Med Math Practice & Review: Essential Dosage Calculations for Nursing Exams
This review session, led by Dr. Ogle, provides step-by-step guidance on solving common medication math problems. The focus is on using dimensional analysis to ensure accuracy and memorizing key metric conversions. All examples include rounding instructions as required in exams.
Key Memorization: Vital Metric Conversions
You must commit these to memory; they will not be provided on exams:
- Volume: 1 L = 1000 mL
- Weight: 1 kg = 2.2 lb
- Time: 1 hour = 60 minutes
- Mass: 1 mg = 1000 mcg
1. Calculating mL per Dose (Oral/Injectable)
Problem: Order is for 60 mg of Lasix BID. Available: 10 mg in 1 mL. How many mLs for one dose?
- Goal: Find mLs.
- Setup: (1 mL / 10 mg) x 60 mg = 6 mL
2. Calculating mL per Dose with Weight-Based Dosing
Problem: Order for a loading dose of Heparin: 75 units per kg for an 81 kg patient. Available: 5000 units in 1 mL. Round to nearest tenth.
- Goal: Find mLs.
- Setup: (1 mL / 5000 units) x (75 units / 1 kg) x 81 kg = 1.215 mL = 1.2 mL (rounded to nearest tenth)
3. Calculating mL per Hour (IV Fluids)
Problem: Ordered: 2 L of IV fluid over 12 hours. How many mLs per hour? Round to nearest whole number.
- Goal: Find mL/hr.
- Conversion: 2 L = 2000 mL
- Setup: (2000 mL) / (12 hr) = 166.66... = 167 mL/hr
4. Calculating mg per Hour (IV Medication)
Problem: Ordered: 1 mg per minute. How many mg per hour over a 6-hour infusion?
- Goal: Find mg/hr.
- Setup: (1 mg / 1 min) x (60 min / 1 hr) = 60 mg/hr (The 6-hour total is a distractor)
5. Calculating Drops per Minute (IV Drip Rate - gtts/min)
Two examples demonstrate different contexts. Always round to the nearest whole drop.
Example 1: Large Volume with Time Conversion
- Order: 2 L over 12 hours. Drop factor: 20 gtts/mL.
- Goal: gtts/min.
- Setup: (20 gtts / 1 mL) x (1000 mL / 1 L) x (2 L / 12 hr) x (1 hr / 60 min) = 55.55... = 56 gtts/min
Example 2: Given Hourly Rate
- Order: 150 mL per hour. Drop factor: 15 gtts/mL.
- Setup: (15 gtts / 1 mL) x (150 mL / 1 hr) x (1 hr / 60 min) = 37.5 = 38 gtts/min
6. Calculating mcg/kg/min: A Multi-Step Infusion Problem
This requires a three-step process, similar to the dimensional analysis used in Arithmetic and Geometric Sequences in Hospital Drug Dosage Calculations for multi-step problems.
Step 1: Convert patient weight from lbs to kg
- Given: Patient weighs 88 lb. (1 kg = 2.2 lb)
- Setup: 88 lb / 2.2 lb/kg = 40 kg
Step 2: Calculate mcg per minute
- Given: Ordered 20 mcg/kg/min.
- Setup: (20 mcg / 1 kg/min) x 40 kg = 800 mcg/min
Step 3: Calculate mL per hour to administer
- Given: Available bag: 100 mg in 50 mL.
- Goal: mL/hr.
- Setup: (50 mL / 100 mg) x (1 mg / 1000 mcg) x (800 mcg / 1 min) x (60 min / 1 hr) = 24 mL/hr
For more practice with metric conversions in medical contexts, refer to Clinical Chemistry Lab Calculations: Spectrophotometry, Beer's Law, and Acid-Base Balance and Mastering Unit Conversions for the Digital SAT Math Exam for foundational skills. Additionally, understanding Calibration in Fluid Mechanics: Improve Measurement Accuracy can enhance your precision with IV drip rate calculations.
Hi, this is going to be a little med-math practice, maybe review for some of you. If you do have any questions, this is Dr. Ogle. I can be reached at [email protected]. So, [email protected]. All right, here we go.All right, this screen is for your review. It is very important that you commit
these to memory. When you go to take your exams and you're doing your med-math, you're going to be expected to have these conversions already down because no one's going to give them to you. So, you should already be well aware of these. This is just a little review for you.All right. So,
typically what we see that's being asked—sometimes you might see capsules or tablets—we're going to go ahead and start with mLs that you would need to give your patient. So, you see the first one says that you have an order for 60 mg of Lasix. You're going to give it two times a day. They are
providing you, however, with 10 mg in 1 mL. So, it wants to know: how many mLs are you going to administer to your patient?Now, this says "two times a day." The questions may say, "How much are you going to give them in a day?" I will say for this, we're just going to figure out what one
dose is. So, I do dimensional analysis. So, it wants to know how many mLs. And please excuse my handwriting; it is not the best, but bear with me.All right. So, it wants to know how many mLs. And what we know is that we have 1 mL, and in that 1 mL, there are 10 mg of our medication. But what
we need is 60 mg. Now, the way I always do this, just as a little review, is that if I need mLs, that's what I have at the top. I want that at the top so that it's going to give me what I need. After that, I start crossing things out. So, I know that I need mLs, and then I'm going
to cross out the milligrams. And then we're just going to go ahead and multiply that across. So you would end up with $1 \times 60$, and you're going to have that divided by 10, which is going to give you your 6 mLs. So for this patient, you're just going to be giving 6 mLs.So hopefully that
all made sense to you. We're going to keep moving along. Make sure you pay attention if it tells you to round a certain way. So for this next one, it's asking how many mLs we're going to give. You see that right there? How many mLs? So make sure that you always know what it's asking. Whatever it's
asking, write that out. It wants to know mLs.So then, what information do we have here? We know that heparin has been prescribed for our patient who is 81 kg. We know that the loading dose is 75 units per kilogram. And what we have available to us is a vial of 5,000 units in 1 mL. So remember I
said I always put whatever I am looking for on the top. So, I'm looking for mLs. So, I know that in 1 mL I have 5,000 units. So, there's my mLs. I need to get rid of those units. So, now I'm going to go back into my question and look, and I see that I have 75 units for every kilogram that my patient
weighs. So, right there, now I can get rid of my units.Now, I want to go across and I'm trying to figure out how to get rid of that kilograms. Well, my patient weighs 81 kilograms. When I do it this way, I can make sure that I have not missed anything and that I can cross out everything and
that I'm going to end up with the correct amount of medication. So, here then I would just do $75 \times 81$ and then I'm going to divide that by the 5,000 units. And I'm doing this along with you, which is going to end up giving me 1.215. But notice what this says: "if rounding is required,
round to the nearest tenth." So looking at the nearest tenth, right? We have this one over here. So what we're going actually give in mLs is going to be 1.2.All right. So hopefully that all made sense. We're going to keep on moving along. All right. Now we are going to go ahead and
look at how you would do milliliters per hour or milligrams per hour. All right. So the question here asks you: how many mLs are you going to run each hour? Okay. So based on that, I'm going to write mLs per hour because I know that's what it needs. Now like I said before, I always want to
keep whatever is on top. That's what I'm going to look at first.Now, but when I look here, I don't have mLs per hour; I have liters. This is where that conversion comes into place that we talked about before. This is why you have to commit these to memory if you haven't already. So, I know that
there are 1,000 mLs in 1 liter. So, now I have my mLs on top just like I wanted. But now I've got to get rid of these liters. So, what do I have? I have 2 L over 12 hours. So, I'm going to write 2 liters over 12 hours. Now I have my liters—I'm so sorry, excuse me—now I can cross out my liters.
Maybe. There we go. And I have my hours.So now I'm just going to multiply again. So, we're going to have that 2,000 over 12, which is going to end up giving you 166.6, and it keeps repeating. When you have exams and practice questions, it should be asking you to round to a certain point. So,
when we're looking at this, we're probably going to round to the nearest whole number. So, just remember that we're looking at that. And because we have that .6, we're going to end up giving our patient 167 mLs per hour.All right. So, let's do another one. This one is milligrams per hour. So,
it wants to know how many milligrams you're going to give every hour. That's right here. So then we look at our question. We see what we've got. I have milligrams at the top. So, I'm going to want milligrams again. So, I'm going to do 1 milligram, because this is what it's telling me,
over 1 minute. But what I need is hours. So since I need hours—this one you should all know—60 minutes is in 1 hour. So now I can get rid of my minutes and I have my hour. So then that's just going to tell me, because I'm going to multiply that across, right? So 60 divided by 1,
I would be giving my patient 60 milligrams every hour of the medication.Now you see the 6 hours in here, right? I didn't need it. If it asked you how much you were going to give total, then you would figure out, you know, every hour you're giving 60 milligrams, how much would you
be giving in a 6-hour period? So, you would do the $60 \times 6$. But that's not what it asked. So, make sure that you look at what it's asking you so you don't give too much, you don't add too many things in that are going to end up hurting you.All right, let's go to the next one.
Maybe.All right. So, now we're looking at our drips per minute. When we do our drips per minute, it's going to give us a drop or a drip factor. Same thing. So we know that it's asking us right here drips per minute. So that's that gtts—you might see it just gtt—but every
minute. So then what have we got? Remember I told you that if I have my drops on the top, I'm looking for where my drops are, right? So, I'm going to put in that we have 20 drips that go in 1 mL, because that's the information I got right here. That's that drop factor. So, then—and
this is going to be written on the IV bag, on the IV tubing—you'll see it where it says drip factor. So, go look at your IV tubing; it'll show that on there for you.So, I have my drops up there and then I have my mLs right here. But if you look, we don't have anything in here that says mLs, right?
We have 2 liters over 12 hours. So, I have to do a conversion. I know that 1,000 mLs equals 1 liter. So, now I can get rid of my mLs. Now, I need to figure out my liters. So, I have 2 liters that are going to go over 12 hours. So now I can get rid of my liters, but I still need these minutes,
right? So it's got to end up in the bottom over here. Well, that's fine because I know that 1 hour has 60 minutes. So now I can cross out my hours and I'm left with my minutes.So now from here, all you're going to have to do—excuse me—is multiply across. So, you're going to be taking your 20
times your 1,000, and then you see that times 2. So, you should get 40,000. Always make sure that you are checking your math. And then we have across the bottom $12 \times 60$, which is going to give you 720. So then you're just going to take that 40,000 divided by that 720. And it's going to
give you 55.55555, a whole bunch of fives. Sorry, I'm running out of room here.So for this one, because it's drops per minute, you're not going to be able to count 55.5555. If you can count that, you are superhuman. So, what you can count though is 55. But for this, we're going to round to the
nearest whole number. So, if you have 55.55 and we want to round to the nearest whole number, right, it's going to end up being 56. So, you're going to have 56. And once again, I am sorry that this is everywhere. 56 drops per minute.All right. So, let's do another one. Once again,
it's asking you how many drips. See, this one says drips per minute, so gtts per minute. I have my drips up on top, so that's what I want. Here's my drop factor. So, I'm going to put that in: 15 drips per 1 mL. So, that's perfect. See, got that at the top. Now, I have that 1 mL. So,
go in here and see what you can find. You have 150 mLs ordered that are going to be delivered an hour. Okay? So, you can cross out your mLs, but you still need to get minutes in the bottom. We already talked about this: 1 hour equals 60 minutes, right? One of those conversions. So,
we cross that out and we're left with minutes on the bottom.So, you see all the drops are on top, minutes are on the bottom. So, once again, we're just going to cross-multiply this out, right? We've got $15 \times 150$. So, that's going to give you 2,250. And then $1 \times 1 \times 60$.
So we're going to have that divided by 60, which is going to end up giving you 37.5. Rounded to the nearest whole number because you can't count that .5, right? So rounded to the nearest whole number, this one is going to be 38 drips a minute. All right.All right. This one is a little bit more
in-depth. So now we were looking at micrograms per kilogram per minute. And if we're doing that, we need to actually figure out certain key components. So the first one we're going to do is figure out how many kilograms a patient weighs. You can do this with dimensional analysis,
which we'll go ahead and do because it might be easier if we do it that way.So we're going to say: how many kilograms do they weigh? And we know that when we're looking at kilograms, 1 kilogram—so we're going to put the kilograms on top—equals 2.2 lb. Now remember we don't have anything in
the bottom, and we need to get rid of the 2.2 lb, and our patient is 88 lb. So 88 lb. So we're just going to do 88 divided by 2.2, and that's going to give you 40 kg. So now you know your patient is 40 kg.All right. So the next component: it wants to know how many micrograms per minute the patient
will receive. So I'm going to do that down here because I'm running out of room. So micrograms per minute. And what do we know? We know that our patient is getting 20 micrograms per kilogram, and they weigh 40 kg, and they're going to get that every minute. Okay. So then we can just
cross this out, cross this out. It leaves us with our minutes. We're going to do $20 \times 40$, and it's going to tell you that they're going to get 800 micrograms a minute.But what if you want to know how many mLs an hour they need to get? Well, here we're going to say that 50 mLs has in
it 100 mg. So there's my mLs. But that's not what we need, right? We need to know the micrograms. So I know, because I know my conversions, that 1 milligram equals 1,000 micrograms. And I just figured out that they're getting 800 micrograms—see, that's from this up here—a minute.
But I need to know how much they're getting in an hour. And I know that 60 minutes equals 1 hour.So, see here, I was able to cross out, cross out, cross this out, cross this out, cross this out, cross this out. And then it's going to leave us with our answer. So, we're going to take our $50
\times 800 \times 60$. It's going to give us a big giant number of 2,400,000. And then we are going to divide that by the $100 \times 1,000$. So, we're going to divide that. Hold, please. Sorry, my calculator wasn't working. Which is going to give us 24. So,
we know that our patient is going to get 24 mLs per hour.
The four key metric conversions you need to memorize are: 1 L = 1000 mL for volume, 1 kg = 2.2 lb for weight, 1 hour = 60 minutes for time, and 1 mg = 1000 mcg for mass. These conversions are critical as they will not be provided on exams and are foundational for solving all medication math problems.
Use dimensional analysis by setting up a ratio of the available concentration to find mL per dose. For example, if the order is for 60 mg of Lasix and the available solution is 10 mg per 1 mL, you calculate (1 mL / 10 mg) x 60 mg = 6 mL. Always cancel units to ensure your answer is in the correct format.
Convert the total volume to mL and divide by the total time in hours. For instance, an order of 2 L of IV fluid over 12 hours equals 2000 mL / 12 hr = 166.66... mL/hr, which rounds to 167 mL/hr if rounding to the nearest whole number.
Use the formula: (drop factor in gtts/mL) x (volume in mL/hr) / (60 min/hr). For example, with a drop factor of 20 gtts/mL and an order of 2 L over 12 hours (167 mL/hr), the calculation is (20 gtts/mL x 167 mL/hr) / 60 = 55.55... gtts/min, rounded to 56 gtts/min. Always round to the nearest whole drop.
Follow a three-step process: first, convert the patient's weight from pounds to kilograms (e.g., 88 lb / 2.2 = 40 kg). Second, calculate mcg per minute (e.g., 20 mcg/kg/min x 40 kg = 800 mcg/min). Third, calculate mL per hour using the available concentration (e.g., 50 mL / 100 mg x 1 mg / 1000 mcg x 800 mcg/min x 60 min/hr = 24 mL/hr).
Always round drops per minute to the nearest whole number, as partial drops cannot be administered. For example, 55.55... gtts/min is rounded to 56 gtts/min, and 37.5 gtts/min is rounded to 38 gtts/min.
Ignore distractors that are not needed for the specific calculation. For example, if an order is 1 mg per minute for a 6-hour infusion, you only need the rate per minute to find mg/hr: (1 mg/min) x (60 min/hr) = 60 mg/hr. The total infusion time is irrelevant for the mg/hr calculation.
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