Dosage Calculations Explained
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Table of Contents
- Introduction to Dosage Calculations
- 1) Know the Metric Conversions
- 2) Know What is Given and What it Needs to be Converted
- 3) Put the Given on Top
- 4) What is Being Converted Goes on Top
- 5) Set Up the Problem So Only Converted Units Remain
- Example Problems
- Problem #1: Methylprednisolone
- Problem #2: Vancomycin
- Problem #3: Weight-based Calculation
Article at a Glance
- Dosage calculations often rely on metric conversions.
- Some metric conversions, like pounds to kilograms, must be memorized.
- Read on to practice dosage calculations with practice problems.
Introduction to Dosage Calculations
This article presents five steps for approaching dosage calculations.
Clinicians may need to calculate how much of a drug to draw up.
1) Know the Metric Conversions
The first step is to know the metric conversions, including:
- There are 1000 micrograms in a milligram (1000 mcg = 1 mg).
- There are 1000 milligrams in a gram (1000 mg = 1 g).
- There are 2.2 pounds in a kilogram (2.2 lbs = 1 kg).
These metric conversions are essential for dosage calculations. Be sure to check out the reference list of metric conversion in the blog post under “Learn These Five Steps and Never Miss Another Nursing Math Problem.”
2) Know What is Given and What it Needs to be Converted
Identify what is given and what it needs to convert to. For example: The order is for 150 milligrams of meperidine. There are 300 milligrams of meperidine available in 2 milliliters. How many milliliters should the patient get?
To calculate the appropriate dose, it needs to be converted from milligrams to milliliters.
3) Put the Given on Top
Put what is given on the top of a fraction. In the example above, the order is for 150 mg of meperidine. The 150 mg goes on top of the fraction:
X mL= (150 mg) 2mL/300mg
The equation begins with “milliliters equals,” since that is what it needs to be converted to.
4) What is Being Converted Goes on Top
The unit being converted goes in the numerator. In this example, 2 milliliters contain 300 milligrams of meperidine. Those 2 milliliters go on top of the fraction because that is what the equation is converting to.
5) Set Up the Problem So Only Converted Units Remain
Set up the problem to cancel out everything except for what is being converted to. The example above is converting from milligrams to milliliters. The problem is set up to cancel out milligrams.
X mL= (150 mg)2 mL/300 mg=300 mL/300= 1 mL
Answer: 1 mL of meperidine is needed to provide 150 mg of the drug.
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Example Problems
The example problems below illustrate how to apply these five steps.
Problem #1: Methylprednisolone
The order is for 60 milligrams of methylprednisolone for an intravenous (IV) push. There are 125 milligrams available in 2 milliliters. How many milliliters should be administered?
The clinician may need to calculate how much methylprednisolone to draw up.
To find milliliters, the equation is set up with “milliliters equals.”
X mL= (60 mg)2 mL/125 mg=120 mL/125= 0.96 mL
60 mg is given. That goes on the top of the fraction. Since the conversion is from mg to mL, input the concentration of methylprednisolone, which is 125 mg of methylprednisolone per 2 mL, into the equation. The 2 mL goes in the numerator to cancel out the units.
Remember, the unit being converted to (milliliters) goes on the top of the fraction.
Next, cancel out the matching units of measurement (i.e., milligrams), so the only units left are milliliters, which is what is being converted to.
Finally, complete the equation. On the top: 60 × 2 = 120. Then, divide 120 by 125. The answer is 0.96 mL.
The problem is structured so all of the given units are canceled out and all that remains are the units being converted to. In problem #1 above, milliliters do not cancel out with anything, so the answer will be in milliliters.
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Problem #2: Vancomycin
Here is a more complex problem. The order is for vancomycin 1.5 grams to infuse over 1.5 hours. There are 1.5 grams available in 250 milliliters. What rate, in mL per hour, does the IV pump need to be set at?
Any medication that has to be infused over a prolonged period like this will be administered via an IV pump. When using an IV pump, the dosage needs to be presented in milliliters per hour.
The units for vancomycin through an IV pump are mL/hour.
The problem is set up to solve for mL/hour. Since mL is on top, that value is placed in the numerator.
X mL/hour= 1.5 grams/1.5 hours×250 mL/1.5 grams= 166.7 mL/hour
The order is for 1.5 grams of vancomycin over 1.5 hours. The 1.5 grams go on the top of the fraction, and the 1.5 hours go on the bottom of the fraction since the answer is looking for the hours in the denominator.
The vancomycin concentration should be 250 mL per 1.5 grams. That concentration helps in the conversion from grams to mL. The grams will cancel out. When this equation is multiplied, it equals 166.7 mL/hour.
X mL/hour= 1.5 grams/1.5 hours×250 mL/1.5 grams= 166.7 mL/hour
Grams will cancel out, leaving mL/hour.
Vancomycin is a common medication in the hospital. When this method and these steps, known as dimensional analysis, are understood, the clinician can make the correct dosage calculations every time.
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Problem #3: Weight-based Calculation
The third and final example is a weight-based calculation. This is probably one of the more difficult problems that clinicians will encounter. Dimensional analysis applies to weight-based problems the same way it applies to drips.
The order is for dobutamine at 5 mcg/kg/min. The patient weighs 330 pounds. There is 1 gram available in each 250 mL vial. What is the rate for administering dobutamine in mL per hour?
Converting the weight from pounds to kilograms is the first step. Divide 330 pounds by 2.2 to arrive at the patient’s weight in kilograms:
330 lbs ×1 kg/2.2 lbs=150 kg
Use the weight to figure out the order for dobutamine:
150 kg ×5 mcg1/kg × min=750 mcg/min
The units for an IV infusion pump are mL per hour. Start with mL on top, which is 250 mL over 1 gram of dobutamine.
Quite a bit of converting is required to convert grams to milliliters. That is where knowing those metric conversions will help work these problems out correctly.
The rest of the equation will look like this:
X mL/hour=250 mL/1 gram×750 mcg/1 min×1 mg/1000 mcg×1 g/1000 mg×60 min/1 hour= 11.25 mL/hour
To eliminate micrograms, remember that 1000 mcg are in 1 mg and 1000 mg are in 1 g. After these conversions, what is left is mL per minute.
To reach the correct answer, minutes need to be converted to hours. Use the conversion of 60 minutes in 1 hour to cancel the minutes.
Now, everything has canceled out, and milliliters/hour is what is left. Multiply these numbers to arrive at the correct answer: 11.25 mL/hour.
These are the five steps for calculating dosages. Knowing common metric conversion rates and understanding how to complete these calculations is essential for calculating the correct dosages.
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