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### Overview

### Nursing Points

#### General

#### Implementation

#### Examples

**Reference Links**

- Dimensional analysis works for any type of med math problem

- Benefits
- ONE formula/process, not many
- Works for all types of calculations
- No need to convert separately
- Rounds at the end (safest!)

- Identify, Convert & Solve
- Start with what you’re looking for
- Transfer units across
- Insert what you know, Convert if you don’t
- Repeat 2 & 3, Cancel units until desired result
- Multiply across the top, divide across the bottom

- Verify

- 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

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

- The nurse notes the patient has Dopamine infusing at 39.3 mL/hr. The bag says 400 mg in 250 mL. The patient weighs 192 lbs. How many mcg/kg/min is the patient receiving?
- 12 mcg/kg/min

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In this lesson we’re going to talk about dimensional analysis. I wrote med math made easy here because we honestly believe that dimensional analysis is the best way to go when it comes to dosage calculations.

The biggest benefit I see to dimensional analysis is that it means you only have to know ONE process. Other ways teach you multiple different formulas to learn. And – while we think we’ve done a pretty good job breaking that down for you in the basics of calculations lesson, we still believe that having only one way to do things every time is way better! The other benefit is that dimensional analysis works for all types of calculations – simple, complex, weight based, lots of conversions or super straight forward – it still works! And there’s no need to do any separate conversions or rounding in the middle of the process. Everything happens with ONE final calculation. We’re going to talk you through the process of dimensional analysis with the same problem we used in the Basics of Calculations lesson, then I’m going to show you how it work for simple AND complex problems by working a few out. In the other med math lessons on the different types of problems, we will use this method, because we honestly feel like it’s the best way to go.

So when you start dimensional analysis, you always start with what you’re looking for and build your equation from there. So let’s read this problem. The 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? So first things first – identify our variables – what are we looking for? Setting a rate on an IV pump always means mL per hour – so write that here, then write an equals sign because we’re going to be setting up an equation. Okay – step 1 – start with what you’re looking for.

Once you’ve got that, the next step is to transfer the units across. So, in this case, we’re going to take the mL from the left and shift it directly over to the right. This will help set us up for success so that we know we end up with the right units in the right place.

Once we’ve transferred our units over, the next step is one you’ll just keep repeating – insert what you KNOW, convert if you don’t. What I mean by what you KNOW is if you have anything provided about those units. So – does the problem say anything about milliliters? Actually – no. So – if you don’t KNOW anything about that unit – we use a conversion. Do we have anything in here that could use a conversion? Yes – we have Liters. So we’re going to convert – 1,000 mL equals 1 L. Now – here’s where we really start to build out this problem…

We’re going to repeat this process of transferring units across, inserting what we know, and converting if we don’t UNTIL we can cancel enough units out to find what we’re looking for. Remember, if you see the same units on the top and the bottom on this side of the equation, they will cancel. So we’ve already got our first 1,000 mL equals 1 L. So now we transfer units – put liters up here. Then insert what we KNOW about liters – what we KNOW is that in 1 L of NS, there is 100 mEq of KCl. So, now we have liters on top and bottom and it cancels. Now we have mEq down here – transfer the units up – insert what we KNOW about mEq. Sometimes I find it helpful to cross out information once I’ve used it because we won’t use it again. So – I’ve already used THIS mEq – so now I need to use the other one. So what I know is 60 mEq – and what about that 60 mEq? It needs to go over 4 hours. So now I have mEq on top and bottom, so it cancels. Remember our goal here is to cancel units until we end up with what we are looking for. Over here, we wrote what we’re looking for – mL/hr. Now, you can see what we have left after we cancel is mL on the top and hr on the bottom – everything else is cancelled, so we are good to go!

Now here’s the fun part and here’s why I love this so much – now you only have to do ONE calculation. Remember this phrase – multiply across the top, divide across the bottom. You’re going to go into your calculator and type this: 1,000 times 1 times 60 divided by 1 divided by 100 divided by 4. Do you see that? Multiply across the top, divide across the bottom. Press equals and you’ll end up with 150. Remember our last step is always to verify…

So we insert the right units – in this case mL/hr – we round if necessary – then we ask ourselves if this makes sense. In 1 L there’s 100 mEq, we’re only giving 60 – so in that 4 hours it should be less than 1000 – 150 x 4 hours is 600, so that all seems right to me.

So a recap of these steps – Start with what you’re looking for, transfer units across, insert what you know, convert if you don’t, and repeat those steps until you cancel enough units to get what you want. If you have seen the basic calculations lesson, you know I give 4 steps. Identify, Convert, Solve, and Verify. These 4 steps here are your identify and convert steps. Step 5 – multiply across the top, divide across the bottom – that’s your solve step. Then the last step is always to verify! Same general process, just a little different in the execution. Now I want you to see how amazing this is – it works for super simple and super complex problems.

Let’s look at a simple one first – the provider orders 650 mg of Acetaminophen PO times 1 dose. You have 325 mg tablets on hand. How many tablets should be given? Okay – start with what you’re looking for. Tablets per dose. You’ll see why I add the “per dose” part here in a second. Then, we transfer our top units across – tabs. Now, what do we KNOW about tabs? Well – we know that 1 tab is 325 mg, right? Great – now we transfer the units up again – now, what else do we know about mg? We already used this one – so now we use the 650. So what do we KNOW about 650 mg? Well, we know there’s 650 mg in one dose! So we cancel the two mg units and what are we left with? Tabs per dose – so have we gotten to what we want? Yep! Now, multiply across the top, divide across the bottom – 1 times 650 divided by 325 divided by 1 = 2 tabs per dose. Verify – does that make sense? Yep! Now – those of you who love math are probably thinking “this girl is crazy, she keeps multiplying and dividing by 1! You don’t have to do that!” – well, you’re absolutely right, you can leave the 1’s out mathematically, but I like to keep them in because it makes sure I don’t accidentally skip over something. So that’s just a personal preference!

Now, we’re going to look at a more complex problem. We have a whole lesson on more complex calculations – so don’t let this confuse you too much, I just want to show you that it’s possible to do. Then – go check out that lesson for a bit more of a talk-through. Okay, The nurse notes the patient has Dopamine infusing at 39.3 mL/hr. The bag says 400 mg in 250 mL. The patient weighs 192 lbs. How many mcg/kg/min is the patient receiving? Start with what we’re looking for – mcg per kg per min. Here’s a big tip – if you have two “pers” – they both go on the bottom. Only 1 unit goes on top. So mcg on top, kg per min on the bottom. Transfer mcg across – do I KNOW anything about mcg? Nope – I need to convert to mg. 1,000 mcg equals 1 mg. Transfer mg over, what do I know 400 mg in 250 mL. Cancel mg. Transfer mL up, what do I know? 39.3 mL per hour. Cancel mL. Now I have hr – what do I know? Well – I know I’m actually looking for minutes here – so let me go ahead and do that conversion – 1 hr equals 60 minutes. Cancel hours. Now – have I gotten to what I want yet? Nope – I still need kg on the bottom here. I have mcg/min, but I need mcg/kg/min. So – I’m going to go ahead and put kg on the bottom, because that’s where I need it – I don’t know anything about kg so I need to convert – 1 kg is 2.2 lbs. Now, what do I know about lbs? The patient weighs 192 lbs. Now lbs cancel. NOW am I left with what I need? Yep! Multiply across the top. 1,000 times 400 times 3.3 times 1 times 2.2 divided by 1 divided by 250 divided by 60 divided by 1 divided by 192. I end up with 12.00833. We typically only round to the tenths place – so we will round to 12, add our units – mcg/kg/min, and ask ourselves if that makes sense. You could do the problem in reverse to see if you get 39.3 mL/hr. I like to also just think about normal dose – which is 5-20 mcg/kg/min, so 12 makes sense. Again, check out the complex calculations lesson to see more like this.

So remember the benefit of dimensional analysis is that we can do our calculations the same way every time, it works for every type of problem, from simple to complex. Ultimately, though, choose the method that works for you – it’s all about being SAFE and getting the right dosages for our patients.

Make sure you check out the individual lessons on oral, IV, injectable, and complex med math calculations to see more examples worked out for you. And check out the cheatsheets and questions attached to this lesson. Now, go out and be your best selves today. And, as always, happy nursing!!

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