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## Introduction

Drug **calculation skills** are an important part of prescribing, as **calculation errors** may lead to significant **patient harm**.

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

**prescribing safety assessment (PSA) question pack**, which contains over

**500 high-quality PSA questions**. We also have a range of prescribing stations in our collection of

**1,300 ready-made OSCE Stations**💊

## 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

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**

**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

= 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**

**Dosing in renal impairment**

**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 first-line treatment for pulmonary embolism. His serum creatinine level is 220 micromol/L.

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…

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**:

**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**:

**Solution**

**Step 1**: Calculate the total daily dose of morphine

MST Continus: 30 mg twice a day

= 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**:

**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

**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**

#### 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 find the volume of nitrofurantoin solution required to achieve a dose of 7.125mg.

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} every 8 hours for 10 days. The child has a height of 66 cm and weighs 7 kg.

Calculate the dose of aciclovir for this patient.

**Solution**

**Step 1**: Calculate the body surface area of the child

= 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**

### Reviewer

#### Izaan Abd Rahman

**Clinical Pharmacist**

### Editor

#### Dr Chris Jefferies

**References**

- Electronic Medicines Compendium. Summary of Product Characteristics. Available from: [LINK]
- British National Formulary. Available from: [LINK]