Pharmaceutical Calculations for OPRA: The 8 Types You Must Master

Calculation questions on OPRA require exact answers. A dose that's rounded differently is wrong. A rate that's off by one decimal place is wrong. There's no partial credit.

Important distinction: OPRA is a closed-book exam — you cannot bring any references, including the AMH or a calculator. You must be able to perform these calculations from memory using pen and paper. This is different from the Intern Written Exam, which is open-book. For OPRA, the formulas, conversion factors, and methods must be memorised.

The good news: the calculation types are predictable. Master these 8 types and you'll handle any calculation the exam throws at you.

Type 1: Dose Per Body Weight

The most fundamental calculation. You'll see it frequently.

Formula: Dose = Weight (kg) × Dose per kg

Worked Example 1: A patient weighing 72kg is prescribed gentamicin 5mg/kg/day in 3 divided doses. What is each individual dose?

Solution:

• Total daily dose = 72kg × 5mg/kg = 360mg/day
• Each dose = 360mg ÷ 3 = 120mg per dose

Worked Example 2: A 58kg patient is prescribed vancomycin 15mg/kg every 12 hours. The available vial is 500mg in 10mL. What volume is required per dose?

Solution:

• Dose = 58kg × 15mg/kg = 870mg per dose
• Concentration = 500mg/10mL = 50mg/mL
• Volume = 870mg ÷ 50mg/mL = 17.4mL per dose

Common Errors:

• Forgetting to divide by the number of doses — the question asks for each dose, not the total daily dose
• Weight given in pounds — convert first: weight in kg = weight in pounds ÷ 2.2
• Not converting to the correct volume when a concentration is provided

Type 2: Concentration and Dilution

Understanding how to dilute stock solutions to a target concentration.

Formula (Dilution): C1 × V1 = C2 × V2

Where:

• C1 = initial concentration
• V1 = initial volume
• C2 = final concentration
• V2 = final volume

Worked Example 1: You have a 10% w/v povidone-iodine solution. How much stock solution and how much purified water do you need to prepare 500mL of a 1% w/v solution?

Solution:

• C1 × V1 = C2 × V2
• 10% × V1 = 1% × 500mL
• V1 = (1% × 500mL) ÷ 10% = 50mL of stock solution
• Purified water = 500mL – 50mL = 450mL

Worked Example 2: You need to prepare 100mL of a 0.5% w/v chlorhexidine solution from a 5% w/v stock. How much stock solution do you need?

Solution:

• 5% × V1 = 0.5% × 100mL
• V1 = (0.5 × 100) ÷ 5 = 10mL of stock solution
• Add purified water to make up to 100mL (i.e., add 90mL)

Common Error: Mixing up which concentration is C1 and C2. C1 is always the stronger (stock) solution.

Type 3: IV Flow Rate Calculations

These appear regularly and have multiple variations.

Key Formulas:

• Drops per minute = (Volume in mL × Drop factor) ÷ (Time in minutes)
• mL per hour = Volume in mL ÷ Time in hours

Standard drop factors (memorise these for OPRA):

• Standard giving set: 20 drops/mL
• Microdrop (paediatric) set: 60 drops/mL
• Blood set: 15 drops/mL

Worked Example 1: An IV infusion of 1000mL normal saline is to be administered over 8 hours using a standard giving set (20 drops/mL). Calculate the flow rate in drops per minute.

Solution:

• Time in minutes = 8 × 60 = 480 minutes
• Drops per minute = (1000mL × 20 drops/mL) ÷ 480 minutes
• Drops per minute = 20,000 ÷ 480 = 41.7 drops/min ≈ 42 drops/min

Worked Example 2 — Dose-based IV rate: Dopamine 400mg in 250mL D5W. Prescriber orders 5mcg/kg/min for an 80kg patient. What is the infusion rate in mL/hr?

Solution:

• Required dose = 5mcg/kg/min × 80kg = 400mcg/min
• Concentration = 400mg/250mL = 1.6mg/mL = 1600mcg/mL
• Rate = 400mcg/min ÷ 1600mcg/mL = 0.25mL/min
• mL/hr = 0.25 × 60 = 15mL/hr

Common Error: Using the wrong drop factor. Read the question carefully — it will specify the giving set type or drop factor.

Type 4: Percentage Concentrations

Understanding w/v, w/w, and v/v is essential.

Definitions:

• % w/v = grams of solute per 100mL of solution
• % w/w = grams of solute per 100g of preparation
• % v/v = mL of solute per 100mL of solution

Worked Example 1: How many grams of sodium chloride are in 500mL of 0.9% w/v normal saline?

Solution:

• 0.9% w/v = 0.9g per 100mL
• In 500mL = (0.9g × 500mL) ÷ 100mL = 4.5g

Worked Example 2: Prepare 200g of 2% w/w hydrocortisone cream using 1% w/w stock cream and hydrocortisone powder.

Solution:

• Required hydrocortisone = 2% × 200g = 4g total
• Already in stock cream: 1% × 200g = 2g
• Additional powder needed = 4g – 2g = 2g hydrocortisone powder

Worked Example 3: How many milligrams of drug are in 15mL of a 2% w/v solution?

Solution:

• 2% w/v = 2g per 100mL = 2000mg per 100mL
• In 15mL = (2000mg × 15) ÷ 100 = 300mg

Common Error: Confusing w/v with w/w. In w/v, the denominator is volume (mL). In w/w, the denominator is weight (g).

Type 5: Unit Conversions

Deceptively simple, but conversion errors are the most common reason for wrong answers.

Key Conversions to Memorise (essential for OPRA):

• 1g = 1000mg
• 1mg = 1000 micrograms (mcg)
• 1mcg = 1000 nanograms
• 1L = 1000mL
• 1kg = 2.2 pounds
• 1 grain = 65mg
• 1 teaspoon = 5mL
• 1 tablespoon = 15mL
• 1mmol/L sodium = 23mg/L (molecular weight of Na)

Worked Example 1: A patient is prescribed levothyroxine 150 micrograms daily. The tablets available are 0.1mg and 0.05mg. How many of each tablet should the patient take?

Solution:

• 150mcg = 0.15mg
• One 0.1mg tablet + one 0.05mg tablet = 0.15mg = 150mcg ✓
• Answer: One 0.1mg tablet and one 0.05mg tablet daily

Worked Example 2: A prescription reads morphine sulfate 0.6g. How many 15mg tablets are needed?

Solution:

• 0.6g = 600mg
• Number of tablets = 600mg ÷ 15mg = 40 tablets

Common Error: Moving the decimal point the wrong direction when converting between mcg and mg. Remember: divide by 1000 to go from smaller to larger units (mcg → mg).

Type 6: Body Surface Area (BSA) and Paediatric Dosing

Calculations involving children require extra precision and often incorporate body weight or body surface area.

Common Approaches:

• Weight-based dosing (most common): mg/kg/dose or mg/kg/day
• Body Surface Area (BSA): Used for some medications (especially chemotherapy and paediatric oncology)

BSA Formula (Mosteller — memorise this): BSA (m²) = √(height in cm × weight in kg ÷ 3600)

Worked Example 1 — Weight-based paediatric dosing: Amoxicillin is prescribed at 25mg/kg/day in 3 divided doses for a child weighing 18kg. The suspension available is 250mg/5mL. What volume is given per dose?

Solution:

• Daily dose = 25mg/kg × 18kg = 450mg/day
• Dose per administration = 450mg ÷ 3 = 150mg
• Volume per dose = (150mg × 5mL) ÷ 250mg = 3mL per dose

Worked Example 2 — BSA calculation: A child is 110cm tall and weighs 22kg. Calculate their BSA, then determine the dose of a medication prescribed at 150mg/m².

Solution:

• BSA = √(110 × 22 ÷ 3600) = √(2420 ÷ 3600) = √0.672 = 0.82 m²
• Dose = 150mg/m² × 0.82m² = 123mg

Common Errors:

• Not checking that the calculated dose falls within the acceptable range — paediatric doses often have maximum limits (e.g., "25mg/kg/day up to a maximum of 500mg per dose")
• Safety check: Always verify that your calculated paediatric dose doesn't exceed the adult dose. If your calculation produces a dose higher than what an adult would receive, something is wrong

Type 7: Creatinine Clearance (Renal Dosing)

Many drugs require dose adjustment based on kidney function. The Cockcroft-Gault equation appears in pharmacy exams.

Cockcroft-Gault Formula (memorise for OPRA):

CrCl (mL/min) = [(140 – age) × weight (kg) × F] ÷ [0.814 × serum creatinine (micromol/L)]

Where F = 1 for males, 0.85 for females

Note: Australian pathology reports serum creatinine in micromol/L. If a question gives creatinine in mg/dL, convert first: Scr (micromol/L) = Scr (mg/dL) × 88.4

Worked Example 1: Calculate CrCl for a 68-year-old female weighing 60kg with serum creatinine of 120 micromol/L.

Solution:

• CrCl = [(140 – 68) × 60 × 0.85] ÷ [0.814 × 120]
• CrCl = [72 × 60 × 0.85] ÷ [97.68]
• CrCl = 3672 ÷ 97.68
• CrCl = 37.6 mL/min

This patient has moderate renal impairment. Many drugs (metformin, DOACs, gabapentin, etc.) require dose reduction at this level.

Worked Example 2: Calculate CrCl for a 45-year-old male weighing 90kg with serum creatinine of 95 micromol/L. Should metformin dose be adjusted?

Solution:

• CrCl = [(140 – 45) × 90 × 1] ÷ [0.814 × 95]
• CrCl = [95 × 90] ÷ [77.33]
• CrCl = 8550 ÷ 77.33
• CrCl = 110.6 mL/min

This patient has normal renal function. Metformin does not require dose adjustment (dose reduction typically at CrCl <30–45 mL/min per AMH).

Common Error: Forgetting the 0.85 factor for females. This changes the answer significantly.

Type 8: Electrolyte and Millimole Calculations

Understanding millimoles and milliequivalents is essential for IV electrolyte questions.

Key Formula: Millimoles = Weight (mg) ÷ Molecular weight

Key Molecular Weights (memorise for OPRA):

• Sodium (Na): 23
• Potassium (K): 39
• Calcium (Ca): 40
• Magnesium (Mg): 24
• Chloride (Cl): 35.5
• Sodium chloride (NaCl): 58.5
• Potassium chloride (KCl): 74.5

Worked Example 1: How many millimoles of sodium are in 1 litre of 0.9% w/v sodium chloride?

Solution:

• 0.9% w/v = 9g NaCl per 1000mL
• Moles of NaCl = 9g ÷ 58.5g/mol = 0.1538 mol
• Since each NaCl gives one Na⁺: mmol Na = 153.8 mmol
• Answer: approximately 154 mmol sodium per litre

(This is why normal saline is often written as "Na 154 mmol/L" on IV fluid labels.)

Worked Example 2: A patient needs 40mmol of potassium chloride. KCl ampoules contain 10mmol in 10mL. How many ampoules are needed and what is the total volume?

Solution:

• Ampoules needed = 40mmol ÷ 10mmol per ampoule = 4 ampoules
• Total volume = 4 × 10mL = 40mL

Common Error: Using the molecular weight of the ion instead of the salt, or vice versa. Read the question carefully — is it asking for mmol of sodium, or mmol of sodium chloride?

Compounding Calculations

While not a standalone "type" in every classification, compounding calculations appear on OPRA and combine several skills.

Worked Example — Alligation method: You need to prepare 100g of 5% w/w ointment. You have 10% w/w and 2% w/w stock ointments. How much of each do you need?

Solution (Alligation Alternate):

• Parts of 10% = 5 – 2 = 3 parts
• Parts of 2% = 10 – 5 = 5 parts
• Total parts = 3 + 5 = 8 parts
• Amount of 10% = (3/8) × 100g = 37.5g
• Amount of 2% = (5/8) × 100g = 62.5g

Verification: (37.5 × 10%) + (62.5 × 2%) = 3.75 + 1.25 = 5g active in 100g = 5% ✓

Practice Problems

Test yourself with these problems. Answers are provided below.

Problem 1: A 65kg patient is prescribed amikacin 7.5mg/kg every 12 hours. What is each dose?

Problem 2: Prepare 250mL of a 0.1% w/v solution from a 1% w/v stock. How much stock solution is needed?

Problem 3: 500mL of D5W is to infuse over 6 hours via a microdrop set (60 drops/mL). What is the flow rate in drops/min?

Problem 4: Calculate CrCl for a 75-year-old male weighing 68kg with serum creatinine of 150 micromol/L.

Problem 5: How many millimoles of potassium are in 20mL of potassium chloride 15% w/v?

Problem 6: A child weighing 25kg is prescribed cephalexin 25mg/kg/day in 4 divided doses. The suspension is 125mg/5mL. What volume per dose?

Answers

1. 65 × 7.5 = 487.5mg per dose
2. 1% × V1 = 0.1% × 250mL → V1 = 25mL stock solution
3. (500 × 60) ÷ (6 × 60) = 30,000 ÷ 360 = 83.3 ≈ 83 drops/min
4. [(140 – 75) × 68 × 1] ÷ [0.814 × 150] = 4420 ÷ 122.1 = 36.2 mL/min
5. 15% w/v = 15g KCl per 100mL → in 20mL = 3g = 3000mg → mmol = 3000 ÷ 74.5 = 40.3 mmol potassium
6. Daily dose = 25 × 25 = 625mg/day; per dose = 625 ÷ 4 = 156.25mg; volume = (156.25 × 5) ÷ 125 = 6.25mL per dose

General Exam Strategy for OPRA Calculations

Before the Exam

1. Practise daily — not weekly, daily. 10 calculations per day for 4 weeks embeds the methods
2. Memorise all formulas — OPRA is closed-book, so you cannot look anything up
3. Memorise key values — drop factors, molecular weights, conversion factors, Cockcroft-Gault formula
4. Practise mental estimation — before calculating precisely, estimate roughly to catch major errors
5. Show your working — develop a consistent format so you can check steps

During the Exam

6. Read the question twice — what exactly is it asking for? (Per dose? Per day? Per hour?)
7. Check units — ensure your answer matches the unit requested
8. Verify reasonableness — does your answer make clinical sense? An adult paracetamol dose of 10g is obviously wrong
9. Don't rush — a careful calculation done once beats a rushed calculation done twice
10. Use estimation to eliminate options — if you estimate ~40 drops/min, you can rule out 12 or 85

Common Traps Across All Types

• Rounding too early — carry extra decimal places through your calculation and only round the final answer
• Unit mismatch — question gives mg, answer needs mcg
• Frequency confusion — "three times daily" vs "every 8 hours" can give different answers depending on the context
• Weight in pounds — always convert to kg first if given in pounds (÷ 2.2)
• Not answering what was asked — calculating the daily dose when the question asks for a single dose
• Forgetting the female factor in Cockcroft-Gault (0.85)
• Confusing w/v and w/w — check the units carefully

Ready to practise more? Check out our OPRA exam preparation resources for full practice question banks, or explore our Intern Written Exam guide for open-book exam strategies.

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References: Australian Pharmacy Council — OPRA Exam Content Guide, Australian Medicines Handbook (AMH), Australian Pharmaceutical Formulary and Handbook (APF), National Competency Standards Framework for Pharmacists in Australia