Pharmacy Calculations

## Dosage Calculations

Dosage calculations are among the most common pharmacy calculation questions asked on tests. They’re also some of the most important calculations to know.

Differences between doses can have enormous clinical consequences. Both pharmacy technicians and pharmacists must have a robust, comprehensive, and error-free understanding and knowledge of dosage calculations.

Below, we study eight different kinds of dosage calculations. Practice each pharmacy calculation question before studying the answer. This way, you can identify any knowledge gaps along the way.

### Sample Problem 1

How many tablets must be prescribed to a patient who needs 4 tablets of drug twice daily for 6/7?

• 4 tablets twice-daily = 8 tablets
• 6/7 refers to 6 days out of 1 week = 8 x 6 = 48 tablets

### Sample Problem 2

A patient enters your pharmacy asking for cough medicine. His clinician prescribed him 15mL of medicine to be taken four times daily 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.

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

28 doses x 15mL = 420mL of cough medicine must be dispensed.

Note: Doses less than 5mL can be delivered using an oral syringe which may be needed, for example, for children or the elderly.

• Number of doses: 28
• Minimum volume to be dispensed: 420mL

### Sample Problem 3

A patient has been prescribed 9mg of drug X to be taken 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 (5/7)
• 14mg required for the next two days (2/7)
• Total dose: 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.

### Sample Problem 4

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

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

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.

### Sample Problem 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.

For these kinds of dosage calculations, you must consult a reference textbook. The BNF (“British National Formulary“, or other international dosing guide) is clear that a “child” is defined as a person under the age of 12 years.

The BNF provides a table with ideal body weights and heights, based on the age of a child. These tables must be consulted when calculating dosage for children. 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

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.

### Sample Problem 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 pediatric injection to be dispensed. Drug X is available in a formulation of 50mg/mL.

The ideal 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.

### Sample Problem 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.

### Sample Problem 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 greatest vitamin concentration?

Note that units are not equivalent.

For vitamin A:

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

Therefore, 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 a greater concentration of vitamin.

## Final Thoughts

Dosage calculations remain one of the most foundational subjects within the broad church of pharmacy calculations.

Here, we have reviewed the basic calculations that you must know, as well as some key factors to consider – such as body weight, the importance of identifying inconsistent units, and the step-by-step methodology that should be followed to work out problems in a logical and consistent manner.