Common Formula Calculations for Medications and IV Infusions

Every nurse must know how to calculate medication dosages and intravenous drip rates. Even with current technology that lets IV pumps compute the flow rates, nurses should be prepared to perform manual calculations that will deliver safe and accurate prescribed amounts.

An essential core competency

Nursing license candidates will certainly encounter drug and IV calculations on their NCLEX. In both the NCBSN NCLEX-PN Test Plan’s Physiological Integrity subcategory of Pharmacological Therapies and the NCLEX-PN Test Plan’s Physiological Integrity subcategory of Pharmacological Therapies, specific nursing actions and competencies are listed. Both test plans clearly state, “Perform calculations needed for medication administration.”

Learn one medication formula and stick with it

Nursing curriculums may offer several ways to calculate medication doses. The Universal Formula and the Dimensional Analysis Formula are the most common. It can be confusing to go back-and-forth between formulas, trying to remember where the dosage or volume belong in the equations. Determine which formula is most helpful for you, then use it to practice for your NCLEX. Once you’re a licensed nurse, remember it throughout your career.

Universal Formula (“Desired over have” Formula) for Medications

Example of Universal Formula:

Provider orders digoxin 0.5 mg PO daily.
Pharmacy delivers 0.25 mg/mL.
Nurse administers 2 mL.

Formula: D/H x V = Dose
Dose = (0.5mg ÷ 0.25mg) x 1 mL
Dose = 2 mL

Dimensional Analysis Formula (Factor Label Formula) for ALL calculations

The DA Formula may seem more complicated, but it doesn’t require memorization. It actually reduces medication errors and can be used for all dosage calculations, including intravenous.

Here are the steps (from Lippincott NursingCenter/Wolters Kluwer):

1. Start with the label (unit of measure) needed in the answer to determine what unit of measure is needed to begin setting up the calculation.
2. Build the calculation by placing information with the same label as the preceding denominator into the equation in the numerator to cancel out the unwanted labels. Repeat until all units of measure not needed in the answer are cancelled out.
3. Calculate to determine the correctly labeled numeric answer. Don’t round any numbers in the equation until you have the final answer.

Example of Dimensional Analysis Formula, using the digoxin example above:

Provider orders digoxin 0.5 mg PO daily.
Pharmacy delivers 0.25 mg/mL.

Step 1: On the left side of the equation, place the label/unit of measure. (how many mL = …..)

Step 2: On the right side, place the information with the same label in the numerator.
How many mL = ^mL⁄_{0.25 mg}

Step 3: Place the information with the same label as the preceding denominator into the equation, to cancel out the unwanted label. Then repeat this step (as necessary) until all the unwanted labels are canceled out.
How many mL = ^{0.5 mg}⁄_{0.25 mg}

Step 4: Multiply the numbers across the numerator, then multiply all the numbers across the denominator. Divide the numerator by the denominator for the final answer with the correct label.
mL = ^{mL x 0.5 mg}⁄_{0.25 mg} = ^{0.5 mL}⁄_0.25 = 2mL

Example of Dimensional Analysis Formula for Intravenous Administration

Provider orders heparin 500 units/hour IV.
Pharmacy delivers heparin 20,000 units in 500 mL D5W.

Step 1: How many ^mL⁄_hr

Step 2: How many ^mL⁄_hr = ^{1 mL}⁄_{40 units}

Step 3: How many ^mL⁄_hr = ^{1 mL}⁄_{40 units} x ^{500 units}⁄_hr

Step 4: How many ^mL⁄_hr = ^{500 mL}⁄_{40 hr} = 12.5 mL/hr

Universal Formulas for Continuous Intravenous (IV) Medications

Although there are universal formulas, some conversions may be required before calculation:

1. Check the drug concentration.
2. Determine the unit of measurement: units/hr, mg/hr, mg/min, mcg/min, mcg/kg/min
3. Depending on how the drug is ordered, use one of the following formulas.

Example of mcg/min:

A patient is receiving nitroglycerin IV 50 mg/500 mL 0.9% Normal Saline at 8 mL/hr. What is the mcg/min dose?

Step 1: ^{50 mg}⁄_{500 mL} x  ^{1000 mcg}⁄_{1 mg} x  ^{8 mL}⁄_hr x  ^{1 hr}⁄_{60 min} =  ^mcg⁄_min

Step 2: ^400,000⁄_30,000 =  ^mcg⁄_min

Step 3: Answer: 13.3 mcg/min

NOTE: Most current IV infusion pumps can be programmed to the 10th or 100th decimal place. If the pump does not have this capability, you may need to round to the nearest whole number.

Example of mcg/kg/min:

A patient with hypotension requires a dopamine infusion at 10 mcg/kg/min. Pharmacy sends dopamine 800 mg in 250 mL of D5W. The patient weights 180 lbs. What is the hourly IV pump rate?

Step 1: Convert 180 lbs to kg: 180 ÷ 2.2 = 81.8181 (Round to 81.8)

Step 2: Solve for mL/hr

Step 3: ^{800 mg}⁄_{250 mL} x  ^{1000 mcg}⁄_{1 mg} x  ^mL⁄_hr x  ^{1 hr}⁄_{60 min} ÷ 81.8 kg = 10 mcg/kg/min

Step 4: ^{800,000 mcg}⁄_{250 mL} x  ^mL⁄_hr x  ^{1 hr}⁄_{60 min} ÷ 81.8 kg = 10 mcg/kg/min

Step 5: ^{3,200 mcg}⁄_mL x  ^mL⁄_hr x  ^{1 hr}⁄_{60 min} ÷ 81.8 kg = 10 mcg/kg/min

Step 6: ^{3,200 mcg}⁄_mL x  ^mL⁄_hr x  ^{1 hr}⁄_{60 min} = 818 mcg/min

Step 7: ^mL⁄_hr =  ^{818 mcg}⁄_min x  ^{1 mL}⁄_{3,200 mcg} x  ^{60 min}⁄_{1 hr}

Step 8: ^mL⁄_hr = 13.63 mL/hr

Patient safety comes first!

Before administering any medication or IV infusion, follow these important steps:

• Does your dosage or infusion rate calculation make sense?
• ALWAYS double-check your calculation!
• Ask another nurse or a pharmacist to verify your calculation.
• Be familiar with therapeutic dosages of common medications.
• Memorize metric conversions.

Where to find reliable formulas… and more

Lippincott Nursing Center and its free resources, do it today. There’s a wide range of information for nursing students as well as nurses with every level of experience and type of specialty.

The Nursing Pocket Cards provide useful and practical information in a compact form. You can download the PDF pages for quick access and to start your own resource file. All Pocket Cards are evidence-based and reflect current practice.

(Note: Nurse Plus does not receive compensation from Lippincott or Wolters Kluwer.)