Medication dosages

Children's doses with Fried's, Young's and Clark's formulas, doses by body weight in mg per kg, and working out how many millilitres of a liquid medicine to give.

Children are not small adults. A dose that's right for a $70$ kg adult could seriously harm a $12$ kg toddler. Before weight-based charts were common, doctors used simple formulas to scale an adult dose down. You'll use them here, and you'll see why the weight-based one is the most trusted.

Three formulas

Formula	Child's dose	Uses	Usually for
Fried's	$\dfrac{\text{age in months} \times \text{adult dose}}{150}$	age in months	babies under $2$
Young's	$\dfrac{\text{age in years} \times \text{adult dose}}{\text{age in years} + 12}$	age in years	children $1$ to $12$
Clark's	$\dfrac{\text{weight in kg} \times \text{adult dose}}{70}$	weight	any child

The numbers in the formulas make sense once you see them. Clark's divides by $70$ because it treats a typical adult as $70$ kg: a $35$ kg child gets half. Fried's uses $150$ months, which is twelve and a half years: the age at which it would give the full adult dose.

Example 1●

The adult dose of a medicine is $500$ mg. Use Fried's formula to find the dose for a $9$-month-old baby.

$\text{dose} = \dfrac{9 \times 500}{150}$

Fried's uses the age in months.

$= 30$ mg

9 times 500 is 4500, and 4500 divided by 150 is 30.

Example 2●●

For the same medicine, find the dose for a $6$-year-old using Young's formula, and for a $22$ kg child using Clark's formula.

Young's: $\dfrac{6 \times 500}{6 + 12} = \dfrac{3000}{18} \approx 167$ mg

Young's: the bottom is the age plus 12, so 6 + 12 = 18.

Clark's: $\dfrac{22 \times 500}{70} \approx 157$ mg

Clark's: weight over 70.

The two formulas give similar doses for a child of typical weight.

A 6-year-old typically weighs about 20 to 22 kg, so the two give similar answers.

InteractiveThree formulas, one child

Try this

Set a $4$-year-old who weighs $16$ kg and compare the three doses. Now make the child $4$ years old but $28$ kg (a big 4-year-old). Which formula notices the difference? Then try a $10$-month-old at $9$ kg. Why does the tool warn you about Young's formula?

Doses by weight and liquid medicines

Most children's medicines today are dosed straight from body weight, written as mg per kg. Paracetamol, for example, is commonly dosed at about $15$ mg per kg for each dose. The packet says how many doses are allowed in a day.

Liquid medicines list their concentration, such as $120$ mg in $5$ mL. To find the volume, work out how many lots of $5$ mL you need:

Volume of liquid medicine

$$\text{volume} = \frac{\text{dose needed}}{\text{strength}} \times \text{volume of that strength}$$

Example 3●●

A $16$ kg child needs paracetamol at $15$ mg/kg. The syrup contains $120$ mg in $5$ mL. How many mL should be given?

$15 \times 16 = 240$ mg

Dose from weight.

$\text{volume} = \dfrac{240}{120} \times 5 = 10$ mL

240 mg is two lots of 120 mg, so two lots of 5 mL.

Your turn

The adult dose of an antibiotic is $250$ mg. Find the dose for an $8$-year-old using Young's formula.

Show the working

$\dfrac{8 \times 250}{8 + 12} = \dfrac{2000}{20} = 100$ mg

Flashcards

Fried's formula

$\dfrac{\text{months} \times \text{adult dose}}{150}$, for babies

Young's formula

$\dfrac{\text{years} \times \text{adult dose}}{\text{years} + 12}$, for ages $1$ to $12$

Clark's formula

$\dfrac{\text{kg} \times \text{adult dose}}{70}$, based on weight

Practice

Use Clark's formula to find the dose for a $30$ kg child when the adult dose is $400$ mg, to the nearest mg.
Use Young's formula to find the dose for an $8$-year-old when the adult dose is $250$ mg.
Use Fried's formula to find the dose for a $15$-month-old when the adult dose is $300$ mg.
Which formula uses the child's weight?
A child needs $180$ mg of a medicine that contains $120$ mg in $5$ mL. How many mL is that?
A medicine is dosed at $15$ mg per kg. What dose does an $18$ kg child need, in mg?
Why is Clark's formula usually more reliable than Young's?
Use Young's formula to find the dose for a $4$-year-old when the adult dose is $1000$ mg.
Exam style: The adult dose of a medicine is $650$ mg. A child weighs $25$ kg. The liquid form contains $250$ mg in $5$ mL. Use Clark's formula to find how many mL the child should be given, to one decimal place.
Exam style: A $10$-year-old weighs $32$ kg. The adult dose is $500$ mg. Find the difference between the doses from Clark's and Young's formulas, to one decimal place.