Intravenous Calculations
After reviewing this chapter, you should be able to:
1. Calculate milliliters per hour (mL/hr)
2. Identify the two types of administration tubing
3. Identify from intravenous (IV) tubing packages the drop factor in drops per milliliter (gtt/mL)
4. Calculate IV flow rate in drops per minute (gtt/min) using a formula method and dimensional analysis
5. Calculate IV flow rate in gtt/min using a shortcut method (mL/hr and constant drop factor)
6. Calculate the flow rate for medications ordered IV over a specified time period
7. Calculate infusion times and completion times
8. Recalculate IV flow rates and determine the percentage (%) of increase or decrease
This chapter will present the calculations performed with intravenous therapy. As stated previously, nurses have a responsibility to make sure that clients are receiving the correct rate. Several methods are presented in the chapter to calculate IV rates: ratio and proportion, dimensional analysis, and the formula and division factor method. Let’s now begin our calculations with determining IV rates in milliliters per hour (mL/hr).
IV FLOW RATE CALCULATION
IV fluids are usually ordered to be administered at rates expressed in mL/hr. Examples: 3,000 mL in 24 hr, 1,000 mL in 8 hr. Small volumes of fluid are often used when the IV fluid contains medications such as antibiotics. Rates for IV fluids are usually expressed in drops per minute (gtt/min) when an infusion device is not used. When an infusion device is used, the rate must be expressed in mL/hr.
Calculating Flow Rates for Volumetric Pumps in mL/hr
When a client is using an electronic infuser such as a volumetric pump, the prescriber orders the volume, and the nurse is responsible for programming the pump to deliver the ordered volume. The prescriber may order the IV volume in mL/hr; however, if not, the nurse must calculate it and program the pump.
Solution Using Formula Method
Example 1:
Client with an infusion pump has an order for 3,000 mL D5W over 24 hours.
Answer:
The pump would be set to deliver 125 mL/hr.
Solution Using Ratio and Proportion
An alternative to the above formula would be to set up a ratio and proportion as follows:
Remember, as stated in the chapter on ratio and proportion, that a ratio and proportion can be set up in several formats. This could have been set up with the desired time for the infusion (usually 1 hr) over the total time ordered in hours, and the other side would be the hourly amount in milliliters labeled “x” over the total volume to be infused in milliliters:
Example 2:
A client with an infusion pump is to receive an antibiotic in 50 mL of 0.9% NS over 30 minutes.
1. Think: The pump infuses in mL/hr. When the infusion time is less than an hour, which often occurs when antibiotics are administered, use a ratio and proportion to determine mL/hr. Remember: 1 hr = 60 min.
Solution Using Ratio and Proportion
Calculating mL/hr Using Dimensional Analysis
Calculation of mL/hr using dimensional analysis is similar to the formula method.
Example 2:
A client with an infusion pump is to receive an antibiotic in 50 mL of 0.9% NS over 30 minutes.
Notice here that the time is less than an hour. The pump delivers mL/hr. Therefore the fraction 1 hr = 60 min is added to the equation.
Practice ProblemsCalculate the flow rate in mL/hr.
1. 1,800 mL of D5W in 24 hr by infusion pump ____________________
2. 2,000 mL D5W in 24 hr by infusion pump ____________________
3. 500 mL RL in 12 hr by infusion pump ____________________
4. 100 mL 0.45% NS in 45 min by infusion pump ____________________
5. 1,500 mL D5RL in 24 hr by infusion pump ____________________
6. 750 mL D5W in 16 hr by infusion pump ____________________
7. 30 mL of antibiotic in 0.9% NS in 20 min by infusion pump ____________________
CALCULATING IV FLOW RATES IN gtt/min
When an electronic infusion device is not used, the nurse manually regulates the IV rate. To manually regulate an IV, the nurse must determine the rate in gtt/min.
IV flow rates in gtt/min are determined by the type of IV administration tubing. The drop size is regulated by the size of the tubing. (The larger the tubing, the larger the drops.) The first step in calculating IV flow rate is to identify the type of tubing and its calibration. The calibration of the tubing is printed on each IV administration package (Figure 22-1).
IV TUBING
IV tubing has a drop chamber. The nurse determines the flow rate by adjusting the clamp and observing the drop chamber to count the drops per minute (Figure 22-2). The size of the drop depends on the type of IV tubing used. The calibration of IV tubing in gtt/mL is known as the drop factor and is indicated on the box in which the IV tubing is packaged. This calibration, which is necessary to calculate flow rates, is shown on the packaging of IV administration sets (see Figure 22-1).
The two common types of tubing used to administer IV fluids are as follows:
Macrodrop Tubing
Macrodrop is the standard type of tubing used for general IV administration. This type of tubing delivers a certain number of gtt/mL, as specified by the manufacturer. Macrodrop tubing delivers 10, 15, or 20 gtt equal to 1 mL. Macrodrops are large drops; therefore large amounts of fluid are administered in macrodrops (Figure 22-3, A).
Microdrop Tubing
Microdrop tubing delivers tiny drops, which can be inferred from the prefix micro. It is used when small amounts and more exact measurements are needed, for example, in pediatrics, for the elderly, and in critical care settings. Microdrop tubing delivers 60 gtt equal to 1 mL. Because there are 60 minutes in an hour, the number of microdrops per minute is equal to the number of mL/hr. For example, if clients are receiving 100 mL/hr, they are receiving 100 microdrops/min (see Figure 22-3, B).
Figure 22-4 shows a comparison of calibrated drops.
Practice Problems
• Knowing the drop factor is the FIRST step in accurate administration of IV fluids.
• The drop factor always appears on the package of the IV tubing.
• Macrodrops are large and deliver 10, 15, or 20 gtt/mL.
• Microdrops are small and deliver 60 gtt/mL.
• To determine flow rates for an electronic infusion device (pump or controller), determine mL/hr by using the following formula:
CALCULATING FLOW RATES IN DROPS PER MINUTE USING A FORMULA
The calculation of IV flow rate in gtt/min can be done by using a formula method or dimensional analysis. Several formulas can be used; this text will focus on the most popular formula used. Calculation of the rate in gtt/min by using dimensional analysis will also be demonstrated in this chapter. The most common calculation necessary when an IV is manually regulated or an infusion device is not used involves solving to determine the rate in gtt/min.
To calculate the flow rate at which an IV is to infuse, regardless of the method used (formula or dimensional analysis), the nurse needs to know the following:
Formula Method
The information is placed into a formula. Let’s examine a formula that might be used. This formula is the most popular when calculating flow rate when the rate can be expressed as 60 minutes or less.
Before calculating, let’s review some basic principles:
1. Drops per minute are always expressed in whole numbers. You cannot regulate something at a half of a drop. Because drops are expressed in whole numbers, principles of rounding off are applied; for example, 19.5 gtt = 20 gtt.
2. Carry division of the problem one decimal place to round to a whole number of drops.
3. Answers must be labeled. The label is usually drops per minute unless otherwise specified. Examples: 100 gtt/min or 17 gtt/min. To reinforce the differences in drop factor, the type of tubing is sometimes included as part of the label. Examples: 100 microgtt/min or 17 macrogtt/min.
Let’s look at some sample problems and a step-by-step method of using the formula to obtain answers.
Example 1:
Order: D5W to infuse at 100 mL/hr. Drop factor: 10 gtt/mL. At what rate in gtt/min should the IV be regulated?
1. Set up the problem, placing the information given in the correct position in the formula.
2. Reduce where possible to make numbers smaller and easier to manage. Note that the labels are dropped when starting to perform mathematical steps.
3. Divide 100/6 to obtain rate in gtt/min. Carry division one decimal place and round off to the nearest whole number.
Dimensional Analysis Method
Let’s look at calculating rate in gtt/min using the process of dimensional analysis. Remember that IV fluids are ordered in small volumes of fluid that usually contain medication or in large volumes to infuse over several hours. Let’s look at the previous examples by using dimensional analysis.
Example 1:
Order: D5W to infuse at 100 mL/hr. Drop factor: 10 gtt/mL. At what rate in gtt/min should the IV be regulated?
1. You are calculating gtt/min, so write gtt/min to the left of the equation, followed by the equals sign (=), and label gtt/min x, since that is what you’re looking for:
2. Extract the information that contains gtt from the problem; the drop factor is 10 gtt/1 mL.
Write this factor into the equation, placing gtt in the numerator.
3. The next fraction is written so that the denominator matches the previous fraction (what you are looking for). Go back to the problem and you will see that the order is to infuse 100 mL in 1 hr. Enter the 1 hr as 60 min in the denominator because you are calculating gtt/min (100 mL/60 min).
4. Now that you have the completed equation, cancel the units and notice that you are left with the desired gtt/min.
Answer:
x = 17 gtt/min; 17 macrogtt/min
Note: Example 1 could have been done without changing the hourly rate to 60 min, but it would have required the addition of a 1 hr = 60 min conversion factor to the equation.
The next step would be to cancel the denominator/numerator mL and hr, leaving the desired gtt and min.
Example 2:
Order: An IV medication of 50 mL NS in 20 min. Drop factor: microdrop (60 gtt/mL). At what rate in gtt/min should the IV be regulated?
1. You are calculating gtt/min, so write gtt/min to the left of the equation, followed by the equals sign (=), and label gtt/min x, since that is what you’re looking for:
2. Extract the information that contains gtt from the problem; the drop factor is 60 gtt/1 mL.
Write this factor into the equation, placing gtt in the numerator.
3. The next fraction is written so that the denominator matches the previous fraction (what you are looking for). Go back to the problem and you will see that the order is to infuse 50 mL in 20 minutes. Enter the third fraction so that 50 mL is in the numerator and 20 minutes is in the denominator.
4. Now that you have the completed equation, cancel the units and notice that you are left with the desired gtt/min.
Calculating Drops per Minute With Large Volumes of Fluid
Remember that IV fluids can be ordered in large volumes to infuse over several hours, for example, 1,000 mL over x hr; or the large volume can be ordered by total volume to infuse and the mL/hr rate of infusion (125 mL/hr). Example: 1,000 mL D5W at a rate of 125 mL/hr. Remember that when a large volume to infuse over several hours is ordered, a preliminary step can be done to change it to mL/hr. Example: 1,000 mL D5W to infuse in 8 hr. Divide the total volume by the number of hours to get mL/hr. In this case, 1,000 mL ÷ 8 hr = 125 mL/hr. Then proceed to calculate gtt/min.
The formula method or dimensional analysis may be used to calculate gtt/min for a volume of fluid to be administered in more than 1 hour. Now let’s look at some examples where a large volume of fluid will infuse over more than 1 hour.
Example 1:
Order: 1,000 mL D5W to infuse in 8 hr. Drop factor: 20 gtt/mL. At what rate gtt/min should IV be regulated?
Solution Using the Formula Method
Answer:
x = 42 gtt/min; 42 macrogtt/min
Solution Using Dimensional Analysis
Order: 1,000 mL D5W to infuse in 8 hr. Drop factor: 20 gtt/mL. At what rate in gtt/min should IV be regulated?
1. Begin by determining mL/hr, converting the time in hours to minutes. 1 hr = 60 min. Now proceed to set up the problem in the dimensional analysis equation.
2. Enter the gtt/min being calculated first, followed by the equals sign (=).
3. Enter the drop factor (20 gtt/mL) with gtt in the numerator.
4. Take from the problem the amount to be administered over 1 hr (60 min) and write the fraction so that it matches the denominator of the fraction immediately before it.
5. Now that you have completed the equation, cancel the units and proceed with the mathematical process to obtain the answer.
Note: The above example could have been done without changing 1 hr to 60 min; however, if it is left as 1 hr, you will need to add the additional fraction (1 hr = 60 min). With the same example, the equation would be stated as follows:
Notice that the conversion factor 1 hr = 60 min is written so the numerator matches the denominator of the fraction immediately before it. To solve the equation, cancel units and proceed as follows:
Remember that determining mL/hr before calculating gtt/min helps to keep the numbers smaller. However, using dimensional analysis also allows you to determine gtt/min without this step by writing one equation; but you would need the conversion factor 1 hr = 60 min. The equation would be stated as follows:
Notice that the volume ordered is written to match the denominator of the fraction immediately before it and that the conversion factor 1 hr = 60 min is written so the numerator matches the denominator before it.
Example 2:
Order: 1,500 mL 0.9% NS in 10 hr. Drop factor: 15 gtt/mL. At what rate in gtt/min should the IV infuse?
Solution Using the Formula Method
Answer:
x = 38 gtt/min; 38 macrogtt/min
Solution Using Dimensional Analysis
Order: 1,500 mL 0.9% NS in 10 hr. Drop factor: 15 gtt/mL. At what rate in gtt/min should the IV infuse?
1. Calculate mL/hr (1,500 mL ÷ 10 hr = 150 mL/hr); convert the time in hours to minutes. Proceed using the steps outlined in Example 1.
Set up the equation without changing 1 hr to 60 min.
Practice ProblemsCalculate the flow rate in gtt/min using the formula method or dimensional analysis.
12. Administer D5RL at 75 mL/hr. The drop factor is 10 gtt/mL.____________________
13. Administer D5 ½ NS at 30 mL/hr. The drop factor is a microdrop.____________________
14. Administer RL at 125 mL/hr. The drop factor is 15 gtt/mL.____________________
15. Administer 1,000 mL D5 0.33% NS in 6 hr. The drop factor is 15 gtt/mL.____________________
16. An IV medication in 60 mL of 0.9% NS is to be administered in 45 min. The drop factor is a microdrop.____________________
17. 1,000 mL of Ringer lactate solution (RL) is to infuse in 16 hr. The drop factor is 15 gtt/mL. ____________________
18. Infuse 150 mL of D5W in 2 hr. The drop factor is 20 gtt/mL.____________________
19. Administer 3,000 mL D5 and ½ NS in 24 hr. The drop factor is 10 gtt/mL.____________________
20. Infuse 2,000 mL D5W in 12 hr. The drop factor is 15 gtt/mL. ____________________
21. An IV medication in 60 mL D5W is to be administered in 30 minutes. The drop factor is a microdrop.____________________
Calculation of IV Flow Rates Using a Shortcut Method
This shortcut method can be used only in settings where the IV sets have the same drop factor. Example: an institution where all the macrodrop sets deliver 10 gtt/mL. This method can also be used with microdrop sets (60 gtt/mL). It is important to note that this method can be used only if the rate of the IV infusion is expressed in mL/hr (mL/60 min). It is imperative that nurses become very familiar with the administration equipment at the institution where they work.
To use this method you must know the drop factor constant for the administration set you are using. The drop factor constant is sometimes referred to as the division factor. To obtain the drop factor constant (division factor) for the IV administration set being used, divide 60 by the drop factor calibration. Box 22-1 shows the constant calculated based on the drop factor for the tubing.
Example:
The drop factor for an IV administration set is 15 gtt/mL. To obtain the drop factor constant:
After the drop factor constant is determined, the gtt/min can be calculated in one step:
Practice ProblemsExample 1:
Administer 0.9% NS at 100 mL/hr. The drop factor is 20 gtt/mL. The drop factor constant is 3.
Solution Using the Shortcut Method
Therefore this problem could be done by using the shortcut method once you know the drop factor constant (division factor).
Notice that the 100 mL/hr rate divided by the drop factor constant gives the same answer.
Solution Using Dimensional AnalysisStep 1:
Note: In the equation, because time is stated as 60 min, the administration set calibration (20) will be divided into 60 (min) to obtain a constant number (3). 3 is the drop factor constant for 20 gtt/mL administration set. Using the drop factor constant, you can calculate gtt/min in one step (divide mL/hr by the drop factor constant).
Solution Using the Shortcut Method
Solution Using Dimensional Analysis
Example 3:
Administer 0.9% NS at 75 mL/hr. The drop factor is 60 gtt/mL. The drop factor constant is 1.
Solution Using the Shortcut Method
Solution Using Dimensional Analysis
Practice Problems
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