Calculations

TOPICS COVERED

1. Amount of drug in a solution

2. Calculation of rate for special IV orders: units/hour; g/hour; mg/hour, mL/hour, mg/minute, milliunits/minute, mcg/minute, mcg/kg/minute

3. Use of the body surface nomogram and calculation, IV medications based on body surface area

4. Patient-controlled analgesia

5. Special types of calculation: heparin, insulin

In Chapter 6, we studied calculations for microdrip and macrodrip factors, the use of the infusion pump, and IV piggyback (IVPB) orders. In this chapter, we consider calculations for orders written in units, milliunits, milligrams, and micrograms; methods of calculating the safety of doses based on kilograms of body weight and body surface area (BSA); and the handling of orders for patient-controlled analgesia (PCA); special types of calculations in relation to continuous heparin infusion and continuous insulin infusion.

This chapter’s dosage calculations are for medications mixed in IV fluids and delivered as continuous infusions. Administering these medications via infusion pumps ensures a correct rate and accuracy of dose (Fig. 7-1). Many infusion pumps can deliver rates less than 1 (e.g., 0.5 mL/hour, 0.25 mL/hour, etc.), and they also can be programmed with the amount of drug, amount of solution, patient/client’s weight, and time unit (minutes or hours). Once the pump is set at an infusion rate, the pump calculates how much drug the patient/client is receiving. You, as the nurse, however, still bear the responsibility for double-checking the calculation and entering the correct information on the infusion pump. (Some hospitals require a “double-check” with two licensed staff to verify the pump is set correctly) (For this chapter, answers will be rounded to the nearest whole number. Time to run is given in hours and minutes—see Chapter 6 for conversion of hours to minutes.)

Because many of the medications that infuse via continuous infusions are very potent, small changes in the infusion rate can greatly affect the body’s physiologic response. In particular, vasopressor drugs such as dopamine, epinephrine, dobutamine, and Levophed (norepinephrine) can affect the patient/client’s blood pressure and heart rate, even in small doses. In most hospital settings, the pharmacy prepares medications and IV solutions.

Amount of Drug in a Solution

These calculations can be complicated. One helpful technique is reduction: Start with the entire amount of drug mixed in solution and then reduce it to the amount of the drug in only 1 mL of solution.

Here’s an example:

Heparin is mixed 25,000 units in 500 mL D5W.

How much heparin is in 1 mL of fluid?

Desired dose: 1 mL

Supply: 25,000 units

Have: 500 mL

FIGURE 7-1
Infusion pump. (With permission from Evans-Smith, P. [2005]. Taylor’s clinical nursing skills. Philadelphia, PA: Lippincott Williams & Wilkins.)

To solve:

Here’s a simple formula you can use for this calculation, instead of the other methods:

Medications Ordered in units/hour or mg/hour

Sometimes patient/client medications are administered as continuous IVs. For these medications, a specific amount of drug is mixed in a specific amount of IV fluid. Check the guidelines (institutional or drug references) to verify dose, dilution, and rate. If any doubts exist, consult with the prescribing physician or healthcare provider.

Units/hour—Calculation of Rate

The order will indicate the amount of drug to be added to the IV fluid and also the amount to administer.

EXAMPLE

EXAMPLE

EXAMPLE

g/hour; mg/hour—Calculation of Rate

The order will indicate the amount of drug added to the IV fluid and the amount to administer.

EXAMPLE

EXAMPLE

mg/minute—Calculation of Rate

The order will indicate the amount of drug added to IV fluid and also the amount of drug to administer. These medications are administered through an IV infusion pump in milliliters per hour.

Note: The dimensional analysis method will combine all of the calculation steps into one equation.

EXAMPLE

EXAMPLE

Medications Ordered in mcg/minute, mcg/kg/minute, or milliunits/minute—Calculation of Rate

Intensive care units administer powerful drugs in extremely small amounts called micrograms (1 mg = 1000 mcg). The orders for these drugs often use the patient/client’s weight as a determinant, because these drugs are so potent.

EXAMPLE

This section shows how to calculate doses in micrograms and in milliunits, and how to use kilograms in determining doses. Most infusion pumps used in hospitals allow you to program these drugs and the pump will calculate the rate for you. However, it is still important to know how to calculate the rate.

mcg/minute—Calculation

Drugs ordered in micrograms per minute are standardized solutions prepared by a pharmacist. They are administered using infusion pumps that deliver medication in milliliters per hour.

To calculate drugs ordered in micrograms per minute, first determine how much of the drug is in 1 mL of solution (see beginning of this chapter). If the drug is supplied in milligrams, convert it to micrograms; then divide that amount by 60 to get micrograms per minute. The final number tells you how much of the drug is in 1 mL of fluid. You can then use one of the three methods to solve for the infusion rate, on the basis of the ordered dosage. The dimensional analysis method will combine all the steps into one equation.

Solving micrograms per minute requires four steps:

1. Reduce the numbers in the standard solution to milligrams per milliliter.

2. Change milligrams to micrograms.

3. Divide by 60 to get micrograms per minute.

4. Use either the formula, ratio, or proportion method to solve for milliliters per hour.

EXAMPLE

EXAMPLE

mcg/kg/minute—Calculation

EXAMPLE

Milliunits/minute—Calculation

In obstetrics, a Pitocin (oxytocin) drip can initiate labor. The standard solution is 15 units in 250 mL. Because 1 unit = 1000 milliunits, you solve these problems in the same way as micrograms per minute.

EXAMPLE

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