Infusion Rate Calculations for the GPhC Exam: Worked Examples

Infusion rate calculations come down to three questions: how much drug per hour, how much drug per mL, and therefore how many mL per hour. Get those in the right order, convert units before you divide, and every infusion question in the GPhC registration assessment becomes the same calculation. Below are the formulae, five worked examples and the mistakes that cost the most marks.

Infusion rates are one of the nine calculation areas the GPhC's Common Registration Assessment framework says will appear in every Part 1 paper, so this is guaranteed marks if you have a reliable method. All drugs and doses in the examples are invented for practice. In real practice, always check doses against the BNF, the SmPC and your local guidelines.

The three formulae you need

Learn these until you can write them without thinking.

Volume over time (fluids) Rate (mL/hour) = total volume (mL) / time (hours)

Drug dose to pump rate Rate (mL/hour) = dose needed per hour (mg/hour) / concentration (mg/mL)

Gravity drip rate Drops per minute = volume (mL) x drop factor (drops/mL) / time (minutes)

The drop factor is printed on the giving set packaging. In UK practice a standard giving set is commonly 20 drops/mL and a blood giving set 15 drops/mL, but always use the figure stated in the question.

Worked example 1: a simple fluid rate

1 litre of sodium chloride 0.9% is prescribed over 8 hours. What rate should the pump be set to, and what drip rate would you need with a 20 drops/mL giving set?

1. Convert: 1 litre = 1,000 mL.
2. Rate = 1,000 mL / 8 hours = 125 mL/hour.
3. Drip rate = 1,000 mL x 20 drops/mL / 480 minutes = 41.67, so 42 drops per minute.

Notice the time is in minutes for the drip rate. Using 8 instead of 480 is one of the most common slips.

Worked example 2: weight-based dose in mg/kg/hour

A 70 kg patient is prescribed Drug A at 0.5 mg/kg/hour. The infusion contains 250 mg in 50 mL. What rate in mL/hour?

1. Dose per hour = 0.5 mg/kg/hour x 70 kg = 35 mg/hour.
2. Concentration = 250 mg / 50 mL = 5 mg/mL.
3. Rate = 35 mg/hour / 5 mg/mL = 7 mL/hour.

Worked example 3: micrograms per kg per minute

This is where most marks are lost, because there are two conversions hidden in one question.

An 80 kg patient needs Drug B at 5 micrograms/kg/minute. The syringe contains 200 mg in 50 mL. What rate in mL/hour?

1. Dose per minute = 5 micrograms x 80 kg = 400 micrograms/minute.
2. Dose per hour = 400 x 60 = 24,000 micrograms/hour = 24 mg/hour.
3. Concentration = 200 mg / 50 mL = 4 mg/mL.
4. Rate = 24 mg/hour / 4 mg/mL = 6 mL/hour.

A quick check: if you had forgotten to multiply by 60, you would get 0.1 mL/hour, which no one would ever set a pump to. A daft-looking answer is a gift; it tells you to look again.

Worked example 4: working backwards from the pump

Questions often give you the pump rate and ask what dose the patient is actually receiving.

A pump is running at 12 mL/hour. The bag contains 500 mg of Drug C in 100 mL. The patient weighs 60 kg. What dose are they receiving in mg/kg/hour?

1. Concentration = 500 mg / 100 mL = 5 mg/mL.
2. Dose per hour = 12 mL/hour x 5 mg/mL = 60 mg/hour.
3. Dose per kg = 60 mg/hour / 60 kg = 1 mg/kg/hour.

Worked example 5: when will it finish?

A 500 mL bag is started at 09:00 and runs at 125 mL/hour. When will it finish?

1. Time = 500 mL / 125 mL/hour = 4 hours.
2. Finish time = 13:00.

If the answer is not a whole number, convert the decimal carefully: 0.25 hours is 15 minutes, not 25.

Quick reference: unit conversions

Write "micrograms" in full in your working, as the BNF does. Abbreviating it is how 1,000-fold errors happen in practice, and the habit helps in the exam too.

The five mistakes that cost the most marks

1. Mixing mg and micrograms. Convert everything to the same unit before you divide.
2. Forgetting per minute versus per hour. Underline the time unit in the question and in the answer it asks for.
3. Using the total dose instead of the hourly dose. Read whether the prescription is a dose per hour, per day or a total.
4. Rounding too early. Keep full figures through the working and round only at the end, to the precision the question asks for or that the device can deliver.
5. Not sense-checking. Ask whether a nurse could realistically set that rate. A syringe pump at 400 mL/hour or 0.01 mL/hour should stop you.

Practise until the method is automatic

Part 1 gives you about 3 minutes per question, and infusion questions are usually multi-step, so speed comes from never having to think about the order of operations. Do ten infusion questions a day for a week, timed, and check every wrong answer for which of the five mistakes caused it.

For the full picture of what else appears in the calculations paper, read our guide to the GPhC registration assessment format. When you are ready to test yourself under exam conditions, you can try a free timed mock paper with a worked rationale for every answer.