## When medicines are in liquid form, the active drug is held within a solution or suspension. So, the available dose is given in terms of the concentration of the solution.

In this section we'll look at how you can calculate the amount of liquid medicine to give a patient. Ensuring each patient is given the right medicine and the right dose is everyone's responsibility which makes this section relevant to everyone in nursing care - even if you are not the individual who initially calculated the dosage. We all play a vital role in checking the dose given to the patient and any of us has the potential to catch an accidental error which might otherwise lead to the wrong dose being provided to those in our care.

**Let's look at an example.**

Pethidine hydrochloride is available as 50 mg/ml

This means that 50mg of the drug are dissolved in every 1ml of liquid. So, it follows that 2ml of the solution would contain 100mg of the drug.

For drugs in liquid form, prescriptions are usually written in terms of weight (e.g. 1 mg), but the drug is usually by concentration (e.g. mg/ml). When we know the prescription (what we want) and the concentration of the drug in solution (what we have), we can calculate how much (the volume of liquid) we need in order to prescribe the dose.

In the 'Tackling number problems' section, the 'PEACE' problem-solving method is introduced. You may wish to review the 'PEACE' method before going further if you've not already done so.

## Mental arithmetic and using a formula

We will now look in more detail at the two main ways of calculating dosage: mental arithmetic and using a formula.

Remember, for either of these approaches you must first be sure that the stock dosage (the drug in liquid form) is in the same units as the required dosage (the prescription).

### Approach one - mental arithmetic

There are different ways you might use mental arithmetic to calculate dosage. Follow the slideshow below to explore a few methods, based on the following example:

A child is prescribed 5 mg of a drug that is available in liquid form as 2 mg per ml.

In this case, if we have 2 mg per ml, it is fairly easy to see that 1 mg would be found in half the volume. So, 1 mg is found in 0.5 ml of solution.

So, if there is 1 mg of active drug in 0.5 ml, we can multiply 0.5 ml of solution by five to get our answer (as we want 5 mg of the drug). 0.5 multiplied by five is equal to 2 and a half millilitres.

### Approach 2- the formula

Now, let's look at how to calculate dosages using a formula. Consider the formula below and then follow the slideshow to see examples of how the formula calculation is done.

Volume to be given = Required dose x Stock volume/ Stock dose

or

Volume to be given = what you want x what it's in / what you've got

Calculate - using the formula

When using the formula approach you may wish to work out the answer using pen and paper, or you may wish to use a calculator. Either of these approaches is acceptable. In fact, using both approaches together is a great way to check your answer.

**Here are some practice examples:**

Try to answer them using whatever method you are most comfortable with. Some of these you may be able to do using mental arithmetic and some will probably require you to use the formula.

### Evaluate

When you have completed your calculation, remember to check your work. Here's a reminder of the ways you might do this:

- repeat the calculation
- ask a colleague to check your answer
- try to calculate the answer again using a different method
- check against the recommended dose range (e.g. using the British National Formulary)
- look for unusually big or small answers.

### Strengths and concentrations

In this section, when we have been describing liquid medicines the concentrations have been described as mg/ml (e.g. 1mg in a 5ml spoonful). However, quite often the strength of a drug is presented as a percentage, as described below:

- % w/v = percentage weight of a substance by volume measured in grams in 100 millilitres
- % w/w = percentage weight of a substance by weight measured in grams in 100 grams
- % v/v = percentage volume of a substance by volume measured in millilitres in 100 millilitres.

The most common of these is %w/v, for example:

- 5% Glucose is 5 grams of Glucose in 100 millilitres
- 50% Dextrose is 50 grams of Dextrose in 100 millilitres.

Use this information to consider these two questions:

### Question 1.

How much sodium bicarbonate is there in a 400ml infusion of 1.26% w/v sodium bicarbonate?

1.26% w/v = 1.26 grams in 100ml

Therefore in 400 ml there is four times as much.

1.26 x 4 = 5.04 g sodium bicarbonate in 400ml

### Question 2.

How many milligrams of sodium chloride in 10 millilitre of a 0.9% normal saline solution?

0.9% means 0.9 grams in 100 millilitres = 900 milligrams in 100 millilitres = 90 mg in 10 ml