Drug Calculations — NMC Numeracy Prep

Reference formulas

Nine calculations cover most of what the NMC numeracy test asks. All UK practice is metric — no household measures — so that's the only system used here. Learn the logic behind each one; ratio and proportion works for all of them if a formula slips your mind mid-exam.

Basic dosage (oral or parenteral)

Desired ÷ Have × Quantity = Amount to give

Order: amoxicillin 500 mg PO. On hand: 250 mg tablets. 500 ÷ 250 × 1 tab = 2 tablets

IV flow rate — mL/hr (infusion pump)

Volume (mL) ÷ Time (hr) = mL/hr

Order: 1000 mL NS over 8 hours. 1000 ÷ 8 = 125 mL/hr

IV drip rate — drops/minute (gravity infusion)

Volume (mL) × Drop factor (drops/mL) ÷ Time (min) = drops/minute

Order: 1000 mL over 8 hours, giving set drop factor 15 drops/mL. 1000 × 15 ÷ 480 = 31.25 → 31 drops/minute

Insulin dosing

Units ordered ÷ Concentration (units/mL) = mL to give

Insulin is dosed in units, never mg or mL directly, and should always be measured with an insulin syringe or insulin pen — NHS patient safety guidance is explicit that a standard syringe should never be used to draw up insulin. Where the unit-to-mL conversion genuinely matters is a variable-rate IV insulin infusion (VRIII), which is always mixed to a standard concentration. 50 units Actrapid made up to 50 mL with 0.9% sodium chloride = 1 unit/mL. Prescribed rate: 4 units/hour.
4 ÷ 1 = 4 mL/hr Never abbreviate "units" as "U" — it's a classic look-alike for "0" or "4" on a written chart.

Reconstitution

Total drug (mg) ÷ Total reconstituted volume (mL) = Concentration (mg/mL)
Then: Desired dose ÷ Concentration = Volume to draw up

Vial contains amoxicillin 500 mg powder. Reconstituting with water for injection gives a total volume of 10 mL. Prescribed dose is 250 mg. 500 ÷ 10 = 50 mg/mL
250 ÷ 50 = 5 mL Reconstitution volumes vary by manufacturer and can include a powder displacement volume — always check the product literature or BNF rather than assuming.

Ratio strength (e.g. adrenaline 1 in 1,000)

1,000,000 ÷ Ratio denominator = Concentration (micrograms/mL)
Then: Desired dose (micrograms) ÷ Concentration = Volume (mL)

Adrenaline 1 in 1,000 for adult anaphylaxis, dose 500 micrograms IM. 1,000,000 ÷ 1,000 = 1,000 micrograms/mL
500 ÷ 1,000 = 0.5 mL Adrenaline 1 in 10,000 for cardiac arrest, dose 1 mg (1,000 micrograms) IV. 1,000,000 ÷ 10,000 = 100 micrograms/mL
1,000 ÷ 100 = 10 mL

Weight-based dosage

Dose (mg/kg/day) × Weight (kg) ÷ Doses per day = Amount per dose

Order: amoxicillin 40 mg/kg/day in 3 divided doses. Child weighs 15 kg. 40 × 15 = 600 mg/day → 600 ÷ 3 = 200 mg/dose

Critical care drip — micrograms/kg/min

(Dose micrograms/kg/min × Weight kg × 60) ÷ Concentration (micrograms/mL) = mL/hr

Order: dopamine 5 micrograms/kg/min. Patient 70 kg. Bag: 400 mg in 250 mL → 1,600 micrograms/mL. (5 × 70 × 60) ÷ 1,600 = 21,000 ÷ 1,600 = 13.1 mL/hr

Safe dose range — check before you calculate

Low end (mg/kg/day) × Weight = Minimum safe daily dose
High end (mg/kg/day) × Weight = Maximum safe daily dose

Vancomycin safe range is 40–60 mg/kg/day. Patient weighs 20 kg. 40 × 20 = 800 mg/day (low) · 60 × 20 = 1,200 mg/day (high) An order for 1,500 mg/day falls outside this range — hold the dose and query the prescriber before giving it, regardless of whether the arithmetic on the order is otherwise correct.

Maximum daily dose (MDD) can override the math

A weight-based calculation can produce a number higher than the drug's absolute ceiling. When that happens, the ceiling wins. Paracetamol is capped near 4,000 mg/24 hours for an adult of normal weight no matter what a per-kg calculation suggests (lower for adults under 50 kg); adrenaline for adult anaphylaxis is a fixed 500 microgram IM dose, not a weight-based one. Always check the current BNF listing after you calculate, not just the formula.

Rounding and writing rules the exam expects

mL/hr on a pump: round to the nearest tenth.
Drops/minute (gravity): round to the nearest whole drop — you can't give a fraction of a drop.
Tablets: round to the nearest half or quarter, only if the tablet is scored.
Write "micrograms" and "nanograms" in full on any chart or order — never abbreviate them. This is a standing NHS medication-safety standard, not just exam style.
Always double-check the order is safe for the patient's weight and age before calculating — the math being correct doesn't make the order correct.

Common conversions
From	To	Factor
1 g	mg	1,000 mg
1 mg	micrograms	1,000 micrograms
1 microgram	nanograms	1,000 nanograms
1 L	mL	1,000 mL
1 stone	kg	6.35 kg
1 kg	stone	0.157 stone

Practice calculator

Enter your own numbers and see the worked steps — good for checking homework problems or testing a formula until it's automatic.

Calculation type

Quiz

Randomly generated problems across all nine calculation types. Type your answer and check it — repetition here is what makes the math fast on exam day.

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