How to calculate drug dosage accurately ?

The lack of basic maths skills can be a major problem when it comes to 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 anesthetic. If opiates or, indeed, most drugs, have been calculated incorrectly, the consequences for patients can be serious. 

If given in too high concentrations, local anesthetic used in epidural infusions can cause extensive motor blockade, leading to immobility and pressure ulcers, which is distressing to the patient.

 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 they are so easy to get wrong. 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).

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 

Therefore, 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

There are many factors taken into consideration when deciding a dose of drug - including age of the patient, weight, sex, ethnicity, liver and kidney function and whether the patient smokes. Other medicines may also affect the drug dose.

Dosage instructions are written on the doctor's prescription or hospital chart, and on the pharmacy label of a prescribed medicine. Dosage instructions are also found on the packaging and inserts of over-the-counter medicines.