PTCE Math: Every Formula You Need, With Worked Examples

The math on the PTCE has a reputation for being the scary part. Honestly, once you know the formulas, it's some of the easiest points on the exam. The numbers are small, there's a calculator built in, and most questions only take two steps.

The part that gave me the most trouble was IV flow rates and drip calculations, so I'll spend a little extra time on those. Everything else on this page is the stuff that comes up again and again: days supply, conversions, insulin, doses by weight and concentrations. Each one has a worked example so you can see the steps, not just the formula.

What math is on the PTCE?

Most of it falls under Order Entry and Processing, which is 22.5% of the exam. PTCB's outline lists it as formulas, ratios, proportions, conversions and Sig codes for working out days supply, quantity, dose, concentration and dilutions. Math also sneaks into other sections, like questions about doses and how long a drug is stable.

Two things worth knowing before you start:

• You don't need to know alligation anymore. PTCB took alligation (and non-sterile compounding) off the exam when the new outline started in January 2026. If your study guide is older, you can skip that chapter.
• You can't bring your own calculator. One is built into the exam, so there's nothing to buy or bring.

The conversions to memorize

These are the numbers every other formula leans on. Know them cold.

Days supply

This is the one you'll use the most, on the exam and at work.

Days supply = quantity dispensed ÷ amount used per day

Example: Take 1 tablet by mouth every 8 hours. Quantity: 42.

• Every 8 hours is 3 times a day, so 3 tablets a day
• 42 ÷ 3 = 14 days

Liquids: same formula, in mL.

Example: Take 7.5 mL by mouth twice a day. Quantity: 150 mL.

• 7.5 mL × 2 = 15 mL a day
• 150 ÷ 15 = 10 days

Eye drops: turn the bottle into drops first. Use 20 drops per mL unless the question gives you a different number. And watch for "both eyes," because that doubles it.

Example: 1 drop in both eyes twice a day. Quantity: 5 mL.

• 5 mL × 20 = 100 drops in the bottle
• 1 drop × 2 eyes × 2 times a day = 4 drops a day
• 100 ÷ 4 = 25 days

If a Sig gives a range or says "as needed," figure the days supply on the most the patient could use in a day.

You can check any of these with the days supply calculator. It shows every step.

Insulin

Insulin is where I see the most mix-ups at work, so it's worth getting comfortable with it.

The key fact: U-100 insulin has 100 units in every mL. From there:

• A 3 mL pen = 300 units
• A box of 5 pens = 1,500 units
• A 10 mL vial = 1,000 units

Example: Inject 25 units under the skin at bedtime. Quantity: one box of 5 pens (3 mL each).

• 5 pens × 300 units = 1,500 units
• 1,500 ÷ 25 = 60 days

A few things that trip people up:

• U-200 and U-300 insulins pack more units into each mL. Always check the strength on the box.
• Priming. Some pharmacies add a couple of units per injection for priming the pen. Mine doesn't. On the exam, only add priming if the question tells you to.
• Sliding scales. "Inject 2 to 10 units with meals" means you figure the days supply on 10 units each time.

The insulin days supply calculator handles pens, vials, boxes and priming if you want to check your work.

Weekly shots with a step-up dose

Insulin isn't the only one. Every so often a GLP-1 like Ozempic trips people up too. It starts at 0.25 mg once a week for 4 weeks, then goes up to 0.5 mg once a week. Because the dose changes, the same pen lasts a different number of days depending on where the patient is in the schedule.

Our pharmacy system usually calculates this for us, but it's good to know how to do it by hand. Treat it like a steroid taper: add up the doses step by step until you run out.

Example (exam-style numbers): A weekly pen holds 2 mg. The patient takes 0.25 mg a week for 4 weeks, then 0.5 mg a week.

• First 4 weeks: 4 × 0.25 mg = 1 mg used, 1 mg left
• 1 mg ÷ 0.5 mg = 2 more weeks
• 4 + 2 = 6 weeks = 42 days

The taper calculator works the same way for steroid tapers and other step-by-step doses.

Doses by weight (mg/kg)

These show up a lot with kids' medicine. Convert pounds to kilograms first, every time.

Example: A child weighs 44 lb. The dose is 10 mg/kg/day, divided twice a day. The suspension is 250 mg/5 mL. How many mL per dose?

• 44 lb ÷ 2.2 = 20 kg
• 20 kg × 10 mg = 200 mg a day
• Divided twice a day = 100 mg per dose
• 100 mg × 5 mL ÷ 250 mg = 2 mL per dose

Read the question slowly. "mg/kg/day" and "mg/kg/dose" give very different answers, and the wrong one is usually sitting right there in the answer choices.

Concentrations and dilutions

Ratio and proportion solves most "how many mL" questions. Set up what you have against what you need.

Example: Amoxicillin 250 mg/5 mL. The dose is 400 mg. How many mL?

• 250 mg is to 5 mL as 400 mg is to x mL
• x = 400 × 5 ÷ 250 = 8 mL

Percent strength means grams per 100 mL.

Example: How many grams of dextrose are in 500 mL of D5W (5% dextrose)?

• 5% = 5 g in every 100 mL
• 500 mL ÷ 100 = 5, and 5 × 5 g = 25 g

Ratio strength works the same way: 1:1,000 means 1 g in 1,000 mL, which is 1 mg/mL. You'll see it with epinephrine.

Dilutions use one formula:

C1 × V1 = C2 × V2 (strength and volume you start with = strength and volume you end with)

Example: How much of a 10% solution do you need to make 200 mL of a 2% solution?

• 10 × V1 = 2 × 200
• V1 = 400 ÷ 10 = 40 mL of the 10% solution, plus 160 mL of diluent to reach 200 mL

IV flow rates (the ones that gave me the most trouble)

PTCB's 2026 outline doesn't name IV flow rates on their own, but they fall under its general "formulas and calculations," and practice tests still include them. The good news is that three formulas cover nearly every question.

mL per hour = total mL ÷ hours

Example: 1,000 mL over 8 hours. 1,000 ÷ 8 = 125 mL/hour

Hours = total mL ÷ mL per hour

Example: 1,000 mL running at 125 mL/hour. 1,000 ÷ 125 = 8 hours

Drops per minute = (total mL × drop factor) ÷ minutes

The drop factor is printed on the IV tubing, in drops per mL (gtt/mL).

Example: 1,000 mL over 8 hours, with tubing that gives 15 gtt/mL.

• 8 hours × 60 = 480 minutes
• 1,000 × 15 = 15,000 drops
• 15,000 ÷ 480 = 31.25, so about 31 drops per minute (you can't count part of a drop, so round to a whole number)

The usual mistakes on these are the units: forgetting to change hours into minutes, or leaving out the drop factor. Write the unit next to every number as you go. If your answer is in mL and the question asked for drops, you skipped a step.

One shortcut: with 60 gtt/mL tubing (called microdrip), drops per minute is the same number as mL per hour. 60 mL an hour on microdrip tubing is 60 drops a minute.

How I got the formulas to stick

Flash cards. It's the same way I learned the drug names: say the brand, the generic and what it's for out loud until it comes without thinking. For the math, try putting the formula on the front of the card and a quick example on the back.

Then do problems, lots of them. Reading a formula and using one under time pressure are two different skills. Gutta's Order Entry lessons cover every formula on this page, with practice questions after each one. And the free Order Entry practice test is a quick check on the Sig codes you need to read the prescription in the first place.

The short version

• Days supply = quantity ÷ amount used per day
• Eye drops: 20 drops per mL, and "both eyes" doubles it
• U-100 insulin = 100 units per mL (a 3 mL pen is 300 units)
• mg/kg: change pounds to kg first (÷ 2.2)
• Percent = grams per 100 mL
• Dilutions: C1 × V1 = C2 × V2
• IV: mL/hr = mL ÷ hours, and drops per minute = mL × drop factor ÷ minutes
• No alligation on the 2026 exam

If you're also wondering what score you need, I broke that down in PTCE passing score explained.

Good luck. You've got this.

Sources: PTCB's PTCE content outline, effective January 2026, its job analysis update (what changed in 2026) and the guidebook's Exam Day page (calculator rules). Ozempic starting dose: Drugs.com. The worked examples are for practice. At work, follow your pharmacy's procedures and your pharmacist.