Mastering PTCE Math: How to Solve Every Dosage Calculation Question Without Stress, A Step-by-Step Tutorial

Dosage math is the most predictable part of the PTCE. The questions follow patterns. If you learn a handful of unit conversions and one reliable setup method, you can solve almost anything under test pressure. This tutorial shows you the exact steps to solve every common dosage calculation without stress, with examples and why each step works.

The right mindset: units first, numbers second

Most errors happen because units don’t match. Numbers are easy once your units line up. Always start by asking: “What unit is the answer in?” Then convert everything to that unit before you calculate. This reduces mistakes and makes your setup obvious.

Second, predict the answer’s size. If you expect around 10 mL and your math gives 0.1 mL or 100 mL, stop and re-check. This “sanity check” catches most slips.

Core conversions you must know cold

Memorize these. You will use them on nearly every problem.

• Weight: 1 kg = 2.2 lb; 1 g = 1000 mg; 1 mg = 1000 mcg.
• Volume (metric): 1 L = 1000 mL.
• Household (if tested): 1 tsp = 5 mL; 1 tbsp = 15 mL; 1 oz (fluid) = 30 mL; 1 cup = 240 mL.
• Insulin: U-100 = 100 units per mL. So 1 unit = 0.01 mL.
• Percent solutions: % w/v = grams per 100 mL (e.g., 3% = 3 g/100 mL).
• Ratio strength: 1:1000 = 1 g per 1000 mL = 1 mg/mL.

The three master methods—and when to use them

1) Desired over Have (D/H × Q)

Use for tablets and liquids when the label gives a direct concentration. You want a dose (Desired, D). You have a strength on hand (Have, H). Q is the quantity that contains H (tablets or mL). The fraction D/H tells you how many “Q” you need. It works because you’re scaling the dose in proportion to what you have.

2) Dimensional Analysis (factor-label)

Use when units are messy or you have several conversions. Write the answer unit on the left. Multiply by fractions so that units cancel diagonally until only the answer unit remains. It works because unit cancellation guards against setup errors.

3) Proportion

Use when the relationship is a simple ratio (e.g., mL per hour). Set up a proportion and cross-multiply. It works because you’re maintaining equal ratios.

A 7-step framework for any dosage question

• 1. Read once for the story, once for the numbers. What is ordered? What is available? What unit is the answer in?
• 2. Write what’s Ordered, what’s on Hand, and the Quantity. O/H × Q fits many problems.
• 3. Convert units early. Get everything into the target unit before solving.
• 4. Choose a method. Start with D/H × Q for simple dose-to-supply. Use dimensional analysis for multi-step or IV math.
• 5. Do the math cleanly. Show the setup. Cancel units.
• 6. Round correctly. Follow clinical rounding rules (see below).
• 7. Sanity check. Is the answer size reasonable? Are the final units correct?

Solid dose forms: tablets and capsules

Pattern: Order in mg. Supply is tablets with mg per tablet.

Method: D/H × Q where Q is 1 tablet unless stated otherwise.

Example 1 (straight): Order: 375 mg. On hand: 250 mg tablets.

• D/H × Q = 375 mg / 250 mg × 1 tablet = 1.5 tablets.
• Answer: 1.5 tablets (only if tablets are scored; otherwise round per policy).

Why it works: 250 mg is “one tablet.” 375 mg is 1.5 times that amount, so you need 1.5 tablets.

Example 2 (multiple tablets per dose): Order: 1 g. On hand: 250 mg tablets.

• Convert 1 g = 1000 mg.
• 1000 mg / 250 mg × 1 tablet = 4 tablets.
• Answer: 4 tablets.

Liquid meds and oral syringes

Pattern: Order in mg. Bottle shows mg per mL or mg per 5 mL.

Method: D/H × Q, where Q is the volume that contains H.

Example: Order: 225 mg. Label: 125 mg per 5 mL.

• 225 mg / 125 mg × 5 mL = 9 mL.
• Answer: 9 mL.

Why it works: If 5 mL contains 125 mg, then 9 mL contains 225 mg by direct proportion.

Weight-based dosing (mg/kg)

Pattern: Order is mg/kg/dose or mg/kg/day. Patient weight in lb or kg. Supply is mg per mL or mg per tablet.

Method: Convert lb to kg if needed. Multiply by mg/kg to find mg per dose. Then use D/H × Q to find mL or tablets.

Example: Order: 15 mg/kg once. Patient: 44 lb. Supply: 100 mg per 5 mL.

• Convert 44 lb ÷ 2.2 = 20 kg (rounded).
• Dose = 15 mg/kg × 20 kg = 300 mg.
• Volume = 300/100 × 5 mL = 15 mL.
• Answer: 15 mL.

Why it works: Weight sets the safe dose. Once you know mg, the concentration gives the volume.

IV pump rates (mL/hr), drip rates (gtt/min), and infusion time

Know the difference:

• mL/hr: Used with infusion pumps.
• gtt/min: Used with gravity tubing; needs drop factor (gtt/mL).
• Infusion time: How long a volume lasts at a set rate.

Example 1 (pump rate): 1000 mL over 8 hours.

• mL/hr = 1000 ÷ 8 = 125 mL/hr.
• Answer: 125 mL/hr.

Example 2 (drip rate): 150 mL over 3 hours. Drop factor: 15 gtt/mL.

• First, mL/min = 150 mL ÷ 180 min = 0.833 mL/min.
• gtt/min = 0.833 × 15 = 12.5 → round to 13 gtt/min.
• Answer: 13 gtt/min (round to the nearest whole drop).

Example 3 (infusion time): Bag 750 mL. Rate: 80 mL/hr.

• Hours = 750 ÷ 80 = 9.375 hr = 9 hr + 0.375 hr.
• Minutes = 0.375 × 60 = 22.5 → 23 minutes (if asked).
• Answer: 9.4 hr or 9 hr 23 min (match format requested).

Percent strength, ratio strength, and dilutions

Percent w/v: grams per 100 mL.

• 3% w/v means 3 g in 100 mL = 3000 mg in 100 mL = 30 mg/mL.

Example (percent): How many mg in 15 mL of 3% solution?

• 30 mg/mL × 15 mL = 450 mg.
• Answer: 450 mg.

Ratio strength: grams per total mL in the ratio.

• 1:1000 = 1 g/1000 mL = 1000 mg/1000 mL = 1 mg/mL.

Example (ratio): Order 0.3 mg of epinephrine 1:1000.

• 1:1000 = 1 mg/mL, so volume = 0.3 mg ÷ 1 mg/mL = 0.3 mL.
• Answer: 0.3 mL.

Dilutions (C1V1 = C2V2): Use when making a weaker solution from a stronger one.

Example: Make 250 mL of 0.9% from a 3% stock.

• C1V1 = C2V2 → 3% × V1 = 0.9% × 250 mL → V1 = 75 mL of 3%.
• Then add diluent to 250 mL total: 250 − 75 = 175 mL diluent.
• Answer: 75 mL of 3% + 175 mL diluent.

Powder reconstitution

Pattern: Vial says “Add X mL to yield Y mL at Z mg/mL.” You need a dose in mg and must find mL to draw up.

Method: Use the reconstituted concentration (mg/mL) for D/H × Q, where Q is 1 mL.

Example: Vial states: Add 8 mL to yield 10 mL with 250 mg/mL. Order: 375 mg IM.

• Volume = 375 mg ÷ 250 mg/mL = 1.5 mL.
• Answer: 1.5 mL.

Why it works: You do not need the powder’s “before” volume; the final concentration after mixing is all that matters.

Units-based meds: insulin and heparin

Insulin (U-100): 100 units per mL. Convert units to mL when the question asks for volume.

Example: Give 20 units of U-100 insulin.

• Volume = 20 units × (1 mL/100 units) = 0.2 mL.
• Answer: 0.2 mL.

Heparin infusions: Often 25,000 units in 250 mL (100 units/mL). Convert prescribed units/hr to mL/hr.

Example: Order: Heparin at 1200 units/hr. Bag: 25,000 units/250 mL.

• Concentration = 100 units/mL.
• mL/hr = 1200 ÷ 100 = 12 mL/hr.
• Answer: 12 mL/hr.

Rounding rules that keep you safe

• Tablets: Round to halves only if scored. Otherwise, round to whole tablets unless the drug allows splitting per policy.
• Oral liquids: Round to the nearest tenth (0.1 mL) for oral syringes unless instructions say otherwise.
• IV pump rates (mL/hr): Usually to the nearest whole number, or one decimal if policy allows.
• Gravity drip (gtt/min): Whole numbers only. You can’t count half a drop.
• Weights: Round kg to the nearest tenth for dosing (e.g., 20.3 kg).
• Significant zeros: Use leading zero before a decimal (0.5 mL). Do not use trailing zeros (5.0 mL → write 5 mL).

Common traps and how to avoid them

• Mismatch units: mg ordered vs. mcg on hand. Convert before D/H × Q.
• Wrong time base: Orders per minute vs per hour. Always match hours with hours, minutes with minutes.
• Forgetting drop factor: You cannot find gtt/min without gtt/mL.
• Percent confusion: 3% means 3 g per 100 mL, not 3 mg per mL. Convert carefully.
• Weight in pounds: Always convert lb to kg first for mg/kg dosing.
• Reconstitution “final volume”: Do not assume added volume equals final volume. Use the label’s “yield” concentration.

Practice set with step-by-step solutions

1) Tablets: Order 875 mg. On hand 250 mg tablets. How many tablets?

• 875/250 × 1 = 3.5 tablets. If scored and splitting allowed, 3.5 tablets.

2) Liquid: Order 360 mg. Label 120 mg/5 mL. How many mL?

• 360/120 × 5 = 15 mL.

3) Weight-based: Order 7.5 mg/kg. Patient 154 lb. Supply 50 mg/mL. mL per dose?

• 154 lb ÷ 2.2 = 70 kg (exact 69.9; round to 70 kg).
• Dose = 7.5 × 70 = 525 mg.
• Volume = 525/50 = 10.5 mL.

4) IV pump: 1.5 L over 12 hours. mL/hr?

• 1500 ÷ 12 = 125 mL/hr.

5) Gravity drip: 500 mL over 4 hours. Tubing 10 gtt/mL. gtt/min?

• mL/min = 500 ÷ 240 = 2.083 mL/min.
• gtt/min = 2.083 × 10 = 20.83 → 21 gtt/min.

6) Infusion time: Rate 75 mL/hr, volume 600 mL. How long?

• Hours = 600 ÷ 75 = 8 hr.

7) Ratio strength: How many mL to deliver 2 mg from 1:1000 solution?

• 1:1000 = 1 mg/mL. Volume = 2 mg ÷ 1 mg/mL = 2 mL.

8) Percent solution: How many mg in 60 mL of 2% w/v?

• 2% = 2 g/100 mL = 2000 mg/100 mL = 20 mg/mL.
• 20 × 60 = 1200 mg.

9) Dilution (C1V1 = C2V2): How much 10% solution to make 500 mL of 3%?

• 10% × V1 = 3% × 500 → V1 = 150 mL of 10%.
• Add 350 mL diluent to make 500 mL.

10) Heparin: Bag 25,000 units/250 mL. Infuse 900 units/hr. mL/hr?

• 100 units/mL. mL/hr = 900 ÷ 100 = 9 mL/hr.

11) Reconstitution: Label after reconstitution: 400 mg/5 mL. Order 260 mg. mL?

• 260/400 × 5 = 3.25 mL → round to 3.3 mL for oral syringe.

12) Insulin: Give 32 units of U-100. mL?

• 32 units × (1 mL/100 units) = 0.32 mL.

Why dimensional analysis prevents most errors

Dimensional analysis forces you to cancel units until only the answer unit remains. If a unit won’t cancel, your setup is wrong. This visual check is powerful under stress.

Example (multi-step DA): Order 6 mcg/kg/min. Patient 70 kg. Concentration 400 mg in 250 mL. Find mL/hr.

• Start with what you want: mL/hr.
• mL/hr = (6 mcg/kg/min) × (70 kg) × (60 min/hr) × (1 mg/1000 mcg) × (250 mL/400 mg).
• Cancel kg, min, mcg, mg until only mL/hr remains.
• Compute: 6 × 70 × 60 × 1 × 250 ÷ (1000 × 400) = 6.3 mL/hr (rounded).
• Answer: 6.3 mL/hr.

Why it works: Each fraction is a true statement that equals 1 in different units. Multiplying by “1” doesn’t change the value, only the units.

Fast mental checks that catch mistakes

• Bigger dose, bigger volume. If your dose increases and your answer volume shrinks, something is off.
• Ballpark by halves. If 125 mg is 5 mL, then 250 mg is 10 mL. Use this to estimate before you calculate exactly.
• Powers of ten. mg to mcg is ×1000. If you go the wrong way, your answer will be off by a thousand.
• Time sense. 1 L over 8 hours is always 125 mL/hr. Use anchors like this to sanity-check similar problems.

Exam-day workflow you can trust

• Underline the target unit in the question.
• Write O/H × Q if it’s a simple tablet or liquid. Otherwise, set up dimensional analysis.
• Convert early (lb to kg, mg to mcg) before plugging numbers in.
• Round at the end, not in the middle, unless a step explicitly requires whole numbers (like gtt/min).
• Label your answer with units and perform a quick reasonableness check.

You do not need to be “good at math” to master PTCE dosage calculations. You need a consistent process, a few conversions, and practice with realistic examples. Focus on units, use D/H × Q for straightforward problems, and switch to dimensional analysis when the path looks messy. With that approach, every dosage question becomes a short, calm checklist—and a correct answer.

G S Sachin

I am a Registered Pharmacist under the Pharmacy Act, 1948, and the founder of PharmacyFreak.com. I hold a Bachelor of Pharmacy degree from Rungta College of Pharmaceutical Science and Research. With a strong academic foundation and practical knowledge, I am committed to providing accurate, easy-to-understand content to support pharmacy students and professionals. My aim is to make complex pharmaceutical concepts accessible and useful for real-world application.

Mail- Sachin@pharmacyfreak.com