formula for dosages is this – the dose equals what you want – so that would be what’s ordered or the desired amount – over what you have – so that would be the available form of the drug – times what it’s in – so what form dose this drug come in. Example. Provider orders 650 mg of Acetaminophen, you have 325 mg tabs. How many tabs would you give? It wants to know our dose – or how many tabs we will give. What we WANT is the order – 650 mg. What we HAVE is 325 mg – and the form it’s in is 1 tab. So 650 mg over 325 mg times 1 tab. The best part about these formulas is that you can actually solve for ANY part of this formula – it’s just basic algebra. So let’s say a patient reports taking 2 Acetaminophen tablets, they are 325 mg tablets – what total amount did the patient take? Well the dose the patient took is 2 tabs. The form we have is 325 mg and it’s in 1 tab. So now the “WANT” part is what we solve for. Again – basic algebra. Divide by 1. Multiply by the 325mg – now you get 650 mg. So you can solve for any of these parts!

Let’s look at the next one – infusions. This is a great formula because you can solve for rate, volume, OR time with this ONE formula – again it’s just algebra. So remember Rate equals Volume over Time. Usually, if we’re talking about IV pump infusions, we usually see mL per hour. But you could also see mL per minute or Liters per minute or liters per hour – or ANY volume per ANY unit of time. Just make sure that all of your units match what you’re looking for! So if I say we’re giving 1000 mL over 8 hours, what’s the rate to set on the pump? ANY time you see – set on the IV pump, it will be mL per hour. SO – 1000 mL over 8 hours = 125 mL/hr. We could also rearrange this formula – if you multiply by time, you’ll see that volume equals rate times time. Then, we can divide by rate and see that time equals volume over rate. So if you know this ONE formula, you can figure out Rate, Volume, AND Time!

The next formula is actually a specialty version of the last one. Instead of just looking at general infusion rates, we’re actually looking at Drip Rates. This is the number of drops (or gtts) per minute – we use this when we’re hanging infusions over gravity instead of with a pump. It doesn’t happen very often, but it can be very helpful if for some reason you don’t have a pump available. What you’ll notice is that our rate equals volume over time is still here – we’re just specializing to add the “drip” part. So now it’s “Drip Rate” = Volume over Time (in this case minutes), then we multiply it by what’s called the Drip Factor. Every set of tubing we use has a drip factor that tells us how many drops there are in one milliliter. Most standard IV sets are 10 drops per mL and ‘micro sets’ are usually 60 drops per mL. So, let’s do a really quick example. You are administering 120 mL over 30 minutes with a drip set that has a drip factor of 15 drops per mL. So volume – 150 mL over time – 30 minutes times drip factor 15. So what we get is 60 drops per minute. Always round to the nearest whole drop.

Okay – so those are the basic formulas – now I just want to run through this 4-step process – we really think this will help you with your med math. And I’m going to use one example through these 4 steps so you can see what it looks like. The four steps are Identify, Convert, Solve, and Verify. I remember “I Can Secure Victory – with med math!!”

Step 1 is Identify – this is all about identifying your variables, what are you working with, what are you looking for. So – what is the order? What is available? and what is it that we are looking for? – based on that you can decide what formula to use. So here’s our example – The provider has ordered for you to administer 60 mEq of KCl IV over 4 hours. The bags from the pharmacy contain 100 mEq in 1 L. What rate should you set the IV pump at?

So what’s ordered? 60 mEq of KCl over 4 hours – so I have a volume and a time. What do I have available? 40 mEq in 250 mL. What am I looking for? The question was what rate to set the pump at – which is always in mL/hr. So now I know that I have a volume and time and I’m looking for a rate, so I’m using the infusion formula. But I also need to determine how much of that bag I’m giving, so I’ll use the dosage formula as well.

The 2nd step is to convert. The goal here is to get ALL of our units to match. If I am looking for mL/hr – I need everything in those units. My available amount was 100 mEq in 1L. I need to convert those Liters to mL. So instead I know it’s 100 mEq in 1000 mL. This is also where you can do your weight-based conversions as well. You HAVE to know your conversion factors – we have a whole cheatsheet on it attached to this lesson. You just have to know them. One big note here is about rounding. Here at NRSNG, our official stance is that you should never round anything until the very end – that ensures the most accuracy and is especially important in pediatric dosing. However, we know that some schools request that you convert along the way – just make sure you know what your school requires when it comes to your school exams.

So, once you have your information and you’ve done your conversions it’s time to solve. For this example, we need to determine how many milliliters to give, then what rate it would be at. So our dosage formula – Dose = what we want – 60 mEq of KCl, over what we have – 100 mEq – times what it’s in – 1000 mL (remember we did that conversion?). So the total volume we need to give is 600 mL. NOW we can transition to the infusion formula to find our rate – Rate = volume – which we now know is 600 mL over time, which we know is 4 hours. 600 divided by 4 = 150 mL/hr.

The very last step is Verify – at this point you’ll do any rounding you need to do. You’ll triple check that you have the appropriate units – in this case mL/hr. Then, you’ll ask yourself if it makes sense – if we had 100 mEq in 1 L and we’re giving 60 mEq – the 600 mL made sense and dividing that over 4 hours is 150 mL/hr, so that makes sense. If you had missed a conversion and had used 1 instead of 1000, you would’ve come up with 0.15 mL per hour. If you ask yourself if that makes sense, then definitely not – doing 0.15 mL per hour for 4 hours doesn’t really make sense. If your answer doesn’t make sense – go back to the beginning and check everything.

So remember these three main formulas – dosage, infusions, and drip rates. Remember the four step process – identify what you have and what you need, convert to matching units, solve using the appropriate formula, and verify that you’ve rounded, used the right units, and that everything makes sense. Make sure you know your conversions and know your rounding rules for your school. Like we said, the SAFEST way is to round at the END of a calculation. And more than anything, remember that we believe in you – you’ve GOT this! You can do it! Just practice, practice, practice!

Make sure you check out all the resources attached to this lesson and keep practicing these problems. Don’t forget to check out the other med math lessons as well. Now, go out and be your best selves today. And, as always, happy nursing!!