## In this section we will cover calculations relating to the giving of fluid medicines over time (continuous infusions), for example drugs provided intravenously through an IV line.

Ensuring each patient is given the right medicine and the right dose is everyone's responsibility. This section is 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.

In the 'Tackling number problems' section, the ‘PEACE’ problem-solving method is introduced. Some of this information is repeated here. You may wish to review the 'PEACE' method before going further if you've not already done so, or, you may wish to jump ahead to the heading ‘Approach 1 – mental arithmetic’ if you're already comfortable with 'PEACE'.

## Plan

Start by thinking through what you need to do.

Your goal is to calculate how many tablets to give a patient based on the required dose (what you want) and the strength of the tablets (what you’ve got). You may also need to consider how much medication they have already taken so you don’t go over the daily dosage.

**Your patient**. It is possible that you may need to take account of the patient’s weight, as the dosage may be dependent on this. This is common in paediatric nursing (great care is needed in this context, as small errors in dose or quantity of medicine may be harmful, due to the infants small body size).

**The units**. Before you can move on to estimation and calculation, you first need to ensure that the drug is in the same units as the prescription. Estimation and calculation is much more difficult if they are in different units and therefore also more likely to lead to a mistake). Converting between metric (SI) units is covered in detail in the 'Metric (SI) units' section of this resource. Once the available drug and prescription are in the same units, you can do an estimate.

**The consequences**. It is also worth pausing to consider the type of medication you are going to administer and the vulnerability of the patient – how serious are the consequences of a mistake? If the consequences of a mistake are serious, you should check the calculation with a colleague, particularly if you are unfamiliar with the medication or patient group.

## Estimate

It is important to first try to estimate the answer before you start to calculate. A number of ways of estimating are covered in the 'Estimation' section of this resource.

## Approach

Before you calculate, remember to ask yourself the following questions.

**WHAT**

There are basically two approaches that can be used to calculate dosage: mental arithmetic and applying a formula.

Using both methods together as a tool for checking your answer is a great approach to give you confidence that you have the right answer.

**HOW**

Here is a summary of the steps you’ll need to follow when calculating dosage.

- Modify the required dosage (the prescription) base on the patient’s weight, if necessary
- Check the units are the same (prescription units are the same as the units of the tablet) and if they are not then convert them to the same unit.
- Choose your method: mental calculation or use the formula.
- Choose your tools: mental arithmetic, pen, paper, calculator.

**WHEN and WHERE **

You may also wish to consider where (and when) you are going to do the calculation – for an important calculation you will probably want to find a quiet place with no distractions. You may wish to consider if you are currently under pressure or fatigued and if there is time to wait to do the calculation when you are in a better “state of mind”

## Calculate

Let’s look at some examples of how to calculate flow rate and drop rate. We’ll start with flow rate.

**Flow Rate**

When using electronic infusion controllers, the flow rate needs to be set. The rate is the volume in ml divided by the duration in hours (mls per hour). This calculation can be expressed as a formula-

Flow rate = Volume (ml) / Time (hours)

**Drop Rate**

When using manual infusion controllers, the drop rate needs to be set (drops per minute). This can be calculated using the following formula-

Drop rate = Drop factor x Volume/60 x Time (hours)

One further part of this formula is the drop factor. On some types of controller, the size of each drop of liquid is governed by the internal mechanics – it is fixed and cannot be altered. Typically, it is written on the machine. This constant quality gives rise to the drop factor:

Drop factor = the number of drops it takes to make up one ml of fluid.

Two common sizes are:

- 20 drops per ml (typically for clear fluids)
- 15 drops per ml (typically for thicker substances, such as blood)

Now that we've looked at some examples, see if you can solve the following problems (there are a mix of flow rate and drop rate questions).

## 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.

## Calculating the duration of an infusion

You may need to calculate how long an infusion will last. Consider this example: How long will a 100ml infusion of sodium bicarbonate last if it is running at 42 drops per minute?

In this example, we'll assume the drop factor for the equipment is 20 drops per ml.

To solve this, we first need to find out how many millilitres are transfused per minute, we do this as follows:

- The drop rate is 42 drops per minute.
- The drop factor is 20 drops per ml.
- If we divide 42 drops per minute by 20 drops per millilitre, we'll find out how many millilitres per minute.
- 42/20 = 2.1 ml per minute.

Now we can divide the overall infusion of 100ml by the millilitres tranfused per minute to get our answer:

100 ml / 2.1 ml per minute = 47.6 minutes.

## Now here's one for you to try

A patient is to be given 1000 ml by IV using a controller with a drip factor of 15 drops/ml.

The infusion starts at 8.00am. If the drip rate was set at 25 drops per minute, at what time would the drip be complete? (The answer is calculated below).

Answer:

- If we divide 25 drops per minute by 15 drops per millilitre, we get how many millilitres per minute = 1.67 ml/min.
- If we then divide 1000ml by 1.67 ml per minute we get 600 minutes.
- 600 minutes = 10 hours
- 8am plus 10 hours = 6pm