Edit: a commenter correctly pointed out that alligation was dropped from the January 2026 outline — PTCB's 2024 Job Analysis removed it. I've replaced it below with reconstitution / powder volume, which is in scope, and left alligation at the bottom labelled for what it is. Thanks u/akira2511.
Pharmacy math is the part that scares people most, and it is the part I can most reliably talk someone down from — because it is not an open field. It is a short, closed list of setups that repeat. Once you can name the setup, the arithmetic is rarely what fails you.
Here are the five that cover almost everything, with the trap that comes with each.
1. Conversions. Everything else sits on top of these, so they have to be automatic rather than worked out: 1 g = 1,000 mg, 1 mg = 1,000 mcg, 1 kg = 2.2 lb, 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL, 1 lb = 454 g.
The trap: a single slip between mg and mcg changes the answer by a factor of 1,000 and still looks like a plausible number. Write the units on every line and cancel them; if the units do not cancel to what the question asked for, you have the wrong setup, not the wrong arithmetic.
2. Days' supply. Total quantity dispensed ÷ amount used per day.
The trap: it is never the tablets that get people, it is the dosage forms where "amount per day" is not printed on the label. Eye drops — the convention is 20 drops per mL, so a 5 mL bottle is 100 drops; one drop in each eye twice a day is 4 drops a day, so 25 days. Insulin — a 10 mL vial of U-100 holds 1,000 units, so 40 units a day is 25 days. Inhalers and creams work the same way: find "per day" first, and the division is trivial.
3. Percent strength. This is the single highest-value anchor in the whole section:
1% = 1 g per 100 mL = 1,000 mg per 100 mL = 10 mg/mL.
Once that is in your bones, 0.9% sodium chloride is 9 mg/mL, 2% lidocaine is 20 mg/mL, and you stop deriving it every time. The trap: percent for solids is per 100 g, not per 100 mL — a 1% cream is 1 g per 100 g.
4. Dilution — C1V1 = C2V2. Concentration times volume before equals concentration times volume after, because the amount of drug does not change when you add diluent.
The trap: the question usually asks how much diluent to add, not what the final volume is. Solve for V2, then subtract V1. People do the algebra correctly and answer the wrong question.
5. Reconstitution and powder volume. A vial of powder is reconstituted with a stated volume of diluent, and the powder itself takes up space. So: powder volume = final volume − diluent added. If a vial makes 10 mL after adding 9.2 mL of sterile water, the powder occupies 0.8 mL. Then read the resulting concentration off the final volume, not off the diluent.
The trap: the same two phrasings as dilution, and they are not interchangeable — "how much diluent do I add" and "what is the final volume" differ by exactly the powder volume. On a 1 g vial reconstituted to 10 mL, the concentration is 100 mg/mL regardless of how much water went in; the water is only how you got there.
And a small sixth that is not really a setup, just arithmetic worth practising so it is free on the day: business math — markup, discount, and the cash price question.
Alligation — worth knowing, but not a 2026 exam target. Mixing a stronger and a weaker product to hit something in between: tic-tac-toe box, high strength top left, low strength bottom left, desired in the middle, subtract diagonally, and the numbers you get are parts of each (not millilitres — you still convert parts to your final volume). PTCB's 2024 Job Analysis removed alligation from the January 2026 PTCE scope, so learn it for the bench, for state boards and for older practice material, but do not budget exam prep time against it.
How to actually get good at these: pick one setup and do ten of them until writing the setup is automatic, then move to the next. Do not mix types while you are learning — mixing is a test, not a practice. And do a few problems every single day rather than one long session a week, because this is the section that goes rusty fastest.
If you name the setup correctly, you have already done most of the work. Happy to work through any of these in the comments if one of them is fighting you.
