Injection Volume Calculations (IM and SC): CBT Practice

Injection questions use the formula you already know from oral liquids: want over have, times what it’s in. What changes is the label. Ampoules are small, their strengths are written two different ways, and the difference between those two ways is a doubled or halved dose.

Way one: per millilitre. “10 mg/mL” means each mL contains 10 mg, whatever the ampoule size.

Way two: per ampoule. “100 mg in 2 mL” describes the whole ampoule. The concentration is 50 mg/mL, but the label never says 50 anywhere. You have to derive it, or use the ampoule totals directly in the formula.

Worked example with the per-ampoule label. Prescription: hydrocortisone 75 mg IM. Stock: 100 mg in 2 mL.

• Want over have: 75 ÷ 100 = 0.75.
• Times what it’s in: 0.75 × 2 = 1.5 mL.

The wrong answer waiting on the exam paper is 0.75 mL, produced by reading “100 mg in 2 mL” as if it said “100 mg/mL”. That’s a half-dose of hydrocortisone. The protection is a reading habit: before calculating, say the concentration to yourself as mg per 1 mL. If the label is per-ampoule, do that small division first.

Direction of division

The other reliable trap is inverted division. Prescribed 7.5 mg, stock 10 mg/mL. Divide the wrong way and you get 1.33 mL instead of 0.75 mL. The logic check is quick: when the dose you want is smaller than the strength per mL, the answer must be less than 1 mL. Bigger dose than strength, more than 1 mL. Decide which side of 1 the answer should sit on before you divide, and the inversion can’t survive.

Volume sanity limits

Injection answers live in a narrow band. IM injections top out around 3 mL in a large muscle, and subcutaneous injections at about 1 to 2 mL; local policy varies but the order of magnitude doesn’t. So a calculated answer of 7 mL for a single SC injection isn’t a big injection, it’s a wrong calculation. Usually a units problem, occasionally a per-ampoule misread.

Decimals, on the other hand, are completely normal here. 0.75 mL, 0.5 mL, 1.5 mL: this is what 1 mL syringes are graduated for. Don’t round an injection volume to make it tidier.

For the underlying method with more worked examples, see the worked numeracy examples in the main guide. Next in the bank: IV drip rates, where time enters the formula for the first time. Questions below first.