Pharmacy calculations and conversions represent one of the most critical skill sets tested on the Pharmacy Technician Certification Board (PTCB) examination, appearing throughout the Order Entry and Processing domain which comprises 22.5% of the exam, as well as integrated into other sections where dosing accuracy is paramount. Mastery of pharmaceutical mathematics is not merely an academic exercise—it is a fundamental patient safety competency that directly impacts medication accuracy and therapeutic outcomes in real-world pharmacy practice. The PTCE assesses your ability to perform a wide range of calculations including metric conversions, household-to-metric conversions, dosage calculations, IV flow rate determinations, percentage strength calculations, and days supply computations, all of which must be executed with precision and confidence. Unlike some exam topics that can be memorized through repetition, pharmacy math requires genuine understanding of mathematical principles, the ability to set up problems correctly using dimensional analysis or ratio-proportion methods, and the critical thinking skills to verify that your answers make logical sense in a clinical context. Common conversion factors you must know cold include: 1 kg = 2.2 lbs, 1 fluid ounce = 30 mL, 1 tablespoon = 15 mL, 1 teaspoon = 5 mL, 1 g = 1,000 mg, and 1 mg = 1,000 mcg, among many others. The exam provides an on-screen calculator, but you must still understand which operations to perform and in what sequence, as calculator misuse is a common source of errors. Many candidates report that calculation questions appear more challenging under exam pressure, making thorough practice with timed questions essential for building both accuracy and speed. Beyond basic arithmetic, you’ll encounter multi-step problems that require you to first interpret prescription abbreviations (like TID, QID, BID), then perform conversions, and finally calculate quantities or days supply—all while maintaining precision to avoid potentially life-threatening medication errors. Percentage strength calculations, particularly for IV solutions like D5W or normal saline, require understanding the relationship between grams of solute and volume of solution. Dosage calculations based on patient weight (mg/kg) are especially critical in pediatric and critical care settings where even small errors can have serious consequences. The ability to convert between different units of measurement seamlessly—from micrograms to milligrams, from pounds to kilograms, from liters to milliliters—is tested repeatedly throughout the exam in various contexts. By practicing diverse calculation problems and developing a systematic approach to problem-solving, you’ll build the mathematical confidence and competence necessary to excel on this crucial component of the PTCB exam and, more importantly, to practice safely and effectively as a certified pharmacy technician.
Practice Questions
Question 1
**A prescription calls for 250 mg of medication to be given four times daily. How many grams will the patient receive in one day?**
A) 0.25 g B) 1 g C) 2.5 g D) 10 g
**Correct Answer: B**
**Explanation:** First, calculate the total daily dose: 250 mg × 4 = 1,000 mg. Then convert milligrams to grams: 1,000 mg ÷ 1,000 = 1 g. The patient will receive 1 gram per day.
Question 2
**How many milliliters are in 2 tablespoons?**
A) 10 mL B) 15 mL C) 30 mL D) 60 mL
**Correct Answer: C**
**Explanation:** One tablespoon equals 15 mL. Therefore, 2 tablespoons = 2 × 15 mL = 30 mL. This is a common household-to-metric conversion that pharmacy technicians must know.
Question 3
**A prescription reads: “Amoxicillin 250 mg/5 mL suspension. Sig: 500 mg PO TID × 10 days.” How many milliliters should be dispensed?**
A) 100 mL B) 150 mL C) 200 mL D) 300 mL
**Correct Answer: D**
**Explanation:** First, determine the dose per administration: 500 mg requires 10 mL (since 250 mg/5 mL means 500 mg/10 mL). TID means three times daily, so daily volume = 10 mL × 3 = 30 mL. For 10 days: 30 mL × 10 = 300 mL.
Question 4
**Convert 5 fluid ounces to milliliters.**
A) 75 mL B) 100 mL C) 150 mL D) 200 mL
**Correct Answer: C**
**Explanation:** One fluid ounce equals 30 mL. Therefore, 5 fluid ounces = 5 × 30 mL = 150 mL. This conversion is essential for processing prescriptions with household measurements.
Question 5
**A patient weighs 176 pounds. What is the patient’s weight in kilograms?**
A) 70 kg B) 80 kg C) 90 kg D) 100 kg
**Correct Answer: B**
**Explanation:** To convert pounds to kilograms, divide by 2.2: 176 lbs ÷ 2.2 = 80 kg. This conversion is critical for calculating weight-based medication doses.
Question 6
**An IV solution is infusing at 125 mL/hour. How many milliliters will the patient receive in 8 hours?**
A) 500 mL B) 750 mL C) 1,000 mL D) 1,250 mL
**Correct Answer: C**
**Explanation:** Multiply the infusion rate by the time: 125 mL/hour × 8 hours = 1,000 mL. This type of calculation is important for monitoring IV therapy.
Question 7
**A prescription requires 0.5 g of active ingredient. How many milligrams is this?**
A) 5 mg B) 50 mg C) 500 mg D) 5,000 mg
**Correct Answer: C**
**Explanation:** To convert grams to milligrams, multiply by 1,000: 0.5 g × 1,000 = 500 mg. Understanding metric conversions is fundamental for pharmacy practice.
Question 8
**How many teaspoons are in 1 fluid ounce?**
A) 2 teaspoons B) 4 teaspoons C) 6 teaspoons D) 8 teaspoons
**Correct Answer: C**
**Explanation:** One teaspoon equals 5 mL, and one fluid ounce equals 30 mL. Therefore, 30 mL ÷ 5 mL = 6 teaspoons per fluid ounce.
Question 9
**A medication is available as 20 mg/mL. How many milliliters are needed to provide a 75 mg dose?**
A) 2.5 mL B) 3.0 mL C) 3.75 mL D) 4.0 mL
**Correct Answer: C**
**Explanation:** Use the formula: Volume = Dose needed ÷ Concentration. Volume = 75 mg ÷ 20 mg/mL = 3.75 mL.
Question 10
**A prescription reads: “Dispense 120 mL. Sig: 1 tsp PO QID.” How many days will this supply last?**
A) 5 days B) 6 days C) 7 days D) 8 days
**Correct Answer: B**
**Explanation:** One teaspoon = 5 mL. QID means four times daily, so daily usage = 5 mL × 4 = 20 mL. Days supply = 120 mL ÷ 20 mL/day = 6 days.
Question 11
**What is the percentage strength of a solution containing 25 g of active ingredient in 100 mL of solution?**
A) 2.5% B) 12.5% C) 25% D) 50%
**Correct Answer: C**
**Explanation:** Percentage strength (w/v) = (grams of solute ÷ mL of solution) × 100. Therefore, (25 g ÷ 100 mL) × 100 = 25%.
Question 12
**A patient is to receive 1.5 L of IV fluid over 12 hours. What is the flow rate in mL/hour?**
A) 100 mL/hour B) 125 mL/hour C) 150 mL/hour D) 175 mL/hour
**Correct Answer: B**
**Explanation:** First, convert liters to milliliters: 1.5 L = 1,500 mL. Then divide by hours: 1,500 mL ÷ 12 hours = 125 mL/hour.
Question 13
**How many grams of dextrose are in 500 mL of D5W (5% dextrose in water)?**
A) 5 g B) 10 g C) 25 g D) 50 g
**Correct Answer: C**
**Explanation:** A 5% solution contains 5 g per 100 mL. For 500 mL: (5 g/100 mL) × 500 mL = 25 g of dextrose.
Question 14
**A prescription calls for 2.5 mg of a medication. The available tablets are 1.25 mg. How many tablets should be dispensed for each dose?**
A) 1 tablet B) 2 tablets C) 3 tablets D) 4 tablets
**Correct Answer: B**
**Explanation:** Divide the prescribed dose by the tablet strength: 2.5 mg ÷ 1.25 mg/tablet = 2 tablets per dose.
Question 15
**Convert 2.5 mcg to mg.**
A) 0.0025 mg B) 0.025 mg C) 0.25 mg D) 2.5 mg
**Correct Answer: A**
**Explanation:** To convert micrograms (mcg) to milligrams (mg), divide by 1,000: 2.5 mcg ÷ 1,000 = 0.0025 mg. This conversion is critical for preventing medication errors with high-alert drugs.
Study Tips
- Memorize key conversion factors and practice them daily
- Use dimensional analysis to set up problems systematically
- Always double-check your work and verify answers make sense
- Practice with the on-screen calculator to build familiarity
- Work through multi-step problems to build confidence
- Focus on understanding concepts, not just memorizing formulas
- Time yourself on practice problems to build speed and accuracy
Good luck with your PTCB exam preparation!