#### Introduction

Dosage calculations are not difficult. In fact, they’re one of the simplest topics in pharmacy calculations. Today we analyze eight examples – none of which should cause any great difficulty for the student. Once you’ve finished studying this section, be sure to review our other 10 pharmaceutical calculation articles. You can find the link to those articles in the adjacent sidebar.

First, let’s spend a few minutes reviewing some basic examples of dosage calculations.

#### Example 1

How many tablets should you prescribe if a patient needs 4 tablets of drug X twice daily for 6/7?

• 4 tablets twice-daily = 8 tablets
• 6/7 refers to 6 days = 8 (6) = 48 tablets

#### Example 2

A patient enters your pharmacy asking for his cough medicine. His doctor prescribed him 15mL of medicine four times a day for 7 days. What number of doses is needed and what minimum volume of cough medicine needs to be dispensed?

Doses are delivered every 5mL – meaning this patient’s dose of 15mL comprises three 5mL spoonfuls. Of course, this 5mL spoonful is not the dose.

4 times a day dosing for 7 days constitutes 28 doses – again, each dose consists of a 5mL spoonful.

28 doses x 15mL = 420mL of medication needs to be dispensed.

Note: Doses less than 5mL can be delivered using an oral syringe – this may be needed in cases of children or the elderly.

• Number of doses a) 28 doses
• Minimum volume to be dispensed b) 420mL

#### Example 3

A patient has been prescribed 9mg of drug X twice-daily for 5/7. She is also prescribed 7mg once-daily (of the same drug) for the remaining 2/7. Drug X is only available in 2mg and 5mg tablets. How many tablets of each strength should be prescribed to the patient?

• 9mg x two times daily = 18mg
• 18mg x 5 days = 90mg for 5 days of drug X
• 14mg required for the next two days (2/7)
• Total dose is 104mg of drug X.

It would be wrong to prescribe twenty 5mg tablets and two 2mg tablets – even though it totals 104mg.

That’s because the patient would run out of 2mg tablets! 9mg dose alone requires 5mg + 2mg + 2mg. There would be no 2mg remaining for the second dose of day one of treatment.

Each daily dose needs two 5mg tablets and four 2mg tablets – which is ten 5mg tablets and twenty 2mg tablets for 5/7.

A further 7mg is required for the next two days – which is two 5mg tablets and two 2mg tablets for 2/7.

In total, the patient needs twelve 5mg tablets (60mg) and twenty-two 2mg tablets (44mg) – leading to the required dose of 104mg.

#### Example 4

Adrenaline is available as an injection of 100 micrograms/mL. A patient needs an intramuscular injection of 0.5mg. How many millilitres of injection are needed to supply the required dose?

First, we need to consider whether our units are consistent – in this case, they’re not.

0.5mg x 1,000 = 500 micrograms.

Adrenaline is available as an injection of 100 micrograms/mL.

Therefore we need 5mL of the available adrenaline formulation.

#### Example 5

The recommended dose of fluconazole for mucosal candidiasis in children is 3mg/kg daily. Calculate the dose needed for a child (3-years old). Suggest an appropriate formulation.

The BNF (“British National Formulary”, or other international dosing guide) is clear that a “child” is any person under the age of 12. The BNF provides a table with ideal body weights and heights, depending on the age of the child. These tables need to be consulted when trying to calculate appropriate child dosing. If the weight of a child is not given, it’s not uncommon to estimate a value. For example, a 6-year old child has an estimated weight between 18kg and 23kg – that is to say, approx. 20kg.

With this in mind, a 3-year old child has an ideal body weight of 14kg. The ideal dose is, then, 14kg x 3mg = 42mg of fluconazole.

What formulation should we choose?

• 50mg, 150mg, 200mg capsules
• 50mg/mL and 200mg/5mL suspensions

It’s clear that capsules are ruled out. Children under the age of 5 should preferably be administered liquid formulations.

The most appropriate formulation is 50mg/5mL of fluconazole suspension.

If there is 50mg in 5mL, then 1mg has 0.1mL.

We need 42mg of fluconazole – 42 x 0.1mL = 4.2mL

Answer: A 3-year old child should be prescribed 4.2mL of fluconazole suspension (50mg/5mL) daily.

#### Example 6

Drug X needs to be dosed at 15mg/kg daily in two divided doses. Calculate the dose for a 6-month old child and the volume of paediatric injection to be dispensed. Drug X is available in a formulation of 50mg/mL.

The idea body weight of a 6-month old child is 7.6kg.

Given that the dose is 15mg per every 1kg – 7.6kg is equivalent to 114mg.

Now that we’ve learned the quantity needed of drug X, we now need to find out how many mLs of the available formulation delivers this exact dose.

If there is 50mg in 1mL of formulation – then 0.02mL must contain 1mg.

If we multiply 0.02mL by 114mg, that gives us 2.28mLs.

However, the question specified that drug X needs to be given in two divided doses.

Answer: 2.28mL of the formulation must be given daily in two divided doses of 1.14mL.

#### Example 7

What oral dose of methotrexate is suitable for a 5-year old child weighing 18kg? The oral dose of methotrexate is 15mg/m2 weekly.

First, we need to learn what the ideal body surface area of a 5-year old child is.

The ideal body surface area for a 5-year old child is 0.74m2.

If there is 15mg in every 1m2, how many mg is in 0.74m2?

Divide 1m2/0.74m2, we learn the proportionate factor difference. In this case, the factor is 1.35.

Answer: By dividing 15mg by 1.35, we learn that the weekly dose of methotrexate should be 11.1mg.

#### Example 8

Formulation X contains 9.25mg of vitamin A (as retinyl acetate) and 400 IU of ergocalciferol. Formulation Y contains 2,240 IU of vitamin A and 10 micrograms of vitamin D. Which formulation contains the the greatest vitamin concentration?

First problem to identify – units are not the same!

For vitamin A:

• 1 IU = 0.344 micrograms.
• 9.25mg of Vitamin A; we need to convert this to micrograms too.
• 9.25mg = 9250 micrograms.
• 9250/0.344 = 26,890 IU

So formulation X contains 26,890 IU of vitamin A and formulation Y contains 2,240 IU of vitamin A.

When we apply the same process to ergocalciferol, we learn that the same quantity of vitamin D is found in both formulations.

Answer: Formulation X contains the greater concentration of vitamins.

#### Conclusion

Dosage calculations are a fundamental part of pharmacy calculations. The above eight examples by no means exhaust the topic. They do, though, introduce you to the concepts you need to know. You may encounter more challenging examples during your study. Even though these examples are more challenging, the same thought processes apply. Break the question down into its component parts. Question whether your answer makes sense.

In time, calculation of doses becomes second nature.