In the first two installments of this blog series we reviewed common drug calculation methods such as the universal formula and dimensional analysis. In Part 3, we’ll take a closer look at dimensional analysis and how to use it to calculate continuous intravenous (IV) drips, beginning with units per hour (u/hr). Don’t forget, every nurse should be comfortable with basic metric conversions. You can find a handy conversion chart in our Nursing Pocket Card: Common Calculations.
 

 

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Answer to Previous Practice Problem

Before we dive in, here are the steps and answer to the practice problem from Drug Calculations: How To Use Dimensional Analysis.

Question: Administer penicillin 0.5 grams p.o. every 6 hours. The pharmacy dispenses penicillin in 250 mg tablets. How many tablets should you administer for each dose?

Step 1: What label is needed? We want to know how many tablets to administer.

First, we need to convert miligrams to grams. The pharmacy dispenses 250 mg tablets of penicillin however, the order calls for 0.5 grams per dose. We know that there are 1000 mg in 1 gram.


250 mg = 0.25 grams per tablet which can now be inserted into the formula.

Step 2: Place same label in numerator. We have 0.25 grams/tablet. Invert it so that tablet is on top.

Step 3: Alternate labels in numerator and denominator so labels cancel out. The desired dose is 0.5 grams per dose.

Step 4: Multiply numerators, multiply denominators, then divide numerator by denominator. 0.5 divided by 0.25 is 2.

Answer: 2 penicillin tablets every 6 hours
 

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Intravenous Drips: Convert units/hour to mL/hour (Wilson, 2013)

Now let’s use dimensional analysis to figure out continuous IV infusions. Let’s begin with a common infusion of heparin.
 
Example 1: Administer heparin 500 units per hour continuous IV. Pharmacy supplies the heparin with a concentration of 20,000 units in 500 mL D₅W (40 units/mL). At what rate should you set the IV pump?
 
Step 1: What label is needed? We want to know the rate on the IV pump (mL/hour) and this is placed on the left side of the equation.

Step 2: Place the same label in the numerator on the right side of the equation. The concentration of the heparin drip is 40 units/mL. Invert so that mL is on top.

Step 3: Alternate labels in numerator and denominator so labels cancel out. The desired dose is 500 units/hour.

Step 4: Multiply numerators, multiply denominators, then divide numerator by denominator.

Answer: 12.5 mL/hour
 
Most institutions utilize infusion pumps that can be programmed to the tenth or hundredth decimal place. If your institution does not have infusion pumps with this capability, you may need to round to the nearest whole number.
 

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Intravenous Drips: Convert units/hour to mL/hour

Next, let’s reverse the process using dimensional analysis. In the next example, you know the IV hourly rate (mL/hour) of the infusion but you need to verify the dose.
 
Example 2: You receive shift report that your patient is on a heparin drip and you want to verify the dose that that patient is receiving. The pump is running at 12.5 mL/hour. The label on the bottle reads 20,000 units in 500 mL D₅W (40 units/mL). How many units/hour is the patient receiving?
 
Step 1: What label is needed? We want to know how many units of heparin the patient is receiving per hour. This is placed on the left side of the equation.

Step 2: Place the same label in the numerator on the right side of the equation. The concentration of the heparin drip is 40 units/mL.

Step 3: Alternate labels in numerator and denominator so labels cancel out. The current drip rate is 12.5 mL/hour.

Step 4: Multiply numerators, then multiply denominators.

Answer: 500 units/hour
This is consistent with the shift report.

Remember These Tips:

• Check that your answer makes sense clinically.
• Double check your work.
• Have a colleague or pharmacist check your work.
• Know general therapeutic drug doses for commonly administered medications

I hope this review has been helpful. Next month, we will review continuous IV infusions for drugs delivered in micrograms per minute (mcg/min) using dimensional analysis. Be sure to check back then!

References:
Cookson, K.L. (2013). Dimensional analysis: Calculate dosages the easy way. Nursing2013, 43(6), 57-62.
Koharchik, L.S. & Hardy, E.C. (2013). As easy as 1, 2, 3! Dosage calculations. Nursing Made Incredibly Easy!, 11(1), 25 – 29.

 

More Resources
Blog	Blog	Blog
Drug Calculations: How to Use Dimensional Analysis	Drug Calculations: How to Calculate Continuous IV Drips (mL/hr)	Drug Calculations: How to Calculate IV Drips (mcg/kg/minute)