# Saved By the Med Math

**Introduction**

Let’s play a game. Put up a finger if: you have ever froze when having to calculate a dose for a medication that wasn’t a typical dose and you had an “oh shit” moment. Put up a finger if: you have ever had to convert mcg to mg and you didn't know which way the decimal moved. Put a finger up if: you have ever had the same medication come in different vial concentrations. Put a finger up if: you have ever had to reconstitute a medication to make a different concentration than the one you have. Put a finger up if: you have ever had to give a dose based off of kilograms but you only knew the patient's weight in pounds. Put a finger up if: you have had to dose a pediatric patient at 10-15-20 kg. Hopefully you had 5-6 fingers up because if you didn't, I'll put up one finger for you and say "bless your heart." ♥️ 🤪👍

Medication errors can occur at any point from the moment you decide we want to give a certain drug to the time that we actually administer the drug. That includes when we reach for a vial with a certain name, mixing the correct dose in the correct amount of solution and administering the correct concentration at the correct rate. THERE IS SO MUCH ROOM FOR ERROR! In fact, there FDA reports that there are more than 100,000 reports each year of suspected medication errors. That’s 274 errors a day, but on the bright side only 273 on leap years. 😏 (1)

Today’s blog is meant to give us tips and tricks on how to do accurate, safe med math. As with any thing, there is more than one way to skin a cat. These are the equations, and tips and tricks that I use for my daily med math. Hopefully they help, as seeing someone else’s way of “skinning the cat” might be helpful.

__Units of Measurement:__

All units be on the lookout, we have a 2319… Ope, sorry, corny joke to break the ice. Let’s talk about Units of Measurement guys! Did someone say history lesson? No? Ok, but since we are talking about history... Let's do a history lesson!!!!! (I love history, and I wrote this paragraph on lots of caffeine.... 😬)

History Lesson: The earliest measurement of weight was based on objects being weighed against another object. Length was based off of the human body, such as the length of a stride or a cubit. A cubit is the length from the tip of your finger to your elbow. You can see how there could be hundreds of thousands of variations in measurements with this method. (4)

Today we have a very set system of measurement. A system of measurement is defined as, “A collection of units of measurement and rules relating them to each other.” (3) The Metric system is the primary system of measurement that we use as medical professionals. Three main units of the metric system include; Meter, Gram and Seconds.

There is a small variation that the United States is bad about, and that is the use of the Imperial system that includes pounds among other measurements. This poses a problem for medical providers because we need to know how to convert to the correct unit for our med-math equations. Not only do we have to know conversions from the imperial system to the metric system, we also need to know our way around the metric system to help accurately calculate medication dosages. Today, I am going to touch base on the main units of measurements that we use which include: Time (seconds-minutes-hours), mass (micrograms, milligrams, grams, Kilograms, and pounds) and Capacity (Milliliters, litters). To do accurate med math we first have to realize that we should be working in the same unit. To do that, we need to know how to fluidly work our way to and from varying units. If we need mcg, then we need to be working in all mcg, not mcg and mg. This is where mistakes are made. Knowing how to do conversions is SUPER important.

**Pounds to Kilograms:**

2.2 lbs = 1 Kg

Example: 30lbs =13.6 Kg

PEARL: Whenever converting from Kg-to-lbs or lbs-to-Kg, the Kg will always be smaller.

**Milliliters to Liters:**

1000 mL = 1 L

Not much to this one: 3 L = 3000 mL

**Hours to minutes:**

60 minutes = 1 hour

There are a lot of medications based on how much of the drug you want to give per minute or the rate we want is typically over minutes or hours. You will see the “60 minutes” play a role as a “constant” in a handful of our math equations that we will discuss coming up.

**MCG-MG-G**

1000 mcg = 1 mg

1000 mg = 1 g

**PEARL:**to flow from mcg-mg-g, we move the decimal place to the left or right by 3 places. We move by 3 decimals when moving up to the next smaller or bigger unit. If we move up to the biggest unit, the decimal gets moved from 3 places to the left. The same is said when we move to the next smallest unit, the decimal gets moved 3 places to the right.

__Basic Med Math__

I call this the basic of basic med math. Medication math is fairly simple and straightforward. I was taught a super easy and simple formula while in nursing school and I have carried it with me in almost all of my medication dosage calculation. We called it the “__Want-over-have__” dosage calculation. It has been the foundation of all med math I have done.

EXAMPLE: Say we wanted to give Fentanyl. Our dose we want to give is 50 mcg via IV push. The vials come in a concentration of 100 mcg/2ml. Simple math for sure but let’s start off with this for easy math and something easy to follow. You need three things for this formula to work.

1. The dose you want- 50 mcg

2. The dose you have- 100 mcg

3. The volume it comes in- 2 ml

NOTE: See how the (mcg) on top and the (mcg) on bottom cancelled each other out? Leaving only (mL) as the remaining unit once the problem is solved.

__Dosage by weight:__

As critical care providers, we do a lot of weight-based dosages. Of course we usually estimate the patient in pounds, but remember in medicine, we do weight-base dosing off of the metric system which uses kilograms. We have already discussed that 2.2 lbs = 1 kg and a Pearl we can take away from that is that the Kg should always be less than the lbs after you have done your weight conversion.

What I want to touch base on right now is a super cool trick that I learned. I have flown for two flight programs. One flight program doses their Norepinephrine and Epinephrine in mcg/kg/min and the other in mcg/min. Not only that, but I usually worked in one dosage form and the sending hospital would have the dose in the other form. I was taught a really cool trick by one of the flight providers that I worked with to easily flow through this.

1. Let’s say we have Norepinephrine: 4mg/250ml running at 10 mcg/min. I want to be able to titrate my Norepinephrine and I need to convert to mcg/kg/min to be in compliant with my patient care guidelines (PCGs). My patient's weight is 137 kgs

You have a dose of 15 mcg/min. What is your dose in mcg/kg/min?

15 mcg/min

**/**137kg = 0.11 mcg/kg/min

** OR**

Now you have a patient whose dose is 0.2 mcg/kg/min. What is our dose in mcg/min?

0.2 mcg/kg/min X 137 kg = 27.4 mcg/min

__Constitution of a Medication:__

The constitution of a medication is measured by the amount of the solute (medication) dissolved in a given amount of solution. I know we are all big on push dose epi, so let’s take a look at how we manipulate the concentration to obtain out 10mcg/ml syringe of push dose epi.

We have our code Epi, for lack of better terms. It’s also the 1:10,000 epinephrine or another name would be the 1mg/10ml amp of Epinephrine. Lots of names, all the same thing. Most importantly, let's break it down into simplest form

**Epinephrine: 1mg/10ml**

1000mcg/10ml --> 100mcg/1ml

If we were to give a dose of “push dose EPI” of 5-10 mcg without reconstituting it to a more manageable concentration, we would be giving 0.05-0.1 ml of our 1mg/10mL syringe of EPI. That’s stupid, guys. We can work a hell of a lot smarter! Which brings up the “push dose epi” that everyone was fan-girling over for a while, and rightfully so.

**To mix our “push dose Epi” syringe we need a concentration of 100mcg/10ml.**

- 1ml of Epinephrine (1mg/10ml) = 100mcg/1mL

- 9ml Normal Saline

__*******Push dose EPI concentration: 100mcg/10ml ---> 10mcg/1ml *******__

__Infusion math:__

In the olden days, after I walked uphill both ways to school, they taught me how to calculate an IV flow rate based on the drip factor. So when I graduated, I bought myself a drip factor conversion card to put on my badge reel and promptly figured out what the drip factor was on our free flowing gravity tubing so I could easily calculate the flow rate. Next, I would literally adjust the clamp to drips coming out of the chamber. Those were wild days, man. Now I laugh as all critical care drips should be placed on a pump. Drip factor tubing is out the door and should be used to secure an ETT if needed rather than calculate an accurate infusion flow rate. (But secretly, if you are still doing drip factor calculations, carry around a badge card with a conversion chart, it's a lifesaver!)

IV pumps have been around since the 90s when the Massachusetts General Hospital implemented the first IV infusion pump in 1996. When used appropriately, IV pumps have helped to significantly decrease medication errors. They have not completely eliminated errors. Errors still occur when dose alerts have been overridden or ignored, or when we manually bypass the pre-programed drug libraries. That being said, our jobs is very detailed oriented in many aspects, so taking the time to assure accuracy in IV medication infusion is of high priority. Not everything is an emergency, slow down. With infusions we can have a handful of variables that we need to calculate. In the next few paragraphs, we are going to be covering: time and IV infusion rate, known dose to unknown rate, and known rate to unknown dose. (2)

**Converting time to IV rate.**** **

We can give our doses over hours or minutes depending on the does that is ordered. Our dose is typically ordered in mL/hr. We can calculate for both hours and minutes with a simple med math calculation.

Dose to be given over rate in **HOURS**:

Variables that we need:

V = Volume (dose)

H = Hours

Example: 1000ml NS given over 8 hours

V = 1000ml * *

H = 8 hrs

Dose to be given over rate in **MINUTES**:

Variables we need:

V = Volume (dose) * *

M = Minutes

Constant: 60 minutes

Example: TXA. 1G/100ml given over 10 minutes

V = 100ml

M= 10 minutes

Constant (60 minutes)

**Known Dose to Unknown Rate:**

We arrive at bedside and one of two things happens, we look at our IV pump and we have a rate going in mLs/hr with a concentration known from looking at the bag, but we don’t know the dose being given… OR we know the dose we want to give but don’t know how many mLs/hr we want to give it at. Let’s start with a known dose, which means we need to figure out our rate.

**Known Dose: **

Convert to the same units

Concentration in lowest form: (dose in bag / Volume)

Plug our numbers into the equation.

__Example:__ Norepinephrine: Concentration- 4 mg / 250 ml. Dose: 10 mcg/min

4mg = 4000mcg (I moved the decimal to the right by 3!)

Concentration of bag: 16 mcg/mL

Plug our numbers into the equation.

**Bonus Problem**: You have Norepinephrine with a concentration of 8 mg/250ml. You still want a dose of 10 mcg/min. What will your rate be!? You can find this answer at the end of the Blog. Seriously try to figure it out without looking at the answer.

**Known Rate to Unknown Dose:**

Now we have arrived at bedside and we know the rate at which we are infusing. We know the concentration on the bag hanging up, but we do NOT know the Dose that has been ordered and the nurse is nowhere to be found.

**Known Rate:**

Convert to the same units

Concentration in lowest form: (dose in bag / Volume)

Known rate:

Plug our numbers into the equation

** Example**: For simplicity, we have Norepinephrine. Concentration- 4mg/250 ml/hr. You have a rate running on the pump at 37.5 ml/hr.

4mg = 4000mcg

Known Rate: 37.5 ml/hr

Concentration of bag: 16mcg/mL

Plug our numbers into our equation

**PEARLS:**

As mentioned though out this blog, medication errors are prevalent and as providers, it is our job to help mitigate and decrease medication errors. Here are some PEARLS that I use in my daily practice that help me be proactive to decrease medication errors.

__Double dose verification__- A lot of us are taught that we need to have double dose verification with pediatric patients. I take this a step forward and do this will all of my patients. When I start working with a new partner I commonly give them my speech of my stupid quirks and stuff. One of those quirks is that I talk though everything, including the dose I am going to give, the concentration and the amount. If I don’t have a partner such as when I worked on the ambulance, I would commonly calculate my dose on my calculator 2-3 times just to verify that I was giving the correct dose.

__Apps__- critical care apps are abundant. These can be extremely helpful as a “double dose” verification method. Talking with other clinicians, I was recommended the “Critical” app. It has been very helpful with dosage calculations of all kinds.

Carrying infusion charts of frequently used infusions. When I first started nursing, specifically flight I printed off infusion charts from our PCGs and carried them with me for quick bedside references. Now, I typically pull up my PCGs on my phone and screenshot my infusion chart of the drug I want to use. This has saved my ass many times and is super-efficient when it comes to time critical drugs that need started.

Practice- don’t wait till you are at bedside to know how to do the calculations. The fact that you took time out of your day to read a “med math blog” proves that you are going above and beyond to help improve your practice with med math and that’s pretty neat in my book. When doing scenarios for training, incorporate med math into the scenarios. This gives you time to practice as well as find errors in your practice in a safe way. My last tid-bit is knowing a ballpark of what your end result should be, that way if you get a totally left field answer, you can identify that a mistake was potentially made and you can recalculate your math.

__Conclusion:__

And breath, you made it through. This blog while not difficult to write is very tedious. Hopefully this blog helps to serve as a reference on how to calculate med math. Remember, we are all human and mistakes will be made. Hopefully no one is hurt in the process but none the less we can all learn and grow from these events. I’ll leave you with a quote that I am sure many of you have heard before.

*“To Err is Human”.*

- *Alexander Pope, 1711.*

Brittany Grandfield, Flight Nurse, 2002 Fifth grade winner of a 5cd disc changer stereo system.

Citations:

1. Center for Drug Evaluation and Research. “Working to Reduce Medication Errors.” *U.S. Food and Drug Administration*, FDA, https://www.fda.gov/drugs/information-consumers-and-patients-drugs/working-reduce-medication-errors.

2. Giuliano, Karen. *Intravenous Smart Pumps Usability Issues, Intravenous Medication Administration Error, and Patient Safety*. 6 Apr. 2018, https://www.ccnursing.theclinics.com/article/S0899-5885(18)30006-6/fulltext.

3. “System of Measurements: Types: Conversion Units: Examples.” *Cuemath*, https://www.cuemath.com/measurement/system-of-measurement/.

4. “The History of Measurement.” *Maths History*, https://mathshistory.st-andrews.ac.uk/HistTopics/Measurement/.

5. Toney-Butler, Tammy J. “Dose Calculation Desired over Have Formula Method.” *StatPearls [Internet].*, U.S. National Library of Medicine, 7 Mar. 2021, https://www.ncbi.nlm.nih.gov/books/NBK493162/.

6. Villanueva, Manuel. “Convert Time to IV Rate.” *Calculate IV Rate as ML/Hr*, https://manuelsweb.com/IVrate.htm.

**Bonus Problem Answer: **

**Rate: 18.75 mL/hr.****Did you get it right?**