Introduction
Nurses are responsible for medication administration, and, as with many other nursing interventions, some risk is involved. NMC requirements for registered nurses, both at the beginning and throughout their careers, include drug administration and calculation skills.
Calculation skills are essential for all healthcare professionals administering medications and are crucial in ensuring safe and effective care, as calculation errors can lead to significant patient harm. Nurses must be able to convert between several units of measurement and comprehend the various measurements used for drug dosages.
Drug calculation cases
The Geeky Medics drug calculation case collection is divided into 8 sections that are commonly tested in nursing, allied health professionals and independent prescribing assessments:
- Calculating volume and doses
- Concentrations
- Converting units
- Dose adjustments
- Health economics
- Infusion rates
- Quantities to supply
- Weight-based dosing
Calculating volume and doses
The universal formula (or desired formula) can be used to calculate the required dose or volume of a medication.
Calculating volume
Example
A 72-year-old man with acute limb ischaemia is prescribed a loading dose of intravenous heparin 4,500 units. Heparin is available as a 25,000 units/5 mL solution for injection.
What volume (mL) of heparin solution for injection should be administered?
First, extract the relevant values:
- D = 4,500
- H = 25,000
- V = 5
Then, input these values into the formula:
- Dose = (4,500 / 25,000) x 5
- Dose = 0.18 x 5
- Dose = 0.9 mL
Therefore, 0.9 mL of heparin should be administered.
Calculating dose
Example
A 24-year-old woman is prescribed oral ibuprofen 400 mg three times a day. Due to her difficulty swallowing, she requires an oral suspension. Ibuprofen is available as an oral suspension of 100 mg/5 mL.
What volume (mL) of ibuprofen oral suspension should be administered per dose?
First, extract the relevant values:
- D = 400 mg
- H = 100 mg
- V = 5 mL
Then, input these values into the formula:
- Dose = (400 / 100) x 5
- Dose = 4 x 5
- Dose = 20 mL
Therefore, 20 mL of the oral suspension should be administered.
Note: The units of measurement must be the same for both the desired amount and the amount on hand.
Order of operations
When solving an equation with multiple calculation steps, these should be performed in a consistent order. This can be remembered as BODMAS:
- Brackets
- Order (i.e. X2 or √)
- Division
- Multiplication
- Addition
- Subtraction
Concentrations
Concentrations can be expressed in multiple ways:
- Mass per volume (i.e. mg/mL)
- Ratio (i.e. 1:10,000)
- Percentage w/v (i.e. 10%)
The dose calculation triangle can be used in these calculation questions.
Mass per volume
For certain medications, the concentration will be expressed as mass (i.e. mg, micrograms, mmol) per volume (i.e. mL, L). For example, amoxicillin 125 mg/5 mL means that there is 125 mg of amoxicillin in 5 mL of the solution.
The concentrations of other drugs, such as insulin and heparin, will be expressed in units/mL.
Calculations for mass per volume are all performed in the same way.
Example
A 19-year-old man in the intensive care unit is prescribed potassium chloride as a 20 mmol/50 mL infusion.
How much potassium chloride (mmol) does each mL of the infusion contain?
The concentration of potassium chloride is 20 mmol in 50 mL.
To determine the amount of potassium chloride in 1 mL, divide the total mass by the volume:
Therefore, each mL contains 0.4 mmol of potassium chloride.
Ratio
The concentration ratio represents the amount of named medication per total volume, e.g. adrenaline 1:1,000, or adrenaline 1:10,000. This is equivalent to adrenaline 1 in 1,000, and adrenaline 1 in 10,000.
The first term of the ratio is the number of grams, and the second term of the ratio is the volume. For example:
- 1:100 = 1 g in 100 mL
- 1:1,000 = 1 g in 1000 mL
- 1:10,000 = 1 g in 10,000 mL
Example
A patient in cardiac arrest requires 1 mg of adrenaline. Adrenaline is available as 1:10,000.
What volume (mL) of adrenaline should be administered?
1:10,000 means 1 g in 10,000 mL.
First, convert grams to milligrams by multiplying by 1000:
Therefore, there are 1,000 mg of adrenaline in 10,000 mL.
Then, extract the relevant values:
- Dose = 1 mg
- Concentration = 1,000 mg/10,000 mL
- Volume = ?
Then, input these values into the dose calculation triangle:
- Volume = dose/concentration
- Volume = 1 / (1,000 / 10,000)
- Volume = 1 / 0.1
- Volume = 10 mL
Therefore, 10 mL of adrenaline is required.
Note: The units of measurement must be the same for both the dose and concentration.
Percentage
The percentage ratio also represents the amount of named medication per total volume, e.g. glucose 5% or calcium chloride 10%.
The percentage is the number of grams in 100 mL:
- 1% = 1 g in 100 mL
- 5 % = 5 g in 100 mL
- 10% = 10 g in 100 mL
Example
A patient receives 20 mL of calcium chloride 10% for electrolyte replacement. Calcium chloride 10% solution for injection is available in 10 mL ampoules.
What dose (g) of calcium chloride has been administered?
Calcium chloride 10% means 10 g in 100 mL.
First, extract the relevant values:
- Dose = ?
- Concentration = 10 g/100 mL
- Volume = 20 mL
Then, input these values into the dose calculation triangle:
- Dose = concentration x volume
- Dose = (10 / 100) x 20
- Dose = 0.1 x 20
- Dose = 2 g
Therefore, 2 g of calcium chloride has been administered.
Note: The units of measurement must be the same for concentration and volume.
Converting units
Calculating doses entails converting different medication units to match the patient’s prescribed dosage. Remember that medications come in various strengths, forms, or units.
Common units
The most common units seen in drug calculations are related to mass. In ascending order, these are:
- Nanograms (ng)
- Micrograms (mcg)
- Milligrams (mg)
- Grams (g)
- Kilograms (kg)
Each unit is 1000 times smaller or larger than the next.
Micrograms
Due to the potential for errors when differentiating between milligrams and micrograms, micrograms should always be written in full to avoid ambiguity.
Converting a larger unit to a smaller unit
To convert from a larger unit to the next smaller unit, multiply by 1,000.
- Kilogram (kg) to grams (g): 1 kg x 1000 = 1000 g
- Grams (g) to milligrams (mg): 1 g x 1000 = 1000 mg
- Milligrams (mg) to micrograms: 1 mg x 1000 = 1000 micrograms
Converting a smaller unit to a larger unit
To convert from a smaller unit to the next more significant unit, divide by 1,000.
- Micrograms to milligrams (mg): 1000 micrograms / 1000 = 1 mg
- Milligrams (mg) to grams (g): 1000 mg / 1000 = 1 g
- Grams (g) to kilograms (kg): 1000 g / 1000 = 1 kg
Example
Convert 0.25 mg to micrograms
Milligrams to micrograms is converting from a larger unit to a smaller unit, so multiply by 1000:
- 0.25 mg x 1000 = 250 micrograms
Example
Convert 300 mg to grams
Milligrams to grams is converting from a smaller unit to a larger unit, so divide by 1000:
Dose-adjustments
Dose adjustments may be required in renal or hepatic impairment, or other biochemical factors. This may include a percentage increase or a percentage decrease.
To calculate the percentage of a figure:
1. Convert the percentage into a decimal by dividing by 100
2. Multiply the dose by the decimal
Example
A patient is prescribed warfarin 8 mg once daily for atrial fibrillation.
Due to a raised INR, the dose is reduced by 25%.
What is the new dose (mg) of warfarin to be administered?
To determine the amount to reduce by, calculate 25% of the current dose.
First, convert 25% to a decimal:
Then, multiply the current dose by the percentage as a decimal:
Then, to calculate the new dose, subtract the dose reduction from the original dose:
Therefore, the new dose of warfarin is 6 mg.
Hint: This can alternatively be calculated in one step by multiplying the original dose by 0.75 (as you will then be administering 75% of the total dose after the 25% reduction): 8 x 0.75 = 6 mg
Health economics
Medication cost and health economics are important considerations in prescribing, particularly in primary care. You may be expected to determine the total cost of a single prescription over a set amount of time, or the cheaper of two comparable medications.
Example
A 47-year-old woman is being discharged from the acute medical unit following a provoked deep vein thrombosis. She is to be prescribed a direct oral anticoagulant for 12 weeks.
The recommended dose of apixaban is 5 mg twice daily. Apixaban is available as 2.5 mg tablets which cost £2.45 per box of 20 tablets.
The recommended dose of dabigatran 150 mg twice daily. Dabigatran is available as 150 mg capsules which cost £45.90 per box of 60 capsules.
What is the difference in cost (£) between a 12 week course of apixaban and dabigatran?
Apixaban
To determine the number of tablets required, multiply the number of tablets per day by the number of days each week and by the number of weeks required:
- 4 tablets x 7 days x 12 weeks = 336 tablets
To determine the number of boxes required, divide the number of tablets required by the number of tablets in each box:
As a partial box cannot be given, round up to the nearest whole number:
To determine the cost, multiply the number of boxes by the cost per box:
- 17 boxes x £2.45 = £41.65
Dabigatran
To determine the number of capsules required, multiply the number of capsules per day by the number of days each week and by the number of weeks required:
- 2 capsules x 7 days x 12 weeks = 168 capsules
To determine the number of boxes required, divide the number of capsules required by the number of capsules in each box:
As a partial box cannot be given, round up to the nearest whole number:
To determine the cost, multiply the number of boxes by the cost per box:
- 3 boxes x £45.90 = £137.70
Cost difference
Lastly, to determine the difference in cost, subtract the cost of apixaban from the cost of the dabigatran:
- £137.70 – £41.65 = £96.05
Infusion rate
To calculate an infusion rate, divide the volume of fluid to be infused by the time to be infused. The rate is typically calculate per hour, to programme a volumetric pump.
Example
A patient is prescribed 1 L of 0.9% sodium chloride to be administered over 8 hours.
What is the required infusion rate (mL/h) of the 0.9% sodium chloride?
Firstly, to convert litres into millilitres, multiply the volume by 1000:
Then, extract the relevant values:
- Volume to be infused = 1000 mL
- Time = 8 hours
- Infusion rate = ?
Then, input these values into the infusion rate equation:
- Infusion rate = 1000 / 8
- Infusion rate = 125 mL/hr
Therefore, the required infusion rate is 125 mL/hr.
Drip rate
The drip rate is calculated when an intravenous infusion is given without the assistance of a mechanical pump.
Note: Infusion rate is typically in hours and drip rate in minutes.
Drop factor
The drop factor is the number of drops it takes to make up one mL of fluid. This information can be found on the giving set packaging, but generally:
- Standard giving set = 20 drops per mL
- Blood giving set = 15 drops per mL
- Micro giving set (paediatrics) = 60 drops per mL
Example
A 77-year-old woman has severe iron deficiency anaemia. The decision is made to transfuse 1 unit of red blood cells over a period of 2 hours.
1 unit of red blood cells has a volume of 280 mL. A standard blood transfusion set administers 15 drops per mL.
What drip rate (drops/min) is required to deliver the blood transfusion?
First, extract the relevant values:
- Volume to be infused = 280 mL
- Time = 2 hours = 120 minutes
- Drop factor = 15 drops per mL
Then, input these values into the drip rate equation:
- Drip rate = (280 / 120) x 15
- Drip rate = 2.333 x 15
- Drip rate = 35 drops/min
Therefore, the required drip rate is 35 drops/min.
Note: Some medications can cause harm or even death if administered without a volumetric pump.
Quantities to supply
Medications may need to be dispensed directly to patients for their own administration. This must be calculated accurately to ensure the correct amount of medication is safely dispensed, which is particularly important for controlled drugs.
Example
A patient with an acute asthma exacerbation is prescribed prednisolone at a daily dose of 40 mg, for five days.
Prednisolone is available as 5 mg tablets.
How many tablets should be supplied to complete the treatment course?
To calculate the number of tablets required per dose, divide the total dose required by the dose per tablet:
Then, to determine the total number of tablets required for the treatment period, multiply the number of tablets per dose by the number of days:
Therefore, 40 tablets of prednisolone should be dispensed.
Weight-based dosing
The necessary dosage for certain medications is determined by body weight. Since body weight is expressed in kilogrammes (kg), the dosage is typically stated as milligrams per kilogram (mg/kg).
Nomograms determine the patient’s body surface area, which is used to prescribe other medications, including cytotoxins. Surface area is expressed in square meters, so the dose is given in milligrams per square meter (mg/m²).
Consequently, the dosage needed for a particular patient can be determined by multiplying by the patient’s weight or surface area.
Example
A 13-year-old girl is admitted to the emergency department for treatment of meningitis. A decision is made to start intravenous benzylpenicillin. She weighs 47 kg.
The recommended dose of IV benzylpenicillin is 50 mg/kg every 6 hours.
What dose (g) of benzylpenicillin should be prescribed?
The required dose is 50 mg per kg.
To determine the dose of benzylpenicillin required, multiply the dose by the weight:
To convert the dose into grams, divide the dose in mg by 1000:
Therefore, 2.35 g of benzylpenicillin should be prescribed.
References
- Lapham R. (2021). Drug Calculations for Nurses: A Step-by-Step Approach. 5th ed. Routledge. 2021. Available from: [LINK].
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