DRUG CALCULATIONS

# How to calculate drug dosage accurately: advice for nurses

The lack of basic maths skills can be a major problem when it comes to nurses administering drugs to patients. Calculations are still a significant source of drug error.

## Author

Steve Haigh is Senior Pharmacist, Medicines Information and Formulary, Sherwood Forest Hospitals

The lack of basic maths skills can be a major problem when it comes to nurses administering drugs to patients. Calculations are still a significant source of drug error.

Parenteral opiates are often relied on to manage acute pain in patients needing effective analgesia. But errors resulting in overdose of intravenous opiate can lead rapidly to respiratory depression. The opiate antagonist naloxone reverses opiate overdose and is usually needed quickly. However, this can cause confusion, because the product is prepared in micrograms. A small volume is involved, and the dose given needs to be titrated against response.

Developing calculation skills relies on understanding decimals to make conversion easier. And when using long division it is essential to get it the right way round. The use of simple, memorable formulae for regular reference can be a great help (Box 1).

## Drug calculations

Drug calculations appear to be impossibly difficult, unless you break them down into small steps. They are vitally important to get right, yet so easy to get wrong. This article will now look at some commonly used drug calculations and the way that mistakes can happen.

## Type A calculations

When the dose you want is not a whole ampoule.

- Prescription states 200mg (milligrams)
- You have an ampoule of 500mg (milligrams) in 4ml (millilitres).

### What volume contains the dose you need?

The easy way to remember this is the famous nursing equation:

**‘What you want, over what you’ve got, times what it’s in’**

**200mg x 4ml / 500mg = 1.6ml**

- What you want x what it’s in / what you’ve got

### Converting units

All weights, volumes and times in any equation must be in the same units. With weights the unit changes every thousand. For example, you need 1000 micrograms (mcg) to make 1 milligram (mg) and 1000 milligrams to make one gram (g) (Box 2).

## Type B calculations

These are infusion rate calculations.

- Prescription states 30 mg/hour
- You have a bag containing 250mg in 50ml

### At what rate (ml/hr) do you set the pump?

**30 x 50 / 250 = 6ml**

## Type C calculations

Infusion rate is required, but dose is ‘mg per kg’.

For example:

- Prescription states 0.5mg/kg/hour
- You have a bag of 250mg in 50ml
- Your patient weighs 70kg

### At what rate (ml/hr) do you set the pump?

**0.5mg/kg/hr x 70kg x 50ml / 250mg = 7ml/hr**

## Type D calculations

Infusion rate required, but dose is in mg/kg/min.

- Prescription states 0.5mg/kg/min
- You have a syringe of 250mg in 50ml
- Your patient weighs 70kg

### At what rate (ml/hr) do you set the pump?

**0.5mg x 70kg = 35mg**

**2100 x 50 / 250mg = 420ml/hr**

## Type E calculations

For example:

- Prescription states 3 micrograms (mcg)/kg/min
- You have a syringe of 100mg in 50ml
- Your patient weighs 70kg

### At what rate do you set the pump (ml/hr)?

**3mcg/kg for a 70kg person is 210mcg**

**210mcg/min = 12 600mcg/hr**

**2.6 x 50 / 100 = 6.3ml/hr**

## Conclusion

A UKCC council meeting in Belfast in June 2000 expressed concern at the lack of basic maths skills (Coombes, 2000; Duffin, 2000) among nurses.

Open reporting systems and ‘no blame’ cultures are recommended by the UKCC (2000) and are helpful in changing ways of working (Alderman, 1997). Reported learning initiatives (Coombes, 2000; Wilson, 2000) are welcome indications of a growing number of practical solutions.

## Want to know more?

Continue learning with a Nursing Times learning unit (worth 2 hours CPD) - Drug Calculations in Practice

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## Test exercises: try these out for yourself (answers below)

### Question 1:

Precription for IV ampicillin 200mg

### Question 2:

Prescription for IV digoxin 187.5mcg

### Question 3:

Precription for IV aminophylline 350mg in 100ml to be given over 30 minutes

### Question 4:

Prescription for dopamine 2mg/kg/hour

### Question 5:

Prescription for IV doxapram 0.1mg/kg/minute

### Question 6:

Prescription for IV noradrenaline 10mcg/kg/minute

### Question 7:

You need to give 500mg of dextrose

### Question 8:

You need to give 5ml of 0.375% bupivacaine

## Answers

### Answer 1

### Answer 2

0.5mg = 500mcg

WIG: 187.5mcg x 2ml / 500mcg = 0.75ml

### Answer 3

### Answer 4

WIG: 140mg x 50ml / 800mg = 8.75ml

So 8.75ml per hour

### Answer 5

### Answer 6

### Answer 7

### Answer 8

### References:

**Alderman C** * (1997) *The drug error nightmare.

*Nursing Times 11: 25, 24-25.*

**Anon. (2000)** Serious drug error taught me the need to brush up my maths. *Nursing Times 96: 34, 23.*

**Coombes R (2000)** Nurses need a dose of maths*. Nursing Times 96: 24, 4.*

**Duffin C (2000)** Poor standard of maths put patients’ lives at risk*. Nursing Times 14: 39, 5.*

**Hutton BM (1998a)** Do school qualifications predict competence in nursing calculations? *Nurse Education Today 18: 25-31.*

**Hutton BM (1998b)** Nursing mathematics: the importance of application*. Nursing Standard* 13: 11, 35-38.

**Lee A (1991)** *Management of continuous epidural block. In: McClure, J.H., Wildsmith, J.A.W. (eds).Conduction Blockade for Postoperative Analgesia.* London: Edward Arnold.

**UKCC (2000)** *Guidelines for the Administration of Medicines.* London: UKCC.

**Wheatley RG, Schug RA, Watson D (2001)** Safety and efficacy of postoperative epidural analgesia. *British Journal of Anaesthesia 87: 1, 47-61.*

**Wilson A (2000)** Use it or lose it. Nursing Times 14: 50, 24.

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