Pharmaceutical Calculations for OPRA: The 8 Types You Must Master

The OPRA is multiple choice: each question has one correct answer and three incorrect options, so a calculation question asks you to pick the right result. The Intern Written Exam is different. Its calculation questions are fill-in-the-blank, and an answer not entered as directed, including the number of decimal places, is marked incorrect.

Important distinction: The OPRA is a closed-book exam: no references and no written materials, so no AMH and no formula sheets. But you are not doing these by hand with pen and paper. The APC says you can bring a calculator (scientific or standard, with no internet, text storage or camera), and Pearson provides an online calculator, a whiteboard notebook and an erasable marker at your desk. Pens, pencils and paper are not allowed. The Intern Written Exam is restricted open-book: you may bring one original paper copy each of the AMH and the APF. For the OPRA, learn the formulas, conversion factors and methods: the APC doesn't say which values a question will supply, although its sample millimole question gives the atomic weights.

The APC does not publish a list of calculation types or a percentage of calculation questions. The OPRA guide lists calculations in Therapeutics and patient care: screening parameters such as BMI and creatinine clearance (5.1), and dose calculations (5.2), which cover amount of drug, number of doses, body weight, body surface area, age, ratio and proportion, percentages, stock solutions, dilution, concentration, alligation, electrolyte solutions, reconstitution, infusion flow rates and isotonicity. Pharmacokinetic calculations sit in content area 3: loading doses, time to steady state and dose adjustment in renal and hepatic dysfunction.

The 8 types below are our own grouping of common topics, not an APC list. They don't cover everything in the guide, such as dosing by age, milliequivalents and milliosmoles, reconstitution, isotonicity, loading doses and BMI, so read the guide's Appendix 1 and practise those too. The doses in these examples are for practising the arithmetic, not dosing advice. GdayPharmacist is independent of the APC, the Pharmacy Board and Ahpra. The APC does not endorse any exam preparation program, including ours, so start with its free exam guide and sample content.

Type 1: Dose Per Body Weight

The most fundamental calculation. The OPRA guide lists dosing by body weight under dose calculations (5.2).

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: the APC guides say exam values are in SI (metric) units, so this is a practice issue rather than an exam one. 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

The OPRA guide lists infusion flow rates under dose calculations (5.2). They 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

Common drop factors (the pack states the real one, so use what the question gives):

• 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 sodium chloride 0.9% 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 glucose 5%. 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, and use the giving set type or drop factor it gives.

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 sodium chloride 0.9% w/v?

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
• Let x = grams of powder. The cream then weighs (200 – x)g, because the final weight must stay 200g
• x + 1% × (200 – x) = 4g
• x + 2 – 0.01x = 4, so 0.99x = 2 and x = 2.02g (to 2 decimal places)
• Answer: 2.02g hydrocortisone powder + 197.98g of 1% cream

Check: 2.02g + (1% × 197.98g) = 2.02g + 1.98g = 4g in 200g, which is 2%.

The shortcut of adding 2g of powder to 200g of cream gives 202g at about 1.98%, not 200g at 2%.

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, and easy to get wrong under time pressure.

Key Conversions to Memorise:

• 1g = 1000mg
• 1mg = 1000 micrograms (mcg; the APC's sample content writes microgram in full)
• 1mcg = 1000 nanograms
• 1L = 1000mL
• 1mmol/L sodium = 23mg/L (atomic weight of Na)

The APC guides say exam values are in SI (metric) units, so older measures are for practice rather than the exam: 1kg = 2.2 pounds, 1 grain = about 65mg, and 1 teaspoon = 5mL. Avoid tablespoons: pharmacy texts use 15mL, but an Australian tablespoon measure is usually 20mL.

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 authorises a total quantity of morphine sulfate 0.6g (not a single dose), supplied as 15mg tablets. How many tablets is that?

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, re-check your working before you answer

Type 7: Creatinine Clearance (Renal Dosing)

Many drugs require dose adjustment based on kidney function. The OPRA guide lists creatinine clearance under screening (5.1), and dose adjustment in renal dysfunction in content area 3.

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. Australian Prescriber's 2019 review of drug dosing in chronic kidney disease prints this same formula and says actual body weight is commonly used, but it also says actual weight overestimates kidney function in obesity (BMI above 30), where adjusted ideal body weight is more reliable. Other references use ideal or lean body weight. In the exam, use the weight the question gives. In practice, check which weight your reference assumes. Pathology reports also give eGFR (mL/min/1.73 m²), which is a different estimate, so don't treat the two as the same number.

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

A creatinine clearance in this range is usually called moderate renal impairment. Many renally cleared medicines need review at this level, and thresholds differ between drugs, so check the product information. Metformin is a good example. The Diabex PI contraindicates it when creatinine clearance is below 60 mL/min, while Kidney Health Australia's CKD handbook (5th edition, 2024) says to consider a lower dose and more monitoring at an eGFR of 30 to 60, and to use it only under specialist supervision below 30. Sources differ, so use the threshold the question or your reference gives, and raise it with the prescriber rather than assuming one number settles it.

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 result does not suggest renal impairment, so renal function is not a reason to adjust metformin here. Thresholds differ between sources: the Diabex PI (revised 21 August 2026) contraindicates metformin below a creatinine clearance of 60 mL/min, and Kidney Health Australia's handbook uses eGFR bands of 30 to 60 and below 30.

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
• Milliequivalents = Millimoles × valency of the ion
• Milliosmoles = Millimoles × number of particles formed in solution (assuming full dissociation)

Key Atomic and Molecular Weights (worth knowing, but check the question first: the APC's sample millimole question gives the atomic weights):

• 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 the 154 mmol/L figure usually quoted for sodium chloride 0.9%.)

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

This is arithmetic only. Concentrated potassium chloride has to be diluted before it is given: the Australian Commission on Safety and Quality in Health Care links undiluted injection to deaths, and the TGA's January 2026 decision moves concentrated ampoules into Schedule 4 from 1 February 2027.

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? Watch the ratio too: one mole of lithium carbonate (Li2CO3) gives two moles of lithium, which is the point of the APC's sample millimole question.

Compounding Calculations

While not a standalone "type" in every classification, these calculations combine several skills. The OPRA guide lists alligation under dose calculations (5.2), and compounding is its own competency standard (8% of questions) in the Intern Written Exam.

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 glucose 5% 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 cefalexin 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. Our suggestion is 10 calculations per day for 4 weeks
2. Memorise all formulas — OPRA is closed-book, so you cannot look anything up
3. Memorise key values — conversion factors, common atomic weights, the Cockcroft-Gault formula
4. Practise mental estimation — before calculating precisely, estimate roughly to catch major errors
5. Show your working — develop a consistent format you can use on the whiteboard notebook, so you can check steps. Practise with the calculator you plan to bring, and try Pearson's online sample test to see the on-screen tools

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), though APC exam values are metric
• 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

If You're Sitting the Intern Written Exam

The calculation rules are stricter than the OPRA's. The APC's sample content says, in summary:

• Calculation questions are fill-in-the-blank, and you enter only the final answer
• Each question says whether to give a whole number or one decimal place
• Only round your final answer, never an intermediate step
• No unnecessary zeros, no units and no symbols such as %, and use a decimal point rather than a comma
• Answers are automatically marked, with no partial marks

The calculator and whiteboard rules are the same as for the OPRA, and you may bring one original paper copy each of the AMH and the APF. Try the online sample test before exam day.

Ready to practise more? Try our free sample questions, check out our OPRA exam preparation resources for practice question banks, or explore our Intern Written Exam page for the restricted open-book exam. Our Intern Written practice questions are multiple choice, so use the APC's sample content and online sample test to rehearse fill-in-the-blank entry.

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References (re-checked 7 November 2026): Australian Pharmacy Council OPRA Exam Guide (30 July 2026, version 2.3), OPRA Exam Sample Content (30 July 2026, version 2.1), OPRA Exam day preparation page, Intern Written Exam Guide (30 July 2026, version 2.2) and Sample Content (July 2026, version 4.1); Diabex Product Information (revised 21 August 2026); Australian Prescriber 2019;42:163-7 (How to adjust drug doses in chronic kidney disease); Kidney Health Australia, CKD Management in Primary Care, 5th edition, 2024; Australian Commission on Safety and Quality in Health Care, high-risk medication alert on intravenous potassium chloride; TGA notice of final scheduling decisions, 19 January 2026.