Pharmacy Technician Math: PTCE Calculations, Days Supply, Formulas & Worked Examples

This guide covers the pharmacy calculation types on the PTCE: what math is tested, which formulas to know, worked examples for the most common question formats, and how to build reliable calculation skills under exam conditions. The math on this exam is technician processing math, not clinical pharmacology. For the full domain context, see the PTCE study guide. For a pass strategy that integrates math with the other three domains, see How to pass the PTCE.

Formula reference sheet (memorize before your first timed set)

Keep this table visible while drilling. Internalize every formula before you move to timed practice.

Exam priority: Days supply and D/H×Q appear most frequently. Lock those first, then conversions, then ratio/proportion and dilution. Skip IV flow/drop-rate drilling unless your practice bank shows them.

What math shows up on the PTCE?

PTCE math lives primarily in the Order Entry and Processing domain, which is 22.5% of the 2026 exam. Calculation-based items are marked with an asterisk in the PTCE Content Outline. You can expect 8 to 10 calculation questions on a given exam.

The calculation types tested under sub-area 4.1:

What was removed in 2026: Alligation calculations and compounding math were removed from the PTCE effective January 6, 2026. Prep resources from before 2026 may include these topics; skip them.

Sig codes you must read instantly

Every calculation starts with sig translation. A misread sig code produces a clean calculation on the wrong problem. For a dedicated abbreviation table and ISMP error-prone list, see pharmacy sig codes.

Build instant recognition for high-frequency sig codes:

Roman numerals also appear in sig codes. Know: I=1, II=2, III=3, IV=4, V=5, X=10, XX=20, XXX=30. "i tab QID" = 1 tablet four times daily.

Exam habit: translate the sig to plain English before touching any numbers. Wrong translation produces a wrong answer even with correct arithmetic.

How do you calculate days supply for the PTCE?

Days supply is the most commonly missed calculation type. The formula is straightforward; the errors come from sig misreads and quantity assumptions.

Core formula: Days Supply = Quantity Dispensed ÷ (Units per dose × Doses per day)

Worked example 1: tablets: Sig: Take 2 tablets BID. Dispensed: 120 tablets.

• Units per dose = 2, Doses per day = 2, Daily use = 4
• Days supply = 120 ÷ 4 = 30 days

Worked example 2: liquid: Sig: Take 10 mL TID. Dispensed: 150 mL.

• Daily use = 10 mL x 3 = 30 mL per day
• Days supply = 150 ÷ 30 = 5 days

Worked example 3: inhaler: 200-actuation inhaler. Sig: 2 puffs BID.

• Daily use = 2 puffs x 2 = 4 puffs per day
• Days supply = 200 ÷ 4 = 50 days

Common traps on exam items:

1. BID vs QID confusion: misread doubles or halves the entire answer
2. "1 to 2 tablets" ranges: use the maximum stated dose unless the stem specifies otherwise
3. PRN with no stated max: do not invent a days supply; the answer is usually "cannot be determined"
4. Ignoring "take two tablets" and treating every dose as one unit
5. Liquid fills where the dispensed quantity is already in packages: apply the same formula per mL

When you miss a days-supply item, rewrite the stem in three lines before reviewing the explanation: sig → daily use → quantity ÷ daily use. That setup is the entire skill.

How do you calculate dose quantities (D/H×Q)?

The D/H×Q formula calculates how many tablets or mL to dispense for a single dose.

Formula: Dose to give = (Desired dose ÷ Have on hand) × Quantity per unit

Worked example: Ordered: 500 mg. Available: 250 mg / tablet.

• (500 mg ÷ 250 mg) × 1 tablet = 2 tablets

Worked example (liquid): Ordered: 150 mg. Available: 100 mg / 5 mL.

• (150 mg ÷ 100 mg) × 5 mL = 7.5 mL

Weight-based dosing follows the same structure but adds a conversion step:

1. Convert patient weight to kg (lb ÷ 2.2 = kg)
2. Multiply: dose (mg/kg) × weight (kg) = total dose in mg
3. Apply D/H×Q to find the volume or tablet count

Unit conversions every pharmacy technician must know

Conversion errors are the second most common source of calculation mistakes. Keep these fluent:

Worked conversion example: Patient weighs 154 lb. Convert to kg for weight-based dosing.

• 154 ÷ 2.2 = 70 kg

Pro Tip: Always convert units before calculating, not after. A unit mismatch at step 1 produces a wrong answer that looks arithmetically correct all the way to the end.

Ratio, proportion, and concentration problems

Ratio and proportion stems ask: "If X amount is in Y volume, how much is in Z volume?"

Method: Set up the known ratio on the left, the unknown on the right, with matching units:

• Known: 250 mg / 5 mL
• Unknown: ? mg / 10 mL
• Cross-multiply: 250 × 10 = 5 × ? → ? = 500 mg

Dilution problems use C1V1 = C2V2: If you have 500 mL of a 20% solution and need to make a 10% solution, how much final volume do you get?

• C1×V1 = C2×V2 → 20% × 500 mL = 10% × V2 → V2 = 1,000 mL

After solving, ask: "Is this answer a realistic prescription or dispensing quantity?" A sanity check catches arithmetic slips before you finalize.

NDC and label details that affect processing

Not every calculation item is arithmetic. NDC identification questions ask whether you understand what the product code communicates.

NDC (National Drug Code) is presented in three segments:

The common NDC format is 5-4-2 (5 digits / 4 digits / 2 digits), though 5-3-2 formats also appear. The product segment (middle) is the most frequently tested: exam items ask which segment identifies the specific drug and strength.

Processing items also include insurance adjudication flags, for example, a "refill too soon" rejection or a "days supply mismatch." These are Order Entry judgment questions, not arithmetic, but they appear in the same practice hub.

Additional worked examples (all calculation types)

Work through every example below. Write the setup before looking at the answer.

Days supply: tablets with variable dose range

Example 4: ibuprofen 400 mg tabs; Sig: i to ii tabs PO Q6H PRN pain; Dispense #120.

• Maximum dose: 2 tablets every 6 hours = 2 × 4 = 8 tablets/day max
• Days supply at maximum: 120 ÷ 8 = 15 days
• On exam stems, use the maximum allowed daily dose when calculating insurance days supply unless told otherwise.

Example 5: metFORMIN 500 mg tabs; Sig: i tab PO BID × 30 days, then ii tabs PO BID; Dispense #180.

• Phase 1 use: 1 × 2 = 2 tabs/day × 30 days = 60 tablets
• Phase 2 use: 2 × 2 = 4 tabs/day; remaining 120 tabs ÷ 4 = 30 days
• Total days supply: 30 + 30 = 60 days (the entire fill covers two months under a step-up dosing regimen)

Example 6: ondansetron 4 mg ODT; Sig: ii tabs SL TID PRN nausea; Dispense #24.

• Daily max: 2 × 3 = 6 tablets/day
• Days supply: 24 ÷ 6 = 4 days

Days supply: liquids

Example 7: amoxicillin 250 mg/5 mL suspension; Sig: 5 mL PO TID; Dispense 150 mL.

• Daily use: 5 mL × 3 = 15 mL/day
• Days supply: 150 ÷ 15 = 10 days

Example 8: cetirizine syrup 5 mg/5 mL; Sig: 10 mL PO QD; Dispense 120 mL.

• Daily use: 10 mL/day
• Days supply: 120 ÷ 10 = 12 days

Example 9: azithromycin 200 mg/5 mL suspension; Sig: 10 mL PO QD × 5 days; Dispense 50 mL.

• Daily use: 10 mL/day × 5 days = 50 mL total needed
• Days supply: 50 ÷ 10 = 5 days (complete course exactly)

Days supply: inhalers

Example 10: albuterol HFA 90 mcg/actuation, 200 actuations; Sig: 2 puffs INH Q4H PRN wheeze.

• Maximum daily use: 2 puffs × 6 times (Q4H) = 12 puffs/day
• Days supply at maximum: 200 ÷ 12 = 16.7 → 16 days (always round down for days supply)

Example 11: fluticasone/salmeterol Diskus 250/50, 60 doses; Sig: 1 puff INH BID.

• Daily use: 1 × 2 = 2 puffs/day
• Days supply: 60 ÷ 2 = 30 days

Dose quantity (D/H×Q)

Example 12: Ordered: amoxicillin 875 mg. Available: amoxicillin 250 mg/cap.

• (875 ÷ 250) × 1 cap = 3.5 capsules
• On the exam, this tests D/H×Q arithmetic. In practice, if a product cannot be split accurately, escalate rather than invent a workaround.

Example 13: Ordered: phenobarbital 30 mg PO. Available: phenobarbital 60 mg scored tablets.

• (30 ÷ 60) × 1 tab = 0.5 tablet (half tablet)
• Scored tablets can be split; verify the drug is appropriate for splitting.

Example 14 (liquid): Ordered: ibuprofen 150 mg. Available: ibuprofen 100 mg/5 mL.

• (150 ÷ 100) × 5 mL = 7.5 mL

Example 15 (weight-based): Child weighs 44 lb. Dose ordered: amoxicillin 40 mg/kg/day in 3 divided doses. Available: 250 mg/5 mL suspension.

• Step 1: Convert weight: 44 ÷ 2.2 = 20 kg
• Step 2: Total daily dose: 40 mg/kg × 20 kg = 800 mg/day
• Step 3: Dose per administration: 800 ÷ 3 = 266.7 mg per dose (approximately 267 mg)
• Step 4: Volume per dose: (267 ÷ 250) × 5 mL = 5.3 mL per dose

Unit conversions: extended practice

Example 16: A patient weighs 198 lb. What is their weight in kg?

• 198 ÷ 2.2 = 90 kg

Example 17: A dose is 0.5 mg. Convert to mcg.

• 0.5 mg × 1,000 = 500 mcg

Example 18: A prescription calls for 2 tablespoons of a syrup. How many mL?

• 2 × 15 mL = 30 mL

Example 19: An oral solution is available in a 6-ounce bottle. How many mL is that?

• 6 × 30 mL = 180 mL

Ratio, proportion, and concentration: extended practice

Example 20 (ratio/proportion): A solution contains 250 mg in 10 mL. How many mg are in 25 mL?

• 250/10 = X/25 → X = 250 × 25 ÷ 10 = 625 mg

Example 21 (percent strength): How many grams of active ingredient are in 250 mL of a 4% w/v solution?

• 4% means 4 g per 100 mL
• 4 g × (250 mL ÷ 100 mL) = 10 g

Example 22 (dilution C1V1=C2V2): You have 200 mL of a 70% isopropyl alcohol solution. How much water do you add to make it 50%?

• C1V1 = C2V2 → 70% × 200 mL = 50% × V2
• V2 = 14,000 ÷ 50 = 280 mL total volume
• Water to add: 280 - 200 = 80 mL

Example 23 (another dilution): You need to prepare 500 mL of a 20% solution. You have a 40% stock. How much stock do you use?

• 40% × V1 = 20% × 500 mL
• V1 = 10,000 ÷ 40 = 250 mL of 40% stock; add 250 mL of diluent

NDC and insurance processing

Example 24: An NDC is formatted 0069-0060-30. Identify each segment.

• Labeler: 0069 (manufacturer/distributor)
• Product: 0060 (drug name, strength, dosage form)
• Package: 30 (package size and type)
• The product segment (middle) is what exam items most commonly ask you to identify.

Example 25 (insurance rejection): A patient presents for a 90-day supply of lisinopril 10 mg; the insurance processes it but rejects with "refill too soon." What is the correct technician action?

• Do not override or bypass the insurance edit.
• Check the previous fill date and days supply on record.
• Inform the patient; explain that the insurance shows it is too early.
• Escalate to the pharmacist if a clinical override (vacation supply, dose change) might apply.

How should I practice pharmacy math for the PTCE?

Do not start with timed speed drills if sig translation is still inconsistent. Use a three-stage progression:

Recommended practice loop:

1. Start a set in Order Entry & Processing practice
2. On each miss, rewrite: sig / daily use / formula setup before reading the explanation
3. Re-attempt a similar item within 24 to 48 hours
4. Once weekly, take a mixed set on free PTCB practice so math is not practiced only in a tidy silo

If Federal Requirements or Patient Safety misses are crowding out math practice time, rebalance using the weak-domain method in How to pass the PTCE. For medication error types and reporting workflows, see PTCB patient safety and medication errors.

Frequently Asked Questions

How many math questions are on the PTCE?

Approximately 8 to 10 of the 80 scored questions on the PTCE involve pharmacy calculations. The number varies by exam version. Calculation-based items are not limited to Order Entry; some Medications and Patient Safety items also require arithmetic. Consistent practice is more reliable than trying to count and skip math questions on exam day.

Was alligation removed from the 2026 PTCE?

Yes. Alligation calculations were removed from the PTCE effective January 6, 2026. Compounding math was also removed. If your study materials predate 2026, skip the alligation and compounding sections. Focus on days supply, dose calculation (D/H×Q), unit conversions, ratio and proportion, and concentration/dilution using C1V1=C2V2.

What is the days supply formula?

Days Supply = Quantity Dispensed ÷ (Units per dose × Doses per day). For liquids: Days Supply = Total mL ÷ mL per day. For inhalers: Days Supply = Total actuations ÷ (Puffs per dose × Doses per day). All three follow the same logic: total quantity divided by daily consumption.

What is the D/H×Q formula used for?

D/H×Q stands for Desired ÷ Have × Quantity. It calculates how many tablets or mL to dispense for a single prescribed dose. Example: Ordered 500 mg, available 250 mg per tablet. (500 ÷ 250) × 1 = 2 tablets. For liquids, Q is the volume per unit (e.g., 5 mL).

How do I convert pounds to kilograms for PTCE problems?

Divide the weight in pounds by 2.2 to get kilograms. Example: 154 lb ÷ 2.2 = 70 kg. Always convert weight to kilograms before applying a mg/kg dose. The reverse conversion is kg × 2.2 = lb.

What does the middle segment of an NDC number identify?

The middle (product) segment identifies the specific drug, its strength, and its dosage form. The first (labeler) segment identifies the manufacturer or distributor. The third (package) segment identifies package size and type. In a 5-4-2 NDC format, the four-digit middle segment is the product code.

Should I memorize every sig code for the PTCE?

Focus on the eight to ten highest-frequency codes: QD, BID, TID, QID, Q4H, Q6H, Q8H, PRN, PO, and HS. Also learn AC (before meals) and PC (after meals). Roman numerals appear in sig codes and are tested separately: I through V and X, XX, XXX. Memorize these as part of your sig code review, not as a separate subject.

Start with one calculation type today

The fastest way to improve calculation scores is to drill one type until it requires no translation effort, then move to the next.

1. Start in Order Entry & Processing practice with days supply items.
2. For each miss, write: sig / daily use / formula setup. Do not look at the answer first.
3. After days supply is consistent, move to dose quantity (D/H×Q), then conversions.
4. Review sample stems: QID tablets per day and Days supply BID.
5. Keep the blueprint in view with the PTCE study guide. For fuller practice volume, see Pricing or the PTCB prep overview.

Complete one untimed Order Entry set today. For every miss, write the three-line setup before reading the explanation.