Level 1 Dimensional Analysis
We’ll start at level 1….super easy ones to give you a feel for the technique. Ready?
Your order reads:
In dimensional
analysis, you always start with what’s ordered. In this case it’s 650 mg of
acetaminophen. You will write this as a fraction, with 650 on top and 1 on the bottom
like so:
Next, you need to know what dosage amounts your medication comes in. This is known
as the conversion factor. In the case of good ol’ Tylenol, we check our blister pack and
see that it’s 325 mg per tablet. The next step is to add the conversion factor also as a
fraction. Since mg is at the top of our first fraction, it will go on the bottom of our next
one so that they cancel each other out. Like so:
As we
move forward into more complicated calculations, it will become more evident that you
know when to stop conversions when you are left only with the information needed to
give the dose. In this case, we want to know how many tablets to give the patient.
Everything except for tablets is crossed out, so we know we are ready to do some math.
1) Multiply across the top: 650 x 1
2) Then divide across the bottom: ÷ 325.
What answer did you get?
Let’s do one more easy one…
For this calculation, let’s
assume midazolam comes in 5 mg tablets. I have no idea if it does, but we’re just
practicing so it’s all good. Hopefully, you’ve set up your calculation like this:
Next, cross out the units that are the same…in this
case it’s mg.
We are no weft with X # of tablets to give our 1 patient. Voila! Now, do your calculation!
Calculating Oral Medication Dosages Using Ratio
and Proportion
Here is an example of how to calculate oral medication dosage using ratio and proportion:
Doctor's order: 125 mg of medication once a day
Medication label: 1 tablet = 250 mg
How many tablets should be administered daily?
In this problem you have to determine how many tablets the patient will take if the doctor order
is 125 mg a day and the tablets are manufactured in tablets and each tablet has 250 mg.
This problem can be set up and calculated as shown below.
250 mg: x tablets = 125 mg
250mg x = 125 mg
x = 125/250 = 1/2 tablet
Here is another example of calculating an oral dosage with a liquid oral medication:
Doctor's order: Tetracycline syrup 150 mg po once daily
Medication label: Tetracycline syrup 50 mg/mL
How many mL should be administered per day?
For this oral dosage problem, you have to find out how many mL of tetracycline the patient will
get when the doctor has ordered 150 mg and the syrup has 50 mg/ml.
This problem is set up and calculated as shown below.
150 mg: x mL = 50 mg: 1 mL
50 x = 150
X = 150/50 = 3 mL
Calculating Intramuscular and Subcutaneous
Medication Dosages Using Ratio and Proportion
The process for calculating intramuscular and subcutaneous dosages is practically identical to
that of calculating oral dosages using ratio and proportion. Here is an example:
Doctor's order: Meperidine 20 mg IM q4h prn for pain
Medication label: Meperidine 40 mg/mL
How many mL or cc will you give for each prn dose?
Using ratio and proportion, this problem is set up and solved as shown below.
20 mg / x mL = 40 mg/1mL
40mg * x = 20mg * 1mL
x = 20mg/40mg * 1mL = 0.5 mL
Now, let's do this one:
Doctor's order: Heparin 3,000 units subcutaneously
Medication label: 5,000 units/mL
How many milliliters will be administered for this patient?
5,000 * X = 3,000
3,000/5,000 = 0.6 mL
Answer: 0.6 mL
Calculating Intravenous Flow Rates Using Ratio
and Proportion
The rule for intravenous flow rates is:
gtts/min = (Number of mLs to be delivered)/(The Number of Minutes) x Drip or drop factor for
the IV tubing
Doctor's order: 0.9% NaCl solution at 50 mL per hour
How many gtts per minute should be administered if the tube delivers 20 gtt/mL?
X gtts per min = (50 x 20)/60 = 1000/60 = 16.6 gtts which rounded off to the closest drop is 17
gtts
Rounded off to: 17 gtt/min
Here's another example:
Doctor's order: 500 mL of 5% D 0.45 normal saline solution to infuse over 2 hours
How many gtt per minute should be given if the tubing delivers 10 gtt/mL?
X gtts per min = (500 x 10)/120 = 5000 / 120 = 41.66 gtts which is 42 gtts when it is rounded off
https://nurseslabs.com/drug-dosage-calculations-practice-quiz/