Calculations
Percentage and Ratio Strength Calculations for OPRA
Concentration expressions — percentage, mg/mL, and ratio strength — are the vocabulary underneath a huge share of OPRA's calculation and dispensing questions, and mixing them up is one of the most common, entirely avoidable sources of lost marks. This guide covers converting between them and the dilution calculations built on top.
Why this topic matters
Concentration expressions appear as an input to nearly every other calculation type on OPRA — dosing, infusion rates, dilutions — so a shaky grasp of converting between them doesn't just cost one question, it introduces errors into every downstream calculation that depends on it.
Learning objectives
- Convert between percentage w/v, mg/mL, and ratio strength expressions
- Apply the C1V1 = C2V2 dilution formula to a worked example
- Account for a displacement value when reconstituting a powder-for-injection
- Recognise the most common conversion mistakes on this calculation type
Core concepts
The three common concentration expressions
Percentage w/v means grams per 100 mL — for example, 0.9% NaCl is 0.9 g per 100 mL, equivalent to 9 mg/mL. mg/mL and mcg/mL are direct mass-per-volume expressions, commonly used for injectable concentrations. Ratio strength expresses concentration as 1 gram in a stated volume — for example, adrenaline 1:1000 means 1 g in 1000 mL, equivalent to 1 mg/mL, while adrenaline 1:10,000 means 1 g in 10,000 mL, equivalent to 0.1 mg/mL.
Converting between percentage and mg/mL
A quick conversion: percentage w/v × 10 = mg/mL. For example, 5% glucose = 5 × 10 = 50 mg/mL. This works because percentage w/v is grams per 100 mL, and converting grams to milligrams (× 1000) while converting the denominator from 100 mL to 1 mL (÷ 100) nets out to a single × 10 factor.
Simple dilution — C1V1 = C2V2
When a stock (more concentrated) solution is diluted to a target (less concentrated) volume, the total amount of drug doesn't change — only the volume it's dissolved in does. This gives the relationship: (stock concentration × stock volume used) = (target concentration × target volume). Rearranging lets you solve for whichever single unknown the question is asking for.
Clinical application
Worked example — simple dilution
How many mL of a 10 mg/mL stock solution are needed to prepare 100 mL of a 2 mg/mL solution? Using C1V1 = C2V2: 10 × V1 = 2 × 100, so V1 = 200 ÷ 10 = 20 mL of stock, made up to a total of 100 mL with diluent.
Worked example — displacement value
Some powder-for-injection products have a displacement value — the powder itself takes up a measurable volume once reconstituted, which must be accounted for to get the true final concentration. For example, a 1.2 g vial of a powder for injection with a displacement value of 0.9 mL: adding 20 mL of water for injection gives a total reconstituted volume of 20 + 0.9 = 20.9 mL, so the true concentration is 1200 mg ÷ 20.9 mL ≈ 57.4 mg/mL — not the 60 mg/mL a candidate would get by ignoring the displacement value.
Common mistakes
- Forgetting the displacement value entirely when reconstituting a powder for injection, overstating the true concentration.
- Mixing up which side of a ratio strength expression is the mass and which is the volume (1:1000 means 1 g in 1000 mL, not 1000 g in 1 mL).
- Applying the percentage-to-mg/mL ×10 shortcut to a percentage w/w or v/v expression, where it doesn't apply the same way as w/v.
- Rearranging C1V1 = C2V2 incorrectly under time pressure — writing out the formula with units before substituting numbers avoids most of these errors.
Exam tips
- • If a question gives a displacement value, treat that as an explicit signal it must be used — omitting it is one of the most reliable ways this calculation type catches out an otherwise correct approach.
- • When two different concentration formats appear in the same question (e.g. a stock given as a ratio strength, a target given in mg/mL), convert both to the same format before applying any formula.
Memory tricks
- • "Percent times ten" — the quick mnemonic for converting a % w/v concentration directly to mg/mL.
Clinical pearls
- 💡 Adrenaline's two common ratio strengths — 1:1000 (1 mg/mL, typically for IM use) and 1:10,000 (0.1 mg/mL, typically for IV use in resuscitation) — differ by a full order of magnitude, making this pairing a deliberately favourite way to test whether ratio-strength conversion is genuinely understood rather than pattern-matched.
Tables
Common concentration expressions
| Expression | Meaning | Example |
|---|---|---|
| % w/v | Grams per 100 mL | 0.9% NaCl = 0.9 g/100 mL = 9 mg/mL |
| mg/mL | Milligrams per mL | Morphine 10 mg/mL |
| mcg/mL | Micrograms per mL | Fentanyl 50 mcg/mL |
| Ratio (1:1000) | 1 g in 1000 mL | Adrenaline 1:1000 = 1 mg/mL |
| Ratio (1:10,000) | 1 g in 10,000 mL | Adrenaline 1:10,000 = 0.1 mg/mL |
Practice MCQs (100% original)
1. Adrenaline 1:10,000 is equivalent to which concentration in mg/mL?
2. How many mL of a 20 mg/mL stock solution are needed to prepare 50 mL of a 4 mg/mL solution?
3. A 1 g vial of a powder for injection has a displacement value of 0.8 mL. If 10 mL of water for injection is added, what is the final concentration?
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Start freeFrequently asked questions
Why does a displacement value matter if it's often less than 1 mL?
Even a small displacement value can materially change a calculated concentration, particularly for smaller total reconstituted volumes, and OPRA calculation questions are typically looking for the precise, correctly-adjusted answer rather than an approximation — a small omitted volume is enough to select the wrong answer option.
Does the ×10 shortcut for converting % w/v to mg/mL work for all percentage expressions?
It applies specifically to % w/v (grams per 100 mL of solution). Percentage w/w (weight per weight, common in creams and ointments) and % v/v (volume per volume) are different expressions and the same shortcut doesn't apply to them in the same way — always confirm which type of percentage a question is using.
Official references
- Australian Pharmaceutical Formulary and Handbook ↗ — Standard pharmaceutical calculation conventions used in Australian practice
- Australian Medicines Handbook ↗ — Product-specific concentration and reconstitution detail