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.
Postoperatively, the epidural route is now common for infusions of opiate and local anaesthetic. If opiates or, indeed, most drugs, have been calculated incorrectly, the consequences for patients can be serious.
If given in too high concentrations, local anaesthetic used in epidural infusions can cause extensive motor blockade, leading to immobility and pressure ulcers, which is distressing to the patient (Lee, 1991). Wheatley et al (2001) call for routine use of prefilled epidural infusion bags to avoid the risk of calculation error when ward staff prepare infusions.
Nursing competence in drug calculations has been a cause for concern (Duffin, 2000; Coombes, 2000). Hutton (1998a) suggests that a degree of ‘deskilling’ has resulted from the increasingly userfriendliness of drug preparations and widespread use of electronic drip counters.
Her research into students’ competence in drug calculations demonstrated a marked improvement on initial test results after a structured revision programme.
Written accounts obtained from students in the study revealed that many felt unable to perform calculations such as long division and fractions without using a calculator, as they had come to rely on these at school.
There is some debate over calculator use. Hutton (1998b) argues that calculators are usually available in areas where calculations are complex, and that their use should be encouraged.
The opinion of the United Kingdom Central Council for Nursing, Midwifery and Health Visiting (UKCC) (now the Nursing and Midwifery Council) is that nurses should not rely too heavily on calculators.
The latest guidelines for the administration of medicines (UKCC, 2000) state that the use of calculators ‘should not act as a substitute for arithmetical knowledge and skill’.
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.
For example:
 Prescription states 200mg (milligrams)
 You have an ampoule of 500mg (milligrams) in 4ml (millilitres).
What volume contains the dose you need?
If you have an ampoule of 500mg in 4ml, and you need 200mg, it can appear to be a daunting calculation. The first step is to find out what volume contains 1mg (4/500) and then multiply it by how many mg you want (200).
The easy way to remember this is the famous nursing equation:
‘What you want, over what you’ve got, times what it’s in’
In this instance:
200mg x 4ml / 500mg = 1.6ml
The common error here is to get it upside down, and divide what you’ve got by what you want. This fortunately gives you a stupid answer, which is obviously wrong, in this case 10ml. You already know that you need a fraction of an ampoule and not two and a bit ampoules, which highlights the error.
To help make sure you get it the right way up, remember “WIG”:

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.
For example:

Prescription states 30 mg/hour

You have a bag containing 250mg in 50ml
At what rate (ml/hr) do you set the pump?
These are the same as type A calculations, only once you have worked out the volume that contains the amount of drug you need, you set the pump to give that amount per hour.
In this instance, work out how many ml contain ONE mg of drug
Using the WIG equation:
30 x 50 / 250 = 6ml
Therefore the calculation shows that, to give 30mg per hour, the infusion pump rate would need to be set at 6ml per hour.
This calculation is straightforward when the rate you want (30mg/hour) and the amount of the drug in the bag (250mg) are both in the same units (mg).
However, if the infusion required that 600 micrograms were to be infused each hour instead, this would first need to be converted into mg before the infusion rate was calculated, that is, 600 micrograms = 0.6mg.
The equation for infusion rate calculation is dose stated in prescription (milligrams per hour) times volume in syringe (in millilitres) divided by the amount in the syringe (in milligrams) equals the infusion rate (millilitres per hour), or:
Dose (mg/hr) x volume in syringe (ml) / Amount in syringe (mg) = Infusion rate
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?
To do this calculation you still use the WIG equation as above, but with one extra step to work out the ‘what you want’.
First you need to convert the mg per kg into total mg by multiplying it by the patient’s weight.
So for a person who weighs 70kg, 0.5mg per kg is the same as 35mg. Once you have calculated this, the infusion rate can be worked out as in the Type B calculations.
In this instance:
0.5mg/kg/hr x 70kg x 50ml / 250mg = 7ml/hr
Type D calculations
Infusion rate required, but dose is in mg/kg/min.
For example:

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?
As before, you will need to calculate what you want by multiplying the amount per kg by the patient’s weight. In this case:
0.5mg x 70kg = 35mg
This time, however, the prescription states the rate per minute. The pump demands that the rate be set in ml per hour, therefore the rate per minute will need to be converted before the equation can be completed, by multiplying 35 by 60; that is, 35mg/min (35 milligrams per minute) is converted to 2100mg/hr (2100 milligrams per hour).
From here, once again we use the type B calculation to find the infusion rate, which as shown will be 420ml/hr.
2100 x 50 / 250mg = 420ml/hr
Type E calculations
Infusion rate is required, but the dose is in mcg/kg/min.
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)?
As before, what you want is calculated by multiplying the amount per kg by the patient’s weight, that is:
3mcg/kg for a 70kg person is 210mcg
Next the prescription rate needs to be converted into rate per hour, that is,
210mcg/min = 12 600mcg/hr
The prescription is in micrograms, but in your syringe you have milligrams. Both need to be in the same units, so you must convert one to the other, in this case mcg to mg. 12 600mcg/hr is the same as 12.6mg/hr.
The calculation is then as follows:
12.6 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.
The risk of error was felt to be unacceptably high, especially in paediatric nursing, where the necessity for calculating dosages according to body weight increases calculation complexity.
The GCSE Mathematics pass at Grade C or above, or equivalent, a compulsory entry requirement for nurse training, was not felt to be adequate preparation for nursing training, and Hutton (1998a) agrees with this.
An anonymous author described personal experience of a drug error (Anon, 2000) and how it almost cost her loss of registration. She was lucky enough to have managers who offered her support, and helped with her realisation of the need for urgent basic maths revision.
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.
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Test exercises: try these out for yourself (answers below)
Question 1:
Precription for IV ampicillin 200mg
You have a vial of 500mg in 10ml
What volume contains the dose you need?
Question 2:
Prescription for IV digoxin 187.5mcg
You have a vial of 0.5mg in 2ml
What volume contains the dose you need?
Question 3:
Precription for IV aminophylline 350mg in 100ml to be given over 30 minutes
You have some vials, 250mg in 5ml
What volume of aminophylline injection do you add to the bag?
What rate do you set the pump at (ml/hour)?
Question 4:
Prescription for dopamine 2mg/kg/hour
You have a 70kg patient and a syringe of 800mg in 50ml
What rate do you run the syringe at (ml/hour)?
Question 5:
Prescription for IV doxapram 0.1mg/kg/minute
You have a 90kg patient and a bag of 500mg in 250ml
What rate do you run the syringe at (ml/hour)?
Question 6:
Prescription for IV noradrenaline 10mcg/kg/minute
You have a 60kg patient and a syringe of 16mg in 50ml
What rate do you run the syringe at (ml/hour)?
Question 7:
You need to give 500mg of dextrose
You have a 250ml bag of 5% dextrose
How many ml do you need to give?
Question 8:
You need to give 5ml of 0.375% bupivacaine
You have a 10ml ampoule of 0.5% bupivacaine and some water for injections
Answers
Answer 1
WIG: 200mg x 10ml / 500mg = 4ml
Answer 2
0.5mg = 500mcg
WIG: 187.5mcg x 2ml / 500mcg = 0.75ml
Answer 3
WIG: 350mg x 5ml / 250mg = 7ml
60 min x 100ml / 30 min = 200ml/hour
NB When you need ml/hour the equation is:
60 x ml to infuse / Duration of infusion
Answer 4
Prescription really says:
2mg/kg/hour
2mg x 70kg = 140mg/hour needed
WIG: 140mg x 50ml / 800mg = 8.75mlSo 8.75ml per hour
Answer 5
Prescription really says: 0.1mg/kg/minute
0.1mg x 90kg = 9mg/minute
9mg/minute = 9 x 60mg/hour = 540mg/hour
WIG: 540mg x 250ml / 500mg = 270ml
So, 270ml per hour
Answer 6
Prescription really says: 10mcg/kg/min
10mcg x 60kg = 600mcg/min
600mcg x 60 min = 36000mcg/hr
36000 / 1000 = 36mg/hr
WIG: 36mg x 50ml / 16mg = 112.5ml
So, 112.5ml per hour
Answer 7
5% means 5g in 100ml, which is the same as 5000mg in 100ml
WIG: 500mg x 100ml / 5000mg = 10ml
Answer 8
We need 5ml of 0.375% solution. This would contain 0.375g in 100ml. So in 5ml there would be 0.375g x 5ml / 100ml = 0.01875g (18.75mg) (line 1)
We have a 0.5% solution (which contains 0.5g (500mg) in 100ml)
We need 18.75mg.
WIG 18.75mg x 100 / 500 = 3.75ml
So, the 18.75mg we need is contained in 3.75ml of our 0.5% solution
So, we take 3.75ml (18.75mg), top it up to 5ml with WFI, and we then have 18.75mg in 5ml (which is 0.375% as shown in line 1)
References:
Alderman C (1997) The drug error nightmare. Nursing Times 11: 25, 2425.
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: 2531.
Hutton BM (1998b) Nursing mathematics: the importance of application. Nursing Standard 13: 11, 3538.
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, 4761.
Wilson A (2000) Use it or lose it. Nursing Times 14: 50, 24.
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