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.
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
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.
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)
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
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
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.
Heparin infusion — weight-based initiation and nomogram titration
Protocol dose (units/kg/hr) × Weight (kg) ÷ Concentration (units/mL) = Initial rate (mL/hr)
Protocol: 18 units/kg/hr. Patient weighs 70 kg. Bag is mixed 25,000 units in 250 mL (100 units/mL).
(18 × 70) ÷ 100 = 12.6 mL/hr
Once running, the APTT ratio tells you how to adjust it — the nomogram gives a units/hr change, which you convert back into mL/hr:
Current rate 12.6 mL/hr. Nomogram step: increase by 200 units/hr.
200 ÷ 100 = 2 mL/hr increase → new rate = 14.6 mL/hr Every trust's nomogram is different — this shows the arithmetic pattern, not a specific protocol to follow. Always use the trust's own heparin chart.
200 ÷ 100 = 2 mL/hr increase → new rate = 14.6 mL/hr Every trust's nomogram is different — this shows the arithmetic pattern, not a specific protocol to follow. Always use the trust's own heparin chart.
Body surface area (BSA) dosing
$$\text{BSA (m}^2\text{)} = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$$
Cyclophosphamide ordered at 750 mg/m². Patient is 165 cm tall and weighs 65 kg.
BSA = √((165 × 65) ÷ 3600) = √2.98 = 1.73 m²
1.73 × 750 = 1,297.5 mg Used for chemotherapy and some paediatric dosing, where a per-kg dose would be too imprecise across a wide size range.
1.73 × 750 = 1,297.5 mg Used for chemotherapy and some paediatric dosing, where a per-kg dose would be too imprecise across a wide size range.
Renal function — creatinine clearance (Cockcroft-Gault)
$$\text{CrCl (mL/min)} = \frac{(140 - \text{Age}) \times \text{Weight (kg)} \times \text{constant}}{\text{Serum creatinine (micromol/L)}}$$
Constant is 1.23 for men, 1.04 for women — this is the SI-unit version of Cockcroft-Gault, matching creatinine reported in micromol/L rather than mg/dL.
68-year-old male, 80 kg, serum creatinine 97 micromol/L. ((140 - 68) × 80 × 1.23) ÷ 97 = 7,084.8 ÷ 97 = 73.0 mL/min This is an estimate of kidney function, not a dose. Once you have it, the actual dose adjustment is always drug-specific — check the BNF's renal impairment guidance for that particular drug next.
68-year-old male, 80 kg, serum creatinine 97 micromol/L. ((140 - 68) × 80 × 1.23) ÷ 97 = 7,084.8 ÷ 97 = 73.0 mL/min This is an estimate of kidney function, not a dose. Once you have it, the actual dose adjustment is always drug-specific — check the BNF's renal impairment guidance for that particular drug next.
| 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 |
Calculations
Eleven worked problems covering unit conversions, dimensional analysis, and the rounding conventions that trip people up most — whole number, nearest tenth, and nearest 10 mg all look similar but aren't interchangeable. Problems 1, 2, 6, and 7 use US customary units (teaspoons, ounces, feet/inches, pounds) rather than UK measures — kept here as general numeracy practice, since the underlying skill (multi-step conversion) is the same one the NMC test asks for in metric form.
1. Household conversion — tsp to mL over multiple days
A prescription reads: "take 2 tsp PO Q6H x 7 days." How many milliliters must be dispensed to complete 7 days of therapy?
$$2 \text{ tsp} \times \frac{5 \text{ mL}}{1 \text{ tsp}} = 10 \text{ mL per dose}$$
$$\frac{10 \text{ mL}}{\text{dose}} \times \frac{4 \text{ doses}}{\text{day}} \times 7 \text{ days} = 280 \text{ mL}$$
2. Household conversion — ounces to mL, volume remaining
If 1 ounce = 30 mL, how many milliliters of sterile water will remain after 50 mL are used from a 16 ounce bottle?
$$16 \text{ oz} \times \frac{30 \text{ mL}}{1 \text{ oz}} = 480 \text{ mL bottle of sterile water}$$
480 mL - 50 mL = 430 mL of sterile water will remain
3. Paediatric daily volume — rounding to the nearest whole number
A paediatric patient is receiving 5.25 mL of drug every 4 hours. How many milliliters will be required for the entire day? Round to the nearest whole number.
5.25 mL (per dose) × 6 times/day = 31.5 mL
Round to the nearest whole number = 32 mL
Round to the nearest whole number = 32 mL
4. BID dose splitting — nearest whole number vs. nearest tenth
A patient requires 410.9 mg of a drug daily. The daily dose will be divided for BID administration. How many milligrams will the patient receive BID? Round to the nearest whole number.
410.9 mg daily ÷ 2 times per day = 205.45 mg BID
Round to the nearest whole number = 205 mg BID What if the problem said "round to the nearest tenth?" The correct answer would then be 205.5 mg. Rounding to the nearest tenth is the same as rounding to one decimal place.
Round to the nearest whole number = 205 mg BID What if the problem said "round to the nearest tenth?" The correct answer would then be 205.5 mg. Rounding to the nearest tenth is the same as rounding to one decimal place.
5. Enoxaparin — rounding to the nearest 10 mg
Enoxaparin 56.5 mg was ordered for a patient. The hospital rounds enoxaparin doses to the nearest 10 mg. What dose should be dispensed?
Correct answer: 60 mg
Rounding to the nearest 10 mg is different than rounding to the nearest tenth.
6. Height conversion — feet and inches to centimeters
A patient is 5'2" tall. What is her height in centimeters? Round to the nearest whole number.
$$5 \text{ feet} \times \frac{12 \text{ inches}}{1 \text{ foot}} = 60 \text{ inches} + 2 \text{ inches} = 62 \text{ inches}$$
$$62 \text{ inches} \times \frac{2.54 \text{ cm}}{1 \text{ inch}} = 157.48 \text{ cm}$$
Round to the nearest whole number = 157 cm
Watch for products that cannot be split
You cannot dispense part of an insulin vial or part of a Byetta pen to a patient, so rounding to the nearest whole vial or pen is required, even if the math itself comes out to a decimal.
Example: A patient takes Novolog 16 units TID before meals. How many vials of Novolog should be dispensed for a 30-day supply?
Answer: The patient takes 48 units per day, or 1,440 units per month. Since each vial of Novolog contains 1,000 units, the patient requires two vials for a 30-day supply.
7. Weight conversion — pounds to kilograms (proportion vs. dimensional analysis)
A patient weighs 176 pounds. What is the patient's weight in kilograms?
Method 1: Proportion. Solve for X by multiplying diagonally and then dividing. Set up in either of the two ways shown.
$$\frac{176 \text{ lbs}}{X \text{ kg}} = \frac{2.2 \text{ lbs}}{1 \text{ kg}} \quad X = 80 \text{ kg}$$
or
$$\frac{176 \text{ lbs}}{2.2 \text{ lbs}} = \frac{X \text{ kg}}{1 \text{ kg}} \quad X = 80 \text{ kg}$$
Method 2: Dimensional analysis. Cancel out the same units diagonally, leaving the desired units.
$$176 \text{ lbs} \times \frac{1 \text{ kg}}{2.2 \text{ lbs}} = 80 \text{ kg}$$
Notice that there is an equal sign (=) between the fractions in a proportion, and a multiplication symbol (×) between the fractions in dimensional analysis.
8. How many milliliters are in 5 liters?
Method 1: Proportion
$$\frac{5 \text{ L}}{X \text{ mL}} = \frac{1 \text{ L}}{1,000 \text{ mL}} \quad X = 5,000 \text{ mL}$$
or
Method 2: Dimensional analysis
$$5 \text{ L} \times \frac{1,000 \text{ mL}}{1 \text{ L}} = 5,000 \text{ mL}$$
9. Convert 5,000 mL to liters
$$5,000 \text{ mL} \times \frac{1 \text{ L}}{1,000 \text{ mL}} = 5 \text{ L}$$
10. Multi-step metric conversion — kilograms to nanograms
How many nanograms are equal to 5 kg? This example requires four separate proportions, or one dimensional-analysis chain (shown).
$$5 \text{ kg} \times \frac{1,000 \text{ g}}{1 \text{ kg}} \times \frac{1,000 \text{ mg}}{1 \text{ g}} \times \frac{1,000 \text{ mcg}}{1 \text{ mg}} \times \frac{1,000 \text{ ng}}{1 \text{ mcg}} = 5 \text{ trillion ng } (5 \times 10^{12} \text{ ng})$$
11. Multi-step metric conversion — nanograms to grams
How many grams are equal to 50,000,000 nanograms?
$$50,000,000 \text{ ng} \times \frac{1 \text{ mcg}}{1,000 \text{ ng}} \times \frac{1 \text{ mg}}{1,000 \text{ mcg}} \times \frac{1 \text{ g}}{1,000 \text{ mg}} = 0.05 \text{ g}$$
From this point forward, worked dimensional-analysis chains will be shown as the final cancellation only — the step-by-step cancel marks are omitted for readability, not because the intermediate steps don't matter.
Want more worked practice?
This set is built for NAPLEX (the US pharmacist licensing exam), not the NMC test directly — but the underlying arithmetic (ratios, unit conversion, dose calculation) is the same skill either way, so it's useful extra practice regardless of which side of the Atlantic you're sitting the exam on. See practice tests with full answers and explanations →
Practice calculator
Enter your own numbers and see the worked steps — good for checking homework problems or testing a formula until it's automatic.
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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