Liquid Medicines and Injections

1. General Numeracy Review

You must be secure with the following rules before beginning work on drug calculations:

• Fractions can be converted into whole or decimal numbers by dividing the top number (numerator) by the bottom number (denominator). For example, ¾ is equal to 3 ÷ 4 = 0.75
• A whole or decimal number can be converted to a fraction by dividing it by 1. For example, 3 can be represented by the fraction ³/1
• To multiply fractions, first multiply the top numbers (numerators) and write this number at the top of your new fraction. Then multiply the bottom numbers (denominators) and write this answer at the bottom of your new fraction. Then cancel down.
• When multiplying, you stay on the top of the line all the way across and then on the bottom line all the way across.
• If you are multiplying a fraction by a whole number, you need to put that whole number over 1 to create the correct fraction - e.g. a 5ml stock solution becomes 5/1. Multiplying both the numerator and the denominator by 5 would give you the wrong answer.

2. What is a drug calculation formula?

A drug calculation formula is a reliable method for setting up the medication information that you have been given. This becomes a mathematical problem which, when solved, will give you the correct dosage for your patient.

You will come across a number of different formulae, depending on the medications and delivery routes involved. You will also find that there is more than one way to set up a particular kind of calculation. Our advice on this is as follows:

FIND THE FORMULA THAT WORKS FOR YOU AND STICK WITH IT!

If you do this, then it is possible to get by with learning just 3 different formulae, providing you know and understand them well.

Reading comprehension is essential to successful drug calculations. It is vital that you are able to understand the meaning of the information given so that you can set up the formula correctly. 

The following chapter will revise the basic NHS1 formula, with clear explanations of each element, and guidelines for setting up the formula and solving it when when your Stock Number is greater than 1.

3. What information do I need?

Let's have another look at our basic formula for calculating medication - NHS1.

If you need a reminder of the elements of the formula, please revisit Topic 4 - Tablets and Capsules.

Remember...

N is for Need

Need = the quantity of medication that the patient needs. This is the quantity ordered by the prescriber and may not match the amount of medication in your stock tablets or capsules.

H is for Have

This element of the formula describes the quantity of medication available to you in one tablet or capsule. It is also known as 'on hand'. 

Once you have worked out what you Need and what you Have, you can set up the first part of the formula.

S is for Stock

This part of the formula refers to the delivery system for the medication. It is sometimes referred to as 'what it's in'. For example, a liquid medication (e.g. Amoxicillin) may contain 250mg of the drug (what you Have) in 5ml of liquid. In this case, the Stock number would be 5.

An injection ampoule (e.g. Diclofenac) may contain 75mg of a drug in 3ml 

ALWAYS REMEMBER THE 1!

It is important always to remember to put the Stock number over 1. For tablets and capsules, this will give you a fraction of 1/1, which may appear unnecessary. However, you need to remember that the Stock numbers will be different for liquids and injections.

Multiplying the Have value by the Stock value, instead of by 1 is a very common error in written drug calculations. 

In the next chapter, we will look at some prescriptions for some common liquid medicines and injections, and work through how to set up the formula in each case.

4. Setting up and solving the formula - Syrups and Suspensions

Flucloxacillin Suspension

A drug chart shows that a patient requires 375g of Flucloxacillin. The label on the bottle gives the strength as 125mg/5ml. 

How much medicine should you give to the patient?

Step 1:  Make sure both amounts (NEED and STOCK) are in the same units

In this case, make sure that both amounts are in milligrams. If you are unsure about how to convert between units of measure, please work through the material in Topic 3 - SI Unit Conversions.

No conversion is necessary in this example.

Step 2: Set up the NHS1 formula

This patient Needs 375mg, and we Have 125mg. Our Stock number is 5ml. Our formula is therefore:

Step 3: Solve the formula

We now have a relatively straightforward multiplication problem to cancel down and solve:

Step 4: Check your answer

Multiplying your answer by the strength of the medicine should take you back to the prescribed amount. If it doesn't, you need to go back and check carefully for any errors.

In this case, we know that we are giving 3 lots of 5ml to make a 15ml dose. We need to check that 125 x 3 actually does equal 375. If it does, we can be confident that our answer is correct.

5. Setting up and solving the formula - Injections

A patient is to receive 80mg of pethidine. The vial contains 100mg in 2ml. 

How much do you give?

Step 1:  Make sure both amounts (NEED and STOCK) are in the same units

In this case, make sure that both amounts are in milligrams. If you are unsure about how to convert between units of measure, please work through the material in Topic 3 - SI Unit Conversions.

No conversion is necessary in this example.

Step 2: Set up the NHS1 formula

This patient Needs 80mg, and we Have 100mg. Our Stock number is 2ml. Our formula is therefore:

Step 3: Solve the formula

We now have a relatively straightforward multiplication problem to cancel down and solve:

Step 4: Check your answer

We can use an alternative calculation strategy to check this answer. This strategy involves using a syringe as a number line, and using either repeated halving and doubling, or adding incrementally:

6. Test Yourself

The following examples from Queen's University Belfast will help you to practise your NHS skills. The screencast is an excellent step-by-step demonstration of the written method of calculation. If your device does not display the entire screen, then clicking on this link will open the resource in a new window.