PCA Nursing Math Problems

Nurses use a great deal of math in their jobs.
••• operation nurse image by Andrey Rakhmatullin from Fotolia.com

A patient-controlled analgesia (PCA) is a means by which a patient can self-administer medication for pain. While the patient controls the PCA, each dosage is smaller than one that a nurse might administer and therefore helps the patient maintains a more level amount of medication within his system. Nurse-administered doses are often larger and therefore peak quickly and can cause nausea or other side effects. Additionally, a larger dose may dissipate before the next scheduled injection.

Do the Math

While the pumps used today usually compute the medication dosage, a nurse needs to know how to do the math to calculate proper dosage. For example, most PCA infusion pumps have a programming system where protocols are stored and displayed. A bar code reader, built into the system, verifies the proper medication and the proper dosage. Additionally, the drugs come in pre-measured, color-coded vials with bar codes. Still, a nurse needs to know the standard formula where by she can divide the amount of medication on hand by the desired dosage per patient infusion to determine the number of doses available.

Infuser Math

The nurse sets the PCA infuser to the dosage prescribed by the patient’s doctor. The pump has a lockout system to prevent the patient from overdosing himself. In this case, an example of the math might be a patient receiving 1 mg of morphine per dose and can have no more than 10 doses per hour. In this case, the patient would be allowed one every six minutes. The pump’s lockout system will block the dose if the patient attempts to administer two in less than a six-minute span.

More Math

Another example of the math a nurse might use in programming an infuser is a patient whose doctor has prescribed the maximum dosage of morphine to 11 mg per hour. The nurse will program the pump to give the patient 1 mg at the top of the hour and, again, allow the patient to self-administer 1 mg every six minutes thereafter.

Infuser Settings

A nurse is required to set the infuser with the physician-prescribed dosage. In some instances, the medication is suspended or dissolved in a solution that helps keep tubing clear and hydrate the patient. The nurse must program the infuser by inputting the amount of medication prescribed and the amount of flushing fluid to insure the proper dosage per demand. Additionally, she must set the computerized lockout time and then have another nurse verify her calculations and sign off on them.


In “Henke’s Med-Math: Dosage Calculation, Preparation and Administration” by Susan Buckholtz and Grace Henke, the authors stress that nurses determining medication dosage need to understand basic mathematics. They must be able to add, subtract, multiple and divide whole numbers and fractions. The authors recommend taking practice exams to discover math weaknesses. “Since calculators are available, why go through the arithmetic?” they ask. “For one thing, using a calculator can actually complicate the process, because you must know what numbers and functions to enter.” Mathematics help a nurse think more logically. Mastering the ability to do the math will enhance nurses' mental processes and build their confidence.

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