11/13/24, 7\:43 PM Guide | Drug calculations

Drug calculations

Table of contents

Introduction

Drug calculation skills are an important part of prescribing, as calculation errors may lead to signi
This is particularly important when prescribing for the elderly and paediatric populations, as they are more vulnerable to
medication-related harm.
Frailty and reduced renal function are commonly seen in the elderly population. Medication doses may need to be adjusted,
as the “safe” dose for a regular adult may no longer be appropriate for them. In contrast, the paediatric population have under-
developed organ systems, and medication doses are often based on the child's age, weight or body surface area.
Common drug calculation errors in clinical practice include miscalculating the concentration of medicine in solution,
incorrect dose unit conversion and incorrect infusion administration rate.

Prescribing Safety Assessment (PSA)

There will be eight questions assessing drug calculation skills in the Prescribing Safety Assessment (PSA). Each question is
worth 2 marks.
Drug calculation topics which may appear in the PSA include
Dose by weight
Dosing in renal impairment
Infusion doses and rate
Opioid conversion
Concentrations
Paediatric calculations

Basic principles

When carrying out a drug calculation, there are some basic principles to keep in mind\:
Convert all dose units to the same units to avoid confusion
Percentage concentrations are expressed as weight/volume (w/v) = 1 g in 100 ml; volume/volume (v/v) = 1 ml in 100 ml;
weight/weight (w/w) = 1 g in 100 g; volume/weight (v/w) = 1 ml in 100 g
For concentration questions, use C1V1 = C2V2
If it is not stated in the question, always use the actual body weight
Record the answer accurately alongside the correct units
The answer must make sense!
C1V1 = C2V2
The equation C1V1 = C2V2 is known as the dilution formula and relates the concentrations and volumes of two solutions.
In simple terms, it means that the amount of a particular substance (the mass) in a solution is constant before and after
dilution.
C = concentration
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V = volume
Concentration 1 x Volume 1 = Concentration 2 x Volume 2
Remember\: Concentration = Mass/Volume (C=M/V)

Dose by weight

Actual body weight

A 50-year-old patient who weighs 105 kg with type 2 diabetes is to be switched to insulin pens. You decide to prescribe a
starting dose of 0.2 units/kg.
Calculate the insulin dose in units for this patient.
Solution
Dose = 0.2 units x body weight
= 0.2 units x 105 kg
= 21 units
Final answer\: 21 units

Ideal body weight (IBW)

You are the FY1 on the respiratory ward. You have been asked to prescribe intravenous aminophylline for a 53-year-old man
who weighs 89 kg and is 165 cm. He was admitted with acute severe asthma and was not previously on theophylline. He is
allergic to penicillin, does not smoke and has no co-morbidities. The consultant has requested an initial loading dose of
6mg/kg and a subsequent maintenance dose of 0.7 mg/kg/hour.
Calculate the loading dose and maintenance dose of intravenous aminophylline for this patient. Round the loading dose to the
closest 10mg, and the maintenance dose to the closest 1mg.
Resources
BNF\: Aminophylline
Ideal body weight calculator
Calculation of ideal body weight for obese patients (BMI>30)
Ideal body weight (kg) = F + 0.91(Height – 152.4cm)
F (constant) = 50 (Male); 45.5 (Female)
Solution
Step 1\: Calculate the body mass index (BMI) for this patient
BMI = weight(kg) / [height(m)]
2
= 89 / [1.65 x 1.65]
= 32.7 kg/m
2
Step 2\: As the BMI is >30 (obese), calculate the patient’s ideal body weight (or use a calculator)
Ideal body weight = 50 kg + 0.91(165 – 152.4)
= 61.5 kg
Step 3\: Calculate the loading dose for aminophylline
Loading dose = 6 mg/kg
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= 6 mg x 61.5kg
= 369 mg
Round to the nearest 10 mg = 370 mg
Step 4\: Calculate the maintenance dose for aminophylline
Maintenance dose = 0.7 mg/kg/hour
= 0.7 mg x 61.5kg /hour
= 43.1 mg/hour
Round to the nearest 1 mg = 43 mg/hour
Final answer\: Loading dose = 370 mg; Maintenance dose = 43 mg/hour

Adjusted body weight

In clinical practice, the adjusted body weight may be used in obese patients who are >20% of their ideal body weight to
prevent overdosing in these patients.
This only applies to some medications with poor distribution in adipose tissues, such as aminoglycosides (e.g. gentamicin and
amikacin) and varies depending on local guidelines.
Resources
Adjusted body weight calculator

Dosing in renal impairment

For more information and examples of dosing in renal impairment, see our guide to prescribing in renal impairment.
A 72-year-old man has been admitted with a pulmonary embolism. He weighs 70kg. According to local guidelines,
subcutaneous enoxaparin is the
What dose of enoxaparin should be prescribed for this patient? Calculate the patient’s renal function using the Cockcroft &
Gault formula.
Resources
BNF\: Enoxaparin
Cockroft & Gault calculator
Product literature states the dose adjustment for enoxaparin in severe renal impairment (CrCl 15 - 30 ml/min) is 1mg/kg
Cockcroft & Gault formula
CrCl (ml/min)= ((140-age) x weight (kg) x F) / (serum creatinine (micromol/L))
F (constant) = 1.23 in male; 1.04 in female
Solution
Step 1\: Calculate the renal function using the Cockcroft & Gault formula (or use a calculator)
CrCl (ml/min)= ((140-72)x 70(kg)x 1.23)/(220 (micromol/L))
= 26.6 ml/min
Step 2\: Calculate the dose for enoxaparin
As the patient has severe renal impairment, according to the product literature, the dose is 1 mg/kg. Therefore...
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Enoxaparin dose = 1 mg x 70 kg = 70 mg
Final answer\: 70 mg

Infusion doses and rate

During your rotation in the emergency department, a 24-year-old woman who weighs 60 kg was brought in by ambulance
following a seizure. Whilst in ED, she develops prolonged seizures and status epilepticus. The consultant has decided to
commence intravenous phenytoin with a loading dose of 1000 mg, which is to be diluted in 100 ml of normal saline.
Calculate the infusion rate of phenytoin for this patient in ml/min. Each 5 ml vial of phenytoin sodium contains 250 mg.
Resources\:
BNF\: Phenytoin
Solution
Step 1\: Calculate the volume of phenytoin required
Volume (ml) of phenytoin = [(Amount of phenytoin required)/(Amount of phenytoin in original pack)] x volume of the original
pack
= [1000/250] x 5 ml
= 20 ml
Step 2\: Calculate the total volume of infusion
Phenytoin = 20 ml
Normal saline = 100 ml
Total volume = 20 ml + 100 ml
= 120 ml
Step 3\: Calculate the infusion rate in ml/min
Maximum infusion rate = 50 mg/min
Our patient requires 1000 mg\: 1000mg/50mg = 20 minutes
Rate of infusion = [total volume for infusion (ml) / total time (minutes)]
= 120 / 20
= 6 ml/min
Final answer\: 6 ml/min

Opioid conversion

A patient requires switching from oral morphine to fentanyl patches as they are now nil by mouth. The patient takes MST
Continus 30 mg twice daily and Oramorph 10mg/5ml, 5 ml four times a day for breakthrough pain.
Using the information provided, what is the recommended strength of fentanyl patch in micrograms/hour for this patient?
Note\: Round down to the nearest patch strength to avoid overdose
Resources\:
BNF\: Prescribing in palliative care
Solution
Step 1\: Calculate the total daily dose of morphine
MST Continus\: 30 mg twice a day
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= 30 mg x 2
= 60 mg
Oramorph 10 mg/5ml\: 5 ml four times a day
= 10 mg x 4
= 40 mg
Total daily dose of morphine = 60 mg + 40 mg
= 100 mg
Step 2\: Calculate the appropriate fentanyl patch strength
Morphine 60 mg = Fentanyl 25
Morphine 120 mg = Fentanyl 50
As we need to round down to the nearest patch strength, fentanyl 25 patch/72 hours should be used
Final answer\: Fentanyl 25 patch

Concentrations

A 40-year-old woman, who weighs 50 kg, is hypokalaemic. She requires a potassium infusion of 500 ml of 0.18% w/v solution.
You have 15% potassium chloride concentrate in stock.
How much 15% potassium chloride concentrate (in ml) is required for this infusion?
Solution
Step 1\: Use C1V1 = C2V2 to calculate the volume of 15% potassium chloride required
C1V1 = C2V2
(0.18 x 500) = (15) x (V2)
V2 = (0.18 x 500)/(15)
= 90/15
= 6ml
Final answer\: 6 ml of 15% potassium chloride concentrate is required

Paediatric dosing

Dose by age

A 6-year-old child presents with fever, sore throat and a “sandpaper” rash which started from the chest and spread towards the
abdomen. You have diagnosed the patient with scarlet fever and decided to prescribe phenoxymethylpenicillin for this patient.
How many bottles of phenoxymethylpenicillin should you prescribe for this patient?
Available pack sizes\:
125 mg/5ml 100 ml
250 mg/5ml 100 ml
Resources\:
BNF\: Phenoxymethylpenicillin
Solution
Step 1\: Identify the dose for this patient based on their age
The patient is 6 years old, therefore 250 mg every 6 hours for 10 days
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Step 2\: Calculate the total volume required for this patient for 10 days
Phenoxymethylpenicillin 250 mg/5ml\: 250 mg every 6 hours = 5 ml four times a day
Total daily volume\: 20ml per day
Total volume over 10 days\: 20 x 10 = 200ml
Final answer\: Supply 2 bottles of phenoxymethylpenicillin 250mg/5ml

Dose by weight

You were required to prescribe nitrofurantoin for a urinary tract infection in a 10-month-old child who weighs 9.5 kg.
Nitrofurantoin suspension comes in 25mg/5ml.
Calculate the dose in ml required for this patient.
Resources
BNF\: Nitrofurantoin
Solution
Step 1\: Calculate the dose of nitrofurantoin for this patient based on their weight
Dose (mg) = 750 micrograms x 9.5 kg
= 7125 micrograms
Step 2\: Convert the units
7125 micrograms = 7125/1000
= 7.125 mg
Step 3\: Calculate the amount of nitrofurantoin in ml required to make a dose of 7.125mg
First, we must calculate the concentration of the nitrofurantoin solution.
Concentration = Mass / Volume (C=M/V)
C = 25/5
C = 5mg/ml
Then, we can rearrange C=M/V to
C = M/V
5 = 7.125/V
V = 7.125 / 5
= 1.425ml
Step 4\: Check if the answer makes sense
Dose = 1.425 ml, however, the patient cannot measure 1.425ml. Round it down to 1.4ml
Final answer\: 1.4 ml (7 mg) 4 times a day for 3 days

Dose by body surface area

A 5-month-old child was admitted with encephalitis following an episode of chickenpox. He requires aciclovir 500mg/m 2
8 hours for 10 days. The child has a height of 66 cm and weighs 7 kg.
every
Calculate the dose of aciclovir for this patient.
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Body surface area formula
Solution
Step 1\: Calculate the body surface area of the child
Body surface area formula - example
= 0.36 m
2
Step 2\: Calculate the dose of aciclovir
Dose = 500 mg x 0.36 m
2
= 180 mg
Final answer\: 180 mg three times a day for 10 days
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Reviewer

Izaan Abd Rahman
Clinical Pharmacist

References

1. Electronic Medicines Compendium. Summary of Product Characteristics. Available from\: [LINK]
2. British National Formulary. Available from\: [LINK]
Source\: geekymedics.com
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