Pharmacy Tech Math for the PTCE: A Guide With Worked Examples

Pharmacy math is the topic PTCE candidates fear most, and the fear is understandable: it is the one part of the exam where you cannot recognize your way to an answer. You have to produce it. The encouraging truth is that PTCE math draws from a small set of repeatable patterns, and every pattern yields to practice.

First, some good news about the 2026 exam

PTCB removed nonsterile compounding from the PTCE effective January 6, 2026, and with it alligation, the mixing-two-strengths calculation that haunted earlier generations of candidates (ptcb.org). If your study material has you drilling alligation grids, it is teaching an exam that no longer exists.

What remains is listed in the official outline’s Order Entry and Processing domain, 22.50 percent of the exam: formulas, calculations, ratios, proportions, conversions, sig codes, and the everyday quantities of pharmacy work, meaning days’ supply, quantity, dose, concentration, and dilutions (ptcb.org). Several Medications-domain knowledge areas are also flagged as calculation-based, so doses and strengths can appear there too.

The core patterns

Nearly every PTCE calculation is one of these:

• Days’ supply: how long a dispensed quantity lasts at the prescribed dose.
• Quantity to dispense: the reverse, how much to dispense for a given duration.
• Dose calculations: converting between what is prescribed and what is on the shelf, including weight-based dosing.
• Unit conversions: pounds to kilograms, milligrams to grams, milliliters to liters, and the household-to-metric conversions.
• Percentage strength: what a concentration like 5 percent w/v actually contains.
• Ratios, proportions, and dilutions: scaling a known relationship up or down.
• Rates: how much per hour, or per minute, from a total volume and time.

Sig code fluency (b.i.d., t.i.d., q6h, and the rest) feeds directly into these, because you cannot compute a days’ supply if you cannot read the directions. Learn the codes cold first.

Here are three fully worked examples in the style of our math workbook, where every problem shows its steps and every answer key is machine-verified.

Worked example 1: days’ supply

A prescription reads: 5 mL by mouth three times daily. The pharmacy dispenses a 150 mL bottle. What is the days’ supply?

Step 1. Find the daily dose in mL. The patient takes 5 mL per dose, three doses per day:

5 mL x 3 = 15 mL per day

Step 2. Divide the total quantity by the daily use:

150 mL / 15 mL per day = 10 days

That is the whole pattern: total quantity divided by daily consumption. Every days’ supply problem, whether it involves tablets, milliliters, or inhaler puffs, reduces to those two steps. The variations only change how much work it takes to find the daily consumption.

Worked example 2: percentage strength

How many grams of dextrose are in 500 mL of D5W (5 percent dextrose in water)?

Step 1. Translate the percentage. A 5 percent weight-in-volume (w/v) solution contains 5 grams of drug per 100 mL of solution. That per-100 definition is what w/v percent means.

Step 2. Scale it to the volume in the problem with a proportion:

5 g / 100 mL = x g / 500 mL

Step 3. Solve for x:

x = (5 x 500) / 100 = 25 g

Percentage-strength problems are pure proportion once you translate the percent sign. The most common error is skipping the translation step and treating 5 percent as 5 grams total. Write out the per-100 statement every time until it is automatic.

Worked example 3: infusion rate

An IV bag contains 1,000 mL to be infused over 8 hours. What is the flow rate in mL per hour?

Step 1. Identify the total volume and total time: 1,000 mL and 8 hours.

Step 2. Divide volume by time:

1,000 mL / 8 h = 125 mL/h

Rate problems are division with attention to units. The exam can dress them up by asking for mL per minute, in which case you do the same division and then convert, dividing the hourly rate by 60. Keeping the units written next to every number is the cheapest insurance against error there is.

How to drill so it sticks

Work problems, do not read them. Watching a solution makes sense in the moment and evaporates by morning. Cover the solution, produce your own, then compare.

Drill by pattern, then mixed. Do a block of days’ supply problems until the pattern is boring, then a block of conversions, and so on. Once each pattern is solid, switch to mixed sets, because the real exam never tells you which pattern is coming.

Demand worked answers from your materials. An answer key that just says “125 mL/h” cannot show you where you went wrong. Every problem in our workbook shows its steps, and every answer is machine-verified, because an error in the answer key is the one error a student cannot catch.

Check your practice volume. Twenty math problems total is a vocabulary quiz. A hundred-plus problems across all the patterns is preparation.

Our free 25-question PTCE practice test includes calculation questions with fully worked, cited answers, so you can measure where your math stands today. Exam content and policies can change, so verify current requirements at ptcb.org.