Nursing Dosage Med Math Calculations | NURSING.com

Nursing math tests are like many of your other exams in nursing school: sometimes there are multiple distractions in the question that you have to weed through to get down to the meat of it. It is important to keep your mind focused on specifically what is asked and what unit you are being asked to answer in.

The question may say something like…

Your patient has 2.5 grams of Vancomycin in 500 ml normal saline to be administered IVPB over three hours ordered, how many milligrams total will this patient receive?

So what are they asking for in this question? They are asking for how many milligrams the patient will receive. We don’t care about the 3 hours, the IVPB, the normal saline, or even the name of the drug! The question is essentially asking you to convert 2.5 g to milligrams.

Below is a table of different abbreviations so you can identify various units of measurement. Later, we’ll discuss converting units more specifically. However, for now… it is important to specify what they’re asking for.

Med Math Step 2: What do you have?

If they match, you’re good. Head on to that next step…

If they don’t, hang on a second… we’ve got to make it so our units match.

Thinking back to our original example… we need to convert grams to milligrams to get the correct answer. We don’t need to worry about the normal saline, the IVPB, or the 3 hours again… the question is merely asking how many milligrams are in 2.5 grams.

Step 3A: Unit Conversion

Okay now that you’re familiar with the specific units, let’s talk about converting them. You may have an order to administer medication in milligrams, but the tablets are in grams. Or you may have a patient who weighs 178 lbs but needs propofol started STAT, which is given in mcg/kg/min. And this isn’t just stuff that you learn in school and never deal with again, you truly need to know this. I promise you, it is valuable.

Let’s go through some basic (you really really need to know this) conversion stuff.

Dosage by Weight

Dosing by weight is something you’ll do frequently. And if you work in pediatrics or with little babies… you’ll be doing this so much that you’ll be able to do this in your SLEEP.

The first thing to know about dosing by weight is that it is almost always done in kilograms. Those of us working in the United States are used to weighing people in pounds, however, it is essential to convert this number to kilograms. Many computerized charting systems will auto-calculate this as soon as you enter the pounds into the chart, however, you must know how to do this on your own.

Pounds and kilograms – There are 2.2 pounds in every kilogram.

2.2 lbs = 1 kg

Burn this into your brain.

Therefore, when looking at these dosing problems, convert your pounds to kilograms first! After this, it’s a pretty straightforward calculation. You multiply your kilograms by the dose to get the answer.

Example 1 …

Your patient weighs 25 lbs. How many mg will you give your patient if they require 2 mg/kg of medication?

• Let’s change our lbs to kg… 25 ÷ 2.2 = 11.36 kg
• 2 mg x 11.36 kg = 22.72 mg

Example 2 …

Your patient weighs 50 kg. They are on a heparin drip and their PTT was subtherapeutic. The protocol says to give them a bolus of 40 units/kg of heparin. How many units of heparin will you give your patient?

• 50 kg x 40 units = 2000 units

Example 3 …

Your patient weighs 19 lbs. The doctor has ordered a 2 mg/kg of medication, which comes in a 100 mg/2 ml vial. How many milliliters will you give?

• Let’s first convert our weight… 19 lbs ÷ 2.2 = 8.636363.. We will round up to 8.64 kg
• 2 mg x 8.64 kg = 17.28 mg dose ordered
• Now it’s just a simple “dooooo daaaaaaa times amount” question!
  • (17.28 ÷ 100 mg) x 2 = 0.3456 ml
  • We will round up our final answer of 0.35 ml

So micrograms are the smallest, kilograms are the biggest… and each is a thousand times smaller or bigger. See my handy-dandy chart below. Basically, to go from micrograms to milligrams, you multiply by 1000. To go from kilograms to grams, you divide by 1000. You’re basically moving your decimal point by 3 places to the left or right, depending on if you need a smaller or larger number.

Micrograms, milligrams, grams, and kilograms all measure mass. However, it’s also important to know how to measure volume as well. Use the same principles to convert microliters, milliliters, liters, and kiloliters.

It’ll be important to know that for school, but when you start on the nursing units… realistically, you’ll most likely be working with liters and milliliters. And if you’re working in the neonatal intensive care unit, you’ll start to see those microliters.

Med Math Step 4: Is time involved?

Is this question asking for a drip rate or a pump rate?

Pump rates refer to what you’ll set your IV pump to… whether it be 50 ml/hr, 25 ml/hr, 600 ml/hr, or 83.3 ml/hr.

Drip rates refer to the number of drops at which the IV fluid is dripping at. Basically, the drip rate reflects the number of drops per minute. You can’t measure a partial drop, so rounding is important with drip rates. Make sure you understand the rules your nursing school has about rounding so you make sure to answer the question appropriately.

IV Pumps Rates

This can be tricky, but I promise… it’s doable. In the real world, your IV meds that need to be given via a pump will typically either tell you the rate to plug in, or they will be ordered to be administered over a certain duration of time (for example, infuse over 3 hours, infuse over 30 minutes, infuse over 6 hours) and many pumps today will enable you to enter the duration and auto calculate the rate.

Honestly, in my humble opinion… I truly believe it is safest if the ordering provider orders the medication to be given over a certain amount of time, and we as the administering nurse merely plug in exactly that time, and the pump calculates your rate.

However, we must at least know how to do this otherwise in the event that we work somewhere that does not have pumps capable of this, or if there is a disaster or issue where you need to infuse by gravity… then the whole drop factor/drip-rate situation comes into play.

Keep in mind… the actual probability of that occurring is small, depending on where you work. However, it doesn’t hurt to at least have a basic understanding of how one would go about calculating a drip-rate. But I digress…

You are most likely going to administer an IV medication on a pump, in milliliters per hour, or ml/hr. Figuring this out is pretty straightforward. You take the total milliliters in the dose to be administered and you divide it over the number of hours you want it to infuse over. Remember, it is milliliters per hour. If you can just remember that and repeat that to yourself in your head, it almost tells you the calculation for you. How many milliliters will I infuse every single hour?

This is pretty straightforward, except the only part that can be somewhat tricky is if you need to give the medication over less than an hour.

If you need to give an IV in less than an hour, you need to figure out what fraction of an hour they’re asking you to give the medication over… is it 15 minutes, 30 minutes, or 45 minutes? 15 minutes is ¼ of an hour, so 0.25. 30 minutes is ½ of an hour, so 0.50, and 45 minutes is 0.75. Keep that in mind if you’re asked to figure out the rate of something administered over less than 1 hour.

Remember, you’re administering this in milliliters per hour, so we have to have our time in hours!

Example 1:

• Administer 500 ml over 2 hours. What’s the rate?
  • 500 ml ÷ 2 hours = 250 ml/hr

Example 2:

• Administer 50 ml over 30 minutes. What’s the rate?
  • 50 ml ÷ 0.5 hours = 100 ml/hr

Example 3:

• 750 ml over 6 hours. What’s the rate?
  • 750 ml ÷ 6 hours = 125 ml/hr

Drip Rates

Full disclosure, guys… the NRNSG team never, ever uses this in practice. Like, none of us. We actually had to look up this because we all learned it in school, but never actually used it in practice. That will probably make you feel better or worse… who knows?  Some nurses who work out in the field or in very specific areas and specific situations may use this… and there’s always planning for the absolute worst (power goes out, all backup generators go out, all batteries die, a massive influx of 9 million patients and unable to use pumps for everyone…)

Also, keep in mind that rounding is important when calculating these drip rates because you can’t give a fraction of a drop. Your instructor should have specifications for how this will be done for your exams (up, down, what to round it to).

First, you must know the kind of tubing you’re dealing with so you know the drop rate. How many drips per milliliter are we talking about here? 15 gtts/ml? 20 gtt/ml? 30 gtt/ml? This information should be given to you in the question..

Next, you take your volume (in milliliters) and divide it by the time (in minutes).

Finally, you’ll take that number and multiply it by that drop factor you were given (gtt/ml).

[ Volume (ml) ÷ time (min) ] x drop factor (gtt/min) = _______ gtt/min

Example 1:

You need to give 1000 ml of normal saline over 4 hours. The drop rate of your infusion set is 20 gtt/min. What’s the drip rate?

• Let’s change our hours to minutes… 4 x 60 = 240 minutes
• (1000 ml ÷ 240 minutes) x 20 gtt/min = 83.3333…
• Let’s round down for our final answer to be 83 gtt/min

Example 2:

You need to infuse 50 ml of an antibiotic over 1 hour. The drop rate of your infusion set is 15 gtt/min. What’s your drip rate?

• Let’s change our hours to minutes… 1 x 60 = 60 minutes
• (50 ml ÷ 60 minutes) x 15 gtt/min = 12.499999…
• Let’s round down for our final answer to be 12 gtt/min

Example 3:

You need to infuse 500 ml of Vancomycin over 3 hours. The drop rate of your infusion rate is 20 gtt/min.

• Let’s change our hours to minutes… 3 x 60 = 180 minutes
• (500 ml ÷ 180 min) x 20 = 55.55554
• Let’s round-up for our final answer to be 56 gtt/min

If you don’t have an IV pump rate or drip rate to worry about, you’re basically going to calculate the dose. With most medications, you’ll give one tab, one syringe full, or something similar. Many things are pre-drawn up in one-time-use packaging to reduce the potential for med errors.

I use this method all the time as a nurse. However, there are some that will require you to give a partial dose. Use this method to determine specifically how much to give. This is necessary because the dose that the patient needs may not always match exactly how it comes. Maybe they need 2 tabs, 6 tabs, 1.75 tabs, or maybe it comes in a 5 ml syringe and they need 2.5 ml, 1 ml, or 10 ml.

Many times, the computer and/or pharmacy will auto-calculate this, but I always double-check this on my phone calculator before administering it. If it’s a high-alert medication or something I don’t routinely give, I’ll double-check my math with a coworker or two. Calculators can also be in the MAR or on the computer you are using if the clinical instructor freaks about having cell phones (mine did).

This quick method was taught to me by a friend.

“Dooooo. Daaaaaa. Times amount.”

Say it again with me.

“Doooooo. Daaaaaaaa. Times amount.”

(Dose ordered ÷ dose available) x amount

So you take whatever dose the physician ordered, divide it by whatever you have available, and multiply that times the amount that the med comes in.

Example 1:

The physician has ordered 2.5 grams and the medication comes in 500 mg/tab. How many tabs will you give?

2.5 grams = 2500 mg

(2500 ÷ 500) x 1 = 5 tablets

Example 2:

The nurse practitioner ordered 50 mg and the medication comes in syringes that are 1000 mg in 4 ml. How many ml will you administer?

(50 mg ÷ 1000) x 4 = 0.2 ml

Example 3:

The PA ordered 100 units and the medication comes in 20 units/ml. How many milliliters will you administer?

(100 ÷ 20) x 1 = 5 ml

PART TWO: Dosage Calculations for Nursing Students (an intro to dimensional analysis)