Master every calculation type on the PTCE — dosage, days supply, IV flow rates, dilutions, and compounding — with formulas, worked examples, and practice problems.
Practice with Flashcards →The Four Calculation Categories
Every pharmacy math problem on the PTCE falls into one of these four areas
Calculate the amount of a drug to dispense from a prescriber's order — using the D/H×Q formula, weight-based (mg/kg) dosing, and unit conversions between metric, household, and apothecary systems.
Calculate how many days a dispensed quantity will last based on the sig (directions). Covers tablets, liquids, eye drops, inhalers, and controlled substances — a high-frequency billing and dispensing topic.
Calculate IV infusion rates in mL/hr and drip rates in gtt/min using macrodrip and microdrip sets. Determine infusion duration and IVPB piggyback timing — critical for hospital pharmacy settings.
Use C₁V₁=C₂V₂ for dilutions, alligation for mixing two concentrations, and powder volume formulas for reconstitution. Covers percent concentrations (w/v, w/w, v/v) and beyond-use dating.
How It Works
Formulas, step-by-step logic, and key reference values for every calculation type
The D/H×Q Method & Weight-Based Dosing
Example: "Amoxicillin 500mg ordered; available as 250mg/5mL suspension." D=500mg, H=250mg, Q=5mL.
If D is in mg and H is in g — convert first. 1g = 1000mg. Mismatched units are the #1 source of calculation errors.
(500mg ÷ 250mg) × 5mL = 2 × 5mL = 10 mL per dose. Always label your answer with units.
If D > H, you'll give more than Q. If D < H, you'll give less than Q. An answer of 50 tablets per dose is a red flag — recheck your math.
Calculating Days Supply from the Sig
Common Sig Codes
Infusion Rate & Drip Rate Calculations
Dilutions, Alligation & Reconstitution
Alligation — Mixing Two Concentrations
Used when you need to mix a higher and lower concentration to get a desired middle concentration.
Compare & Reference
Filter by calculation type to compare formulas, units, and exam tips side by side.
| Concept | Category | Formula / Value | When to Use | Exam Gotcha |
|---|---|---|---|---|
D/H × Q Formula | Dosage | (Desired ÷ Have) × Quantity | Any time you need to find how much to give based on what's available | Units must match! If D is in mg and H is in g, convert first or the answer will be wrong by 1000× |
Weight-Based Dose | Dosage | mg/kg × weight (kg) | Pediatric dosing, renal dosing, oncology. Always convert lbs to kg first. | 1 kg = 2.2 lbs. Divide weight in lbs by 2.2 to get kg. Do NOT multiply — that's a common error. |
Unit Conversion — Weight | Dosage | 1 g = 1,000 mg = 1,000,000 mcg | Whenever the ordered dose and available dose use different units | mcg to mg: divide by 1000. mg to g: divide by 1000. Moving left on the prefix scale = multiply × 1000. |
Unit Conversion — Volume | Dosage | 1 tsp=5mL · 1 tbsp=15mL · 1 oz=30mL | Household measurement prescriptions, pediatric liquid dosing for patients at home | 1 tablespoon = 3 teaspoons = 15 mL. Don't confuse tsp and tbsp — a 3× error on a liquid dose can be dangerous. |
Tablets/Capsules Days Supply | Days Supply | Qty ÷ (tablets per dose × doses per day) | Any solid dosage form where quantity dispensed is a count of units | Read the sig carefully: "i–ii tabs" means 1 to 2 tablets. Use the MAXIMUM dose (ii) for days supply calculation. |
Liquid Days Supply | Days Supply | Total mL ÷ mL per day | Suspensions, syrups, solutions ordered in mL per dose | Convert household measurements: "1 tsp TID" = 5mL × 3 = 15mL/day. Then divide total volume by 15. |
Inhaler Days Supply | Days Supply | Total actuations ÷ (puffs × times/day) | MDIs (metered dose inhalers) with a known actuation count in the canister | The canister says "200 actuations" — that's the TOTAL, not per day. Divide by daily use to get days supply. |
Eye Drop Days Supply | Days Supply | (Volume mL × 20 drops/mL) ÷ drops per day | Ophthalmic solutions dispensed by volume (mL) with a drop-based sig | Estimate 20 drops per mL (or 1 drop = 0.05 mL). "OU" = both eyes. "OD" = right eye. "OS" = left eye. |
IV Flow Rate (mL/hr) | IV Rate | Volume (mL) ÷ Time (hr) | Programming an IV pump or verifying an infusion rate | Time must be in hours. Convert minutes to hours (divide by 60) before using this formula. |
Drip Rate (gtt/min) | IV Rate | (Volume × Drop Factor) ÷ Time (min) | Manually regulating gravity IV infusion sets without an electronic pump | Drop factor is on the IV tubing package: 10, 15, or 20 gtt/mL (macrodrip) or 60 gtt/mL (microdrip). Never assume. |
Microdrip Shortcut | IV Rate | With 60 gtt/mL set: gtt/min = mL/hr | Whenever you're using a 60 gtt/mL (microdrip) administration set | This only works with microdrip sets. Don't apply it to macrodrip sets — that's the #1 IV drip rate mistake. |
Infusion Time | IV Rate | Volume (mL) ÷ Rate (mL/hr) = Time (hr) | Determining when an IV bag will run out, or verifying if a rate is correct for a desired duration | Convert the answer from decimal hours to hours and minutes. 0.5 hr = 30 min. 0.25 hr = 15 min. |
Dilution — C₁V₁=C₂V₂ | Compound | C₁ × V₁ = C₂ × V₂ | Preparing a less concentrated solution from a more concentrated stock solution | Concentrations can be in any unit (%, mg/mL) as long as both C values use the SAME unit. Volumes must also match units. |
Powder Volume | Compound | PV = FV − DV | Reconstituting a dry powder (antibiotic vial) — the powder itself takes up space | Always calculate powder volume BEFORE reconstituting. If label says "add 90mL water to get 100mL," PV = 10mL — the powder already contributes volume. |
Alligation | Compound | Subtract diagonally across the desired concentration | Mixing two different concentrations of the same drug to reach a target concentration | The result is a RATIO of parts, not volume. Multiply each part fraction by the total desired volume to get actual mL needed. |
Percent Concentration (w/v) | Compound | % w/v = grams per 100 mL | Most liquid drug concentrations: 0.9% NaCl = 0.9g per 100mL = 9 mg/mL | Normal Saline = 0.9% NaCl. D5W = 5% dextrose = 5g/100mL. D10W = 10% = 10g/100mL. Know these by memory. |
Worked Examples
Step-by-step solutions for each calculation type — study the method, not just the answer.
Practice Quiz
10 PTCE-style calculation questions — show your work, then check the explanation
🧮 Calc Wizard
Tell the wizard what you're solving and get the right formula with a guided walkthrough.
Memory Hooks
Tap each card to reveal — 8 high-yield facts for exam day
Tap any card to flip it
