1.07 Calculating medication dosages

In Australia, as in other countries around the world, a significant number of people are admitted to hospital each year for taking an incorrect dosage of medication.

The dosage is a measure of the amount of medication to be given or administered (e.g. $30$30 mL every $4$4 hours). 

Medicines can be administered in a variety of forms. They can be taken orally in the form of tablets, capsules, caplets, liquids, or through an inhaler. In some cases, they can be administered through the skin by applying a cream or ointment. They can also be given internally by injection or intravenous infusion.

Most medication dosages, prescribed for a particular condition, will depend on a person's age and weight. The dosage requirements need to be correct in order for the medicine to work appropriately. Correct dosage is particularly important with medicines in liquid form, as these require exact measurements to be made.

Giving the correct dosage

The clearest information about dosage directions can be found in the dosage panel, displayed clearly on the medication's packaging. The dosage panel contains facts about active ingredients, warnings about side effects, and detailed instructions for administering the medication.

Due to the small amounts of active ingredients contained in most medications, we usually use milligrams (mg) rather than grams (g). For liquids, we use millilitres (mL) rather than litres (L).

A milligram is one thousandth of a gram. So to convert from grams to milligrams we multiply by $1000$1000. The same applies for converting millilitres into litres.

For example, 

To convert from milligrams to grams, we divide by $1000$1000. The same applies for converting litres into millilitres. 

For example,

Practice question

Question 1

Strength and concentration

Most medication comes packaged in a limited number of strengths and concentrations. This is called stock medication. The 'active' ingredient or drug is combined with various 'neutral' ingredients to form a tablet or capsule, or it is diluted in a volume of liquid. 

The stock strength of a medication, is the amount of drug it contains. This amount is displayed on the medication packaging, usually in milligrams (mg). 

The concentration describes how many milligrams of the drug there are in each tablet or, in the case of liquids, how many milligrams there are in a certain number of millilitres. 

In clinics and hospitals, doctors or nurses administering prescribed medications to patients, will use the following formula:

$\text{Volume required}=\frac{\text{strength required}}{\text{stock strength}}\times\frac{\text{volume of stock}}{1}$Volume required=strength requiredstock strength​×volume of stock1​

Worked example

Example 1

A certain medication for children (aged $3$3 months to $12$12 years) contains the drug ibuprofen at a concentration of $100$100 mg in $5$5 mL. If a child is prescribed $2000$2000 mg of ibuprofen, what volume of medication should they take?

Solution

There are several ways we can do this question. We can use the formula above or we can use ratios. To use the formula, we notice that the 'stock strength' is $100$100 mg, the 'volume of stock' is $5$5 mL, and the 'strength required' is $2000$2000 mg. 

Substituting these values into the formula:

Worked example

Example 2

A patient is prescribed $750$750 mg of a medication. The available tablets each have a strength of $500$500 mg. How many tablets should be given?

Solution

Here the 'strength required' is $750$750 mg and the 'stock strength' is $500$500 mg. 

Substituting these values into the formula:

Correct dosages for children

In Australia, giving the wrong dose of medication to children is the most common cause of accidental poisoning in children under $12$12 months old. 

Children are particularly sensitive to medicine, even those sold over-the-counter. Many medications can be harmful or fatal to children, particularly if the dosage is incorrect. Even a small change in dosage (too much or not enough), can make a big difference to how their bodies cope with the difference.

Medication dosages that may be suitable for adults, will need to be adjusted for children. Here we look at three different formula that were specifically developed for this purpose. Known as Young's, Clark's and Fried's formulas, they are named after the physicians who first developed them. All of the formulas are based on adapting an adult dosage of medication, to suit the needs of a child. 

Young's formula

Young's formula is named after a physician from England, Dr Thomas Young (1773-1829). It is used for children aged from $1$1 to $12$12 years and is based on the child's age in years.

Worked example

Example 3

An $11$11 year old girl is prescribed codeine. The adult dosage for codeine is $500$500 mg. How much codeine should the girl be prescribed, based on Young’s formula? Round your answer to the nearest milligram.

Solution

Substituting the child's age of $11$11 and the adult dosage of $500$500 mg into the formula:

Practice question

Question 2

Clark's formula

Clark's formula is named after Dr Cecil Belfield Clark (1894-1970), a physician originally from Barbados, who worked in London for fifty years. 

Clark's formula is used for children aged from $2$2 to $17$17 years and is based on the child's weight in kilograms.

$\text{Child dosage}=\frac{\text{weight in kg}\times\text{adult dosage}}{70}$Child dosage=weight in kg×adult dosage70​

Worked example

Example 4

A child is prescribed $386$386 mg of ibuprofen. The adult dosage is $600$600 mg. What is the approximate weight of the child, based on Clark’s formula? Give your answer to the nearest kilogram.

Solution

Here we are finding the value of a variable that is not the subject of the original formula. We begin by substituting known values into the formula, then solve the resulting equation for the child's weight.

Practice question

Question 3

Fried's formula

Fried's formula is named after an Israeli, Dr Kalman Fried (1914-1999), who developed the formula while observing children at a hospital in Jerusalem.

Fried's formula is similar to Clark's formula, except that it has been modified for infants (children aged from $1$1 to $2$2 years). For this reason, the formula uses the child's age in months, rather than its weight.

$\text{Dosage for children 1-2 years}=\frac{\text{age (in months)}\times\text{adult dosage}}{150}$Dosage for children 1-2 years=age (in months)×adult dosage150​

Worked example

Example 5

A $2$2 year old child is prescribed paracetamol. The adult dosage is $600$600 mg and has a concentration of $100$100 mg in $5$5 mL. How much must the child take based on Fried’s formula?

Solution

The child's age must be in months when using Fried's formula and $2$2 years is equivalent to $24$24 months. Substituting into Fried's formula we can calculate the correct child dosage:

We can now work out the volume of medicine required for the child that has a strength of $96$96 mg, given that the stock strength is $100$100 mg and the volume of stock is $5$5 mL:

Practice question

Question 4