## Pharmaceutical Calculations — Calculation of Doses

This is the fourth of our seven part series on pharmaceutical calculations, this time dealing with calculation of doses.

This is another relatively straightforward section of pharmaceutical calculations but unfortunately some people do actually get these types of question wrong. Nonetheless, this section will go through 8 examples of such dosage calculations, varying each question accordingly. It starts off with basic calculations and then proceeds to look at dosage calculations for children then finally concluding with dosages involving international units.

##### Example 1

How many tablets should a pharmacist prescribe if the patient requires 4 tablets of Drug X twice daily for 6/7?

4 Tablets twice-daily = 8 tablets
6/7 referring to 6 days = 8 x 6 => 48 tablets

##### Example 2

An angry patient enters your pharmacy demanding his cough medication. The doctor prescribed him a dosage regimen of 15mL four times a day for 7 days. Calculate the quantity of doses this patient will take as well as the total quantity of cough medication to be dispensed?

A dose of medication is delivered per every 5mL so this patient’s dose of 15mL consists of three 5mL spoonfuls. This 5mL spoonful should not be called the dose.
The patient needs to take the dose 4 times a day for 7 days constituting 28 doses, again, each dose consisting of a 5mL spoonful.
28 doses x 15mL = 420mL of medication that needs to be dispensed.
Note: Doses less than 5mL can be delivered using an oral syringe. This may be necessitated in young adults or elderly patients.

##### Example 3

Despondent patient Y is prescribed 9mg of Drug X twice-daily for 5/7. In addition, this same patient is prescribed 7mg once-daily of the same drug for the next subsequent 2/7. However, Drug X is only available in 2mg and 5mg tablets. Bearing this in mind, how many tablets of each strength should be prescribed to the patient?

9mg x Two Times Daily = 18mg
18mg x 5 days = 90mg/5 days of Drug X
14mg required for the next two days (2/7)
Thus, the total dosage regimen requires 104mg.
Hence, twenty 5mg tablets and two 2mg tablets can be prescribed.

##### Example 4

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

First of all, we need to bear in mind whether or not 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.
Hence, we’ll need 5mL of the available adrenaline formulation.
In more awkward examples that don’t multiple as easily, sets can be used as we did in the first three sections of this series.

##### Example 5

The recommended dose of fluconazole for mucosal candidiasis in children is 3mg/kg daily. Your job is to calculate the dose of fluconazole for a child aged 3 years old. In addition, suggest an appropriate formulation.

The BNF is very clear that a child is defined as that which is under the age of 12. The BNF also provides a table with ideal body weights and heights depending on the age of the child. You can find this table here. Tables such as this need to be consulted when trying to calculate the appropriate dose for a child. If the weight of a child is not given in the table then it’s usual to estimate a value between its neighbours in the table. For example, a 6 year old child would have an estimated weight between 18kg and 23kg i.e. 20kg.

Bearing this in mind, a 3 year old child has an ideal body weight of 14kg. Thus, the ideal dose would be 14kg x 3mg = 42mg of Fluconazole.
However, we face a dilemma. How are we to provide an appropriate formulation? We have a choice:

-->50mg, 150mg, 200mg capsules
-->50mg/mL and 200mg/5mL suspensions

It should be obvious that the capsules are automatically ruled out. In addition, children under the age of 5, according to the BNF, should preferably have liquid formulations rather than that of tablets or capsules.

The most appropriate formulation would therefore be the 50mg/5mL of fluconazole suspension.
So how many mL’s of this suspension should be given per day?
If there is 50mg in 5mL, then in 1mg we have 0.1mL (simply by dividing 5mL/50mg).
We need 42mg of fluconazole so we multiple 42 x 0.1mL = 4.2mL
Thus, a 3 year old child required 4.2mL of fluconazole suspension daily.

##### Example 6

Drug X has a dose of 15mg/kg daily in two divided doses. Try to calculate the dose for a 6 month old child and the volume of paediatric injection to be provided. The available formulation of Drug X is 50mg/mL.

The idea body weight of a 6 month old child is 7.6kg.
Hence, given that the dose is 15mg per every 1kg, then 7.6kg is equivalent to 114mg.

So now that we’ve discovered the quantity of Drug X, we now need to find out how many mL’s of the available formulation will deliver this quantity to the child.
If there is 50mg in 1mL of formulation then this must mean that 0.02mL contains 1mg.
Thus, if we multiple 0.02mL by 114mg then that gives us 2.28mL’s. However, the question specified that Drug X needs to be given in two divided doses.
With this in mind, we can conclude that 2.28mL of the formulation must be given daily in two divided doses of 1.14mL.

##### Example 7

What oral dose of methotrexate would be suitable for a 5 year old child who weighs 18kg? The oral dose of methotrexate is 15mg/m2 weekly.

We need to find out what the ideal body surface area of a 5 year old child is. The wondrous BNF (or more detailed nomograms) can help us in this regard.
The body surface area happens to be 0.74m2 for a 5 year old child weighing 18kg.
If there is 15mg per every 1m2, then how many mg is in 0.74m2?
If you divide 1m2/0.74m2, then we can find the proportionate factor difference. In this case, it works out as 1.35.
By dividing 15mg by 1.35, we find 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 while Formulation Y contains 2,240 IU of Vitamin A and 10 micrograms of Vitamin D. Which product contains the most vitamins?

The first problem you should immediately identify is that the units are not the same. This problem needs to be rectified before anything else.

For Vitamin A
1 IU = 0.344 micrograms.
We have 9.25mg of Vitamin A so we need to convert this to micrograms too.
9.25mg = 9250 micrograms.
9250/0.344 = 26,890 IU

So Product A contains 26,890 IU of Vitamin A and Product B contains 2,240 IU of Vitamin A.
Once you sort out ergocalciferol in the same way, you find that the same quantity of Vitamin D can be found in both products.

On analysis, we find that Product A contains the most vitamins.

The next section in our seven-part series on pharmaceutical calculations focusses on Displacement Values.

By | 2016-02-12T19:03:43+00:00 December 1st, 2014|Pharmaceutical Calculations|10 Comments

Mastering the Science of Medicines

1. Jetski October 27, 2015 at 03:03

Hey, thanks for this post...love your site...keep it up!

2. Eman February 2, 2016 at 17:55

Question / The rectal dose of sodium thiopental is 45mg/kg of body weight. How many milliliters of 10%w/v solution should be used for a person weighing 150Ib

3. ebo3961 February 3, 2016 at 06:08

150lbs = 68kg
45mg x 68 = 3060mg
10% in 100ml = 10g /100ml
3060/10 x100 = 30.6 = 31ml

4. Calixto Arcuri February 3, 2016 at 15:59

How would you calculate to remove the powder in 2 capsules of a 40mg capsule of vyvanse ( Amphetamine/Lisdexamfetamine) and to then convert it into a 70mg capsule? ( by measuring the mass )
what steps would I have to follow to create this amount?

5. Aisimbo March 9, 2016 at 20:40

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6. vafaei April 16, 2016 at 13:03

How can we determine essential oil solutions isotonic?
For example::Dropping an essential oil solution to eye.
How caculate the dosage of oil?

7. Esrael July 7, 2016 at 06:00

Thanks lots! Very useful site.

8. Student February 6, 2017 at 00:46

Please could you ammend example 3.
If the patient were to receive only 2 mg tablets and the other 20 tablet as 5mg, they would struggle to achieve the 16mg dose for the first 2 days.

Day 1, 1st dose = 9mg+7mg= 16mg
Day 1, 2nd dose= 9mg.

The first dose woul have to be 2 of 5mg tablets plus 3 of 2mg tablets. If 3 of 5mg tablets are used, the patient would require a 1mg tablet. The second dose would consume 2 of the 2mg tablets and leave none left for subsequent days.
Hope this helps.

9. Patrick J Cernohous April 20, 2017 at 18:45

Dr. Prescribed(Fluconazole 200mg),1 tablet per week for 4 months.

How many tablets, in total, shall be dispensed?

10. Hania May 29, 2017 at 02:19

Thank you for the sample questions. However, will you please correct the solution of example 3.
The patient requires to have 9 mg twice a day for 5 days and 7 mg once a day for 2 days. It would be impossible for him to achieve
the required dosage with 20, 5 mg and and only 2 , 2 mg tablets.

For instance to get the 9 mg dosage , he should consume one 5 mg and two 2 mg tablets. He wont be able to continue this regimen , as he would not have further 2 mg tablets , But loads of 5 mg tablets through which he cant achieve the required said dosage of 9 mg.

Instead he should be dispensed 12 , 5 mg tablets and 22 , 2 mg tablets
and instructed to to consume one, 5 mg and two 2 mg tablets for 5 days
and one , 5 mg and one, 2 mg tablets for 2 days.

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