Pharmacy technician math on the PTCE

Math on the PTCE isn't a separate section. PTCB's 2026 content outline marks individual knowledge areas with an asterisk when "some or all of this statement reflects calculation-based knowledge," and those asterisks are spread across all four domains. The main one is area 4.1 in Order Entry and Processing, which lists "formulas, calculations, ratios, proportions, conversions, Sig codes... abbreviations, medical terminology, and symbols for days supply, quantity, dose, concentration, dilutions."

The good news is that it's a small set of techniques used over and over. Here they are with a worked example of each.

1. Unit conversions

Almost every problem starts with getting units to match. The conversions pharmacy work relies on most:

• 1 kg = 1,000 g; 1 g = 1,000 mg; 1 mg = 1,000 mcg
• 1 L = 1,000 mL
• 1 kg = 2.2 lb
• 1 teaspoon = 5 mL; 1 tablespoon = 15 mL
• 1 fluid ounce is about 30 mL (29.57 mL exactly; pharmacy problems usually round to 30)

Example: a patient weighs 176 lb. What is that in kilograms? 176 / 2.2 = 80 kg.

2. Ratio and proportion (dose and quantity)

Most dose problems are one proportion: what you have is to what you need.

Example: amoxicillin suspension is 250 mg per 5 mL. The dose is 400 mg. How many mL?

250 mg / 5 mL = 400 mg / x mL, so x = (400 x 5) / 250 = 8 mL.

Weight-based doses add one step. Example: the 80 kg patient above needs 5 mg/kg. That's 5 x 80 = 400 mg.

3. Days supply

Days supply = quantity dispensed / quantity used per day.

Example: 60 tablets, sig "1 tab PO bid" (twice a day). The patient uses 2 tablets a day, so 60 / 2 = 30 days.

Liquids, inhalers, insulin and eye drops add conversion steps and a few real traps. Days supply calculation: formula and traps goes through them.

4. Percent strength

For solutions, % w/v means grams per 100 mL. A 1% solution has 1 g of drug in every 100 mL.

Example: how many grams of dextrose are in 500 mL of D5W (5% dextrose in water)? 5 g per 100 mL x 500 mL = 25 g.

Ratio strength is another way of writing the same thing: 1:1,000 means 1 g in 1,000 mL, which is 0.1%.

5. Dilutions (C1V1 = C2V2)

When you dilute a stock solution, the amount of drug stays the same while the volume grows. So concentration x volume before equals concentration x volume after.

Example: you need 100 mL of a 5% solution and have 20% stock. How much stock?

20% x V1 = 5% x 100 mL, so V1 = (5 x 100) / 20 = 25 mL of stock, brought up to 100 mL with 75 mL of diluent.

6. Alligation

Alligation answers the related question: how much of each of two strengths do you mix to get a strength in between? You subtract diagonally across a small grid to get parts.

Example: mix 10% and 2% to make 5%. Parts of 10% = 5 - 2 = 3. Parts of 2% = 10 - 5 = 5. So the ratio is 3 parts 10% to 5 parts 2%. Check: (3 x 10 + 5 x 2) / 8 = 40 / 8 = 5%.

Alligation method explained covers turning parts into real volumes, and the case where one ingredient is plain diluent.

7. IV flow and drip rates

• Flow rate (mL/hr) = total volume / total hours.
• Drip rate (gtt/min) = volume (mL) x drop factor (gtt/mL) / time (min).

Example: 1,000 mL over 8 hours is 1,000 / 8 = 125 mL/hr. With a 15 gtt/mL set, that's 125 x 15 / 60 = 31.25, which rounds to 31 gtt/min.

IV flow rate and drip rate formulas has more examples, including infusion time.

8. Roman numerals and sig codes

Area 4.1 names Roman numerals and sig codes along with the math, and they matter because a misread sig breaks the calculation that follows it. Know the basic numerals (i = 1, v = 5, x = 10, l = 50, c = 100, and subtraction when a smaller numeral comes first, as in iv = 4 and ix = 9) and the common frequency codes (daily, bid, tid, qid, q4h, q6h, prn).

How to practice

• Write the units at every step. Most wrong answers on these questions come from a unit that silently changed, like mg that should have been mcg, or hours that should have been minutes.
• Estimate first. If 250 mg is in 5 mL, a 400 mg dose has to be a bit less than double 5 mL. If your answer is 80 mL, you've slipped a decimal.
• Do problems, not definitions. Knowing that C1V1 = C2V2 exists earns nothing. Solving twenty of them does.

The free calculators for days supply, alligation and IV flow rate are useful for checking your own practice answers. They're not a substitute for doing the math by hand, since you'll be working the problems yourself on the exam.

For the rest of the exam, the 2026 PTCE content outline covers what changed this year. Encodr's PTCB course, which includes a calculations unit built around practice problems, is being built now and isn't live yet. The PTCB exam page will have it at launch.