Maths

Introduction

All nurses need to be competent in the calculation of medication dosages. Trained nurses need to know how to calculate required dosages accurately, including the calculation of doses of tables, doses of solutions, and intravenous fluid rates and medications.

These drug calculations will require the application of some basic mathematic calculations such as addition, subtraction, multiplication, and division. In addition, you will need to be able to:

Arithmetic for nursing calculations

Before you start calculating medication dosages, you may want to review your knowledge on basic mathematic calculations and fractions, percentages and decimals.

There are lots of online resources to help you develop and practice your maths skills. These maths worksheets cover underlying maths skills.

You can also access videos and resources on the underlying maths skills that you will need in order to effectively calculate drug dosages here:

If you would like to test you rmaths skills, complete the Numeracy Success Indicator (NSI).

Units of measurement

Converting units of measurement

In this section, you will learn:

• What units of measurement exist for weight, volume and time
• How to convert weight and volume units of measurement from larger to smaller units
• How to convert weight and volume units of measurement from smaller to larger units
• How to work with time calculations

Medication dosage orders are provided and dispensed in a variety of ways. It is important that you familiarise yourself with the terminology used to measure weight and volume, and how to convert from larger to smaller units- and vice versa.

When applying formulas to calculate dosages, make sure that you are using the same units of measurement; this means that, in some cases, you will need to convert units of measurement. This section will show you how weight and volume are measured.

Units of measurement: weight

The gram is the basic unit of weight. The most common multiple of a gram is the kilogram, which is 1000 times greater than the gram. The most common subdivision of a gram is the milligram, which represents 1/1000 of a gram- or 0.001 g. The table below shows equivalencies between units of weight:

Units of measurement: volume

The litre is the basic unit of volume; a subdivision of a litre is the millilitre. The table below shows the equivalence between litre and millilitre:

Converting from larger to smaller units

Because all metric units are multiples or subdivisions of the major units, you can convert units by dividing by the appropriate multiple or multiplying by the appropriate subdivision.

If you need to convert between a larger a smaller unit (for example, from kilogram to gram), you will multiply by 1000, or move the decimal point 3 places to the right.

• For example, to convert 2 kg to g:

2 kg will convert to 2000 g

2kg x 1000= 2,000g

Or move the decimal point 3 places to the right: 2kg ► 2000 g

• To convert 3.4 L into mL.

3.4 L x 1000= 3400 mL

Or move the decimal point 3 places to the right: 3.4 L  ► 3400 mL

Converting from smaller to larger units

To convert from smaller to larger units, divide by 1000 or move the decimal point three places to the left.

• To convert 300 mg into g:

300mg/1000= 0.3 g

OR move decimal point three places to the left 300 mg ►0.3 g

• To convert 1700 mL into L:

1700 mL/1000 = 1.7 L

OR move the decimal point three places to the left

1700 mL ►1.7 L

Convert units of measurement

Choose the correct option

Q1- Convert 0.69 g to mg:
Incorrect. Hint: check how many places you need to move the decimal point to the right.
Incorrect. Hint: You need to convert from a larger to a smaller unit.
Correct! Since you are converting from a larger to a smaller unit, you need to multiply by 1000 or move the decimal point three places to the right.
Q2- Convert 0.08 mg to mcg:
Incorrect. Hint: check how many places you need to move the decimal point to the right.
Incorrect. Hint: You need to convert from a larger to a smaller unit.
Correct! Since you are converting from a larger to a smaller unit, you need to multiply by 1000 or move the decimal point three places to the right.
Q3- Convert 865 mg to g:
Incorrect. Hint: you are converting from a smaller to a larger unit.
Incorrect. Hint: check how many places you need to move the decimal point to the left.
Correct! Since you are converting from a smaller to a larger unit, you need to divide by 1000 or move the decimal point three places to the left.
Q4- Convert 4000 mL to L:
Incorrect. Hint: you are converting from a smaller to a larger unit.
Incorrect. Hint: check how many places you need to move the decimal point to the left.
Correct! Since you are converting from a smaller to a larger unit, you need to divide by 1000 or move the decimal point three places to the left.
Q5- Convert 0.75 L to mL:
Incorrect. Hint: check how many places you need to move the decimal point to the right.
Incorrect. Hint: You need to convert from a larger to a smaller unit.
Correct! Since you are converting from a larger to a smaller unit, you need to multiply by 1000 or move the decimal point three places to the right.

Time calculations

When working with time,  you will need to be able to convert time into fractions and then decimals. This is needed in order to calculate IVT rates, for example.

First of all, make sure you are familiar with how time is measured and the equivalencies between units of time:

• 60 seconds (sec) = 1 minute (min)
• 60 minutes = 1 hours (hr)
• 24 hours = 1 day
• 7 days = 1 week
• 52 weeks = 1 year

For instance, one hour and fifteen minutes can be expressed as a fraction:

1 ¼

To convert the fraction ¼ into decimals, you will divide the top number by the bottom number in the fraction: ¼= 0.25

Thus, one hour and fifteen minutes can be expressed as 1.25 hr (1+0.25)

If you have to convert minutes into decimals, you will follow a similar procedure:

15 minutes can be expressed as a fraction of an hour: 15/60 mins

If we divide the top number by the bottom number, we obtain 0.25 hr

Remember to always include the unit of time measurement that you are using.

Time calculation

Convert the following into decimals:

Q1- 90 minutes
Correct! 90/60= 1.5 hr
Incorrect. Try again.
Incorrect. Try again.
Q2- Five and three quarters of an hour
Incorrect. Try again.
Correct! Five and a three quarters of an hour = 5 and 3/4 hr. If we divide 3/4, we obtain 0.75. Thus, 5 and 0.75 hr= 5.75 hr
Incorrect. Try again.
Q3- 20 minutes
Incorrect. Try again.
Incorrect. Try again.
Correct! 20/60= 0.33 hr
Q4- 160 minutes
Incorrect. Try again.
Incorrect. Try again.
Correct! 160/60= 2.67 hr

Further resources

There are lots of online and printed resources to help you develop your skills to calculate medication dosages:

Calculating dosages

In this section, you will learn:

• The difference between strength and volume
• How to use proportions with liquid solutions
• How to calculate the dosage required (tablet and volume doses)
• How to calculate dosages by patient weight

Drugs may be administered via several routes. Drugs that are administered orally are usually in tablet, capsule or liquid form. Drugs can also be administered by injection or intravenous infusion. Thus, you will need to be able to calculate dosages for oral and liquid medications.

When using formulas, the most important step is to identify- and understand- what each part of the formula means. Before applying the formula to calculate medication dosages, this module will review important concepts that will help you identify what information you need to look for, and how to use the formula.

How to calculate dosages

Strength and volume

Most drugs are available in a limited number of strengths or concentrations. To calculate medication dosages, you will use the stock required, stock strength and volume as part of the formula. It is important to understand what it is meant by strength and volume, as you will need to check this information about the drug to use it correctly in the formula.

This video shows you the difference between strength and volume. The strength is the amount of drug in units or g, mcg, while the volume is the amount of liquid in which the drug has been diluted:

How to use proportions with liquid solutions

This video is particularly helpful if you need further information on how to read the stock strength and stock volume of medication (that is, the amount of drug and solution available), and how to calculate the volume of solution required.

Formula to calculate dosages

The formula to calculate the required dose includes the stock required (prescribed by the doctor), the stock strength (amount of drug available) and volume (amount of solution available).

Before you apply the formula, take into consideration two key aspects:

• The dose and form in which the drug is available. For example, the drug could be presented in mg/tablet or capsule, or mg diluted in solution (mg/ml). The volume of the drug can be in tablets/capsules or vials (mL).
• Ensure that all dosages are expressed in the same units of measurement (i.e. mgc, mg, g). In some cases, you will need to convert them (see section on units of measurement for further information)

Dose = Stock Required    x    Volume

Strength                       1

In the next section, this formula will be applied to calculate oral (tablets) and volume doses.

Calculating oral doses

To calculate oral doses, the formula can be simplified. The volume is not needed in this case because the drug comes in tablets.

Number of tablets = Dose ordered

Stock Strength

EXAMPLE 1: If the order is 50mg Phenergan, and the stock strength is 25mg tablets, the formula will look like this:

50 mg = 2 tablets

25 mg

EXAMPLE 2: In this example, the order is 0.125 mg Digoxin, and the stock strength is 62.5 mcg tablets.

We first have to ensure that we are using the same units of measurement for stock strength and stock required. In this case, the stock strength is presented in mcg, but the order is in mg. Therefore, you will need to convert the order dose from milligrams (mg) to micrograms (mcg) so that you have the same units:

0.125 mg X 1000 = 125 mcg

If you need to review how to convert units of measurement, see section on units of measurement above.

Once stock strength and dose ordered are expressed in the same units of measurements, the formula can be applied:

Dose = 125 mcg   = 2 tablets

62.5 mcg

Calculate tablet doses

This activity will guide you through the process to calculate tablet doses.

Q1- A patient is prescribed paracetamol 1g, orally. The stock available is 500 mg tablets. Calculate the number of tablets required.
Q1- A patient is prescribed paracetamol 1g, orally. The stock available is 500 mg tablets. Calculate the number of tablets required.
Do you need to convert units of measurement?
Q1- A patient is prescribed paracetamol 1g, orally. The stock available is 500 mg tablets. Calculate the number of tablets required.

Do you need to convert units of measurement?

Yes, in this example the stock available is expressed in mg, and the dose required is expressed in g.

Thus, you need to convert the order dose from g to mg. To convert from larger to smaller units:

1g X 1000= 1000 mg

Q1- A patient is prescribed paracetamol 1g, orally. The stock available is 500 mg tablets. Calculate the number of tablets required.

The dose prescribed is now expressed in mg: 1000 mg.

Applying the formula:

Dose= Dose ordered/ Stock Strength

Dose= 1000/500= 2 tablets

Q2- 25 mg captopril PO is prescribed. How many 50 mg tablets should be given?
Q2- 25 mg captopril PO is prescribed. How many 50 mg tablets should be given?

Do you need to convert units of measurement?

Q2- 25 mg captopril PO is prescribed. How many 50 mg tablets should be given?

Do you need to convert units of measurement?

No, in this example strength and dose required are expressed in mg.

Q2- 25 mg captopril PO is prescribed. How many 50 mg tablets should be given?

Applying the formula:

Dose= Dose ordered/ Stock Strength

Dose= 25/50= 0.5 or 1/2 tablets

Q3- Dixogin 125 micrograms is prescribed. Tablets available are 0.25 mg. How many tablets should be given?
Q3- Dixogin 125 micrograms is prescribed. Tablets available are 0.25 mg.How many tablets should be given?

Do you need to convert units?

Q3- Dixogin 125 micrograms is prescribed. Tablets available are 0.25 mg.How many tablets should be given?

Do you need to convert units?

Yes, in this example dose required is expressed in mcg and strength is expressed in mg.

Thus, you will need to convert from smaller to larger units of measurement:

125 mcg/1000= 0.125 mg

Q3- Dixogin 125 micrograms is prescribed. Tablets available are 0.25 mg.How many tablets should be given?

Dose required is now expressed in mg: 0.125 mg

Applying the formula:

Dose= Dose ordered/ Stock Strength

Dose= 0.125/0.25= 0.5 or 1/2 tablets

Calculating volume doses

The formula will now be applied to calculate volume doses, including the volume of stock solution. If the order is 450mg Amiodarone, and the stock strength is 150mg/3mL suspension, the formula will look like this:

Dose = Stock Required    x    Volume

Stock Strength              1

Dose  = 450 mg   x   3 mL =  9 mL

150mg           1

Remember to include the unit of measurement in the result: mL, as you are using a liquid solution of the drug.

Calculate volume doses

This activity will guide you through the process to calculate volume doses.

Q1. A child is ordered epilim elixir 120 mcg. Stock strength is 0.08 mg/2mL. How much solution should be poured for each dose?
Q1. A child is ordered epilim elixir 120 mcg. Stock strength is 0.08 mg/2mL. How much solution should be poured for each dose?
Do you need to convert units?
Q1. A child is ordered epilim elixir 120 mcg. Stock strength is 0.08 mg/2mL. How much solution should be poured for each dose?

Do you need to convert units?

Yes, in this example the dose required is expressed in mcg, and the stock strength is expressed in mg.

Thus, to convert from smaller to larger units:

120mcg/1000= 0.12 mg

Q1. A child is ordered epilim elixir 120 mcg. Stock strength is 0.08 mg/2mL. How much solution should be poured for each dose?

Dose required is now expressed in mg: 0.12 mg.

Applying the formula:

 Dose = Stock Required x Volume Stock Strength 1

 Dose = 0.12 mg x 2 mL 0.08 mg 1

Q2. A patient is ordered morphine hydrochloride 100 mg. Stock strength is 40 mg/mL. Calculate the volume to be given.
Q2. A patient is ordered morphine hydrochloride 100 mg. Stock strength is 40 mg/mL. Calculate the volume to be given.

Do you need to convert units?

Q2. A patient is ordered morphine hydrochloride 100 mg. Stock strength is 40 mg/mL. Calculate the volume to be given.

Do you need to convert units?

No, in this example stock strength and stock required are expressed in mg.

Q2. A patient is ordered morphine hydrochloride 100 mg. Stock strength is 40 mg/mL. Calculate the volume to be given.

Applying the formula:

 Dose = Stock Required x Volume Stock Strength 1

 Dose = 100 mg x 1 mL = 2.5 mL 40 mg 1

Calculating dosages by patient weight

Drug dosages are often ordered according to the patient’s weight. Therefore, you will need to take into account the weight of the patient when calculating dosages.

How to calculate a single dose based on body weight

In this case, you will need to calculate the size of a single dose based on the recommended dosage (in mg per kg per day) and the patient’s weight.

For example, a child is prescribed paracetamol at a dose of 15 mg/kg/dose, 4 doses daily. If the child’s weight is 28kg, to calculate the size of a single dose:

For each kilo of weight, the child should receive 15 mg of drug. Thus: Dose= 15mg (prescribed dose) x 28 (child’s weight in kg) = 42mg dose required

How to calculate volume doses

To calculate the drug suspension dose, you will use the formula to calculate drug dosages that uses the stock strength, stock required and volume strength.

Following the previous example: paracetamol is ordered for children at a dose of 15mg/kg/dose to a maximum of 4 doses per day. A child’s weight is 28kg, and the stock strength is 24mg/mL.

Stock required= 420 mg (this is the stock required that was calculated in the previous step using the child’s weight)

Dose = Stock Required    x    Volume

Stock Strength              1

Dose = 420 mg  x  1 mL  = 17.5 mL of suspension per dose

24 mg      1

Finally, we know that each dose is 420 mg, and the child can have 4 doses per day.

Therefore: 420 mg X 4 = 1680 mg per day. This is the maximum amount of drug that the child can receive per day.

Calculate dosages by patient weight

This activity will guide you through the process to calculate doses by patient weight.

Q1- A child is prescribed penicillin V. The recommended dosage is 16 mg/kg/day; 4 doses daily. If the child's weight is 18 kg, calculate the size of a single dose.
Q1- A child is prescribed penicillin V. The recommended dosage is 16 mg/kg/day; 4 doses daily. If the child's weight is 18 kg, calculate the size of a single dose.

The child should receive 16 mg/kg/day. First of all, you will calculate total dosage by weight:

16 mg (recommended dosage) x 18 (child's weight in kg)= 288 mg per day

Q1- A child is prescribed penicillin V. The recommended dosage is 16 mg/kg/day; 4 doses daily. If the child's weight is 18 kg, calculate the size of a single dose.

The daily dosage is 288 mg. We know that the child will receive 4 doses daily:

288 mg per day divided by 4 (number of daily doses)= 72 mg per single dose

Q2- A child weighting 24 kgs is ordered Erythromycin 600 mg TDS. Erythromycin is available as a suspension of 100 mg/mL. The recommended dose for children is 60-80 mg/kg/day in three divided doses. What is the maximum safe individual dose for this child?
Q2- A child weighting 24 kgs is ordered Erythromycin 600 mg TDS. Erythromycin is available as a suspension of 100 mg/mL. The recommended dose for children is 60-80 mg/kg/day in three divided doses. What is the maximum safe individual dose for this child?

First, we will calculate the maximum dose per day:

80 mg (maximum recommended dose per day) x 24 (child's weight in kg)= 1920 mg/day. This is the maximum safe dose that the child should receive per day.

Q2- A child weighting 24 kgs is ordered Erythromycin 600 mg TDS. Erythromycin is available as a suspension of 100 mg/mL. The recommended dose for children is 60-80 mg/kg/day in three divided doses. What is the maximum safe individual dose for this child?

We have calculated that the maximum dose per day is 1920 mg. To calculate the maximum safe individual dose:

1920 mg divided by 3 (number of daily doses)= 640 mg per maximum individual dose

Intravenous fluid calculations

Fluid calculation in mL/hr

In Intravenous Therapy, you will need to calculate the fluid rate for infusion in mL/hr. You will need to take into account the time (in hours) to set the intravenous pump. The formula to calculate the fluid rate is:

Note: The volume must be in millilitres (mL).

Example 1:

If an anaesthetist orders N/Saline 1 L to run over 8 hours, the formula will look like this:

1000 mL = 125 mL/hr. Therefore, you will set the intravenous rate at 125 mL/hr

8 hrs

Note that we converted 1 L into 1000 mL as we need to use the volume ordered in mL

Note that if the time is given in minutes, you will need to convert minutes into hours to use this information in the formula. If you need more information about converting units of time, check the Time Calculations section. Alternatively, you can use this formula:

Rate (mL/hr) = Volume (mL) x60

Time (in mins)

Example 2:

75 mL of fluid needs to be infused over 20 minutes:

Rate (mL/hr) = Volume (mL) x60

Time (in mins)

= 75 mL x 60  = 225 mL/hr

20 min

Fluid calculation in drop rate

To calculate fluid drops per minute, you will use the same elements as in the previous formula, but you will have to also include the drop factor (assume a drop factor of 20 unless otherwise stated).

Note: We divide by 60 to convert the drop rate to minutes

Example:

If an anesthetist orders N/Saline 1L to run over 6 hours, the formula will look like this:

1000 mL  X    20   = 55.6 dpm (that is, 56 drops each minute if you round up)

6                 60

If the time is given in minutes, you can use this formula:

Example:

If a patient is to have 300 mL of dextrose 5% run through in 50 minutes:

300 mL x 20 (drop factor)   = 6000      =  120 drops/min

50 minutes                            50

Calculate fluid rates in mL/hr and drop rates

This activity will guide you through the process to calculate fluid rates in mL/hr and drop rates

Q1. 500 mg of drug X is to be administered in 120 mL of Normal Saline over 90 minutes. At how many mL/hour should the pump be set?
Q1. 500 mg of drug X is to be administered in 120 mL of Normal Saline over 90 minutes. At how many mL/hour should the pump be set?

The time is given in minutes. In this example, we will convert minutes into hours:

90 minutes = 90/60 = 1.5 hrs

Q1. 500 mg of drug X is to be administered in 120 mL of Normal Saline over 90 minutes. At how many mL/hour should the pump be set?

Using the formula:

 Total volume ordered (in mL) = fluid in mL/hr Time (in hours)

120 mL/1.5 hr = 80 mL/hr

Q2. 0.5 litre of dextrose 4% in 1/5 normal saline is to run over 12 hours. The administration set delivers 20 drops/mL. Calculate the required drip rate in drops per minute.
Q2. 0.5 litre of dextrose 4% in 1/5 normal saline is to run over 12 hours. The administration set delivers 20 drops/mL. Calculate the required drip rate in drops per minute.

The formula to use is:

 Total volume ordered (in mL) x drop factor = drops per minute (dpm) Time (in hours) 60

Since we have to use mL, we will convert 0.5 litre to mL:

0.5 L x 1000 = 500 mL

Q2. 0.5 litre of dextrose 4% in 1/5 normal saline is to run over 12 hours. The administration set delivers 20 drops/mL. Calculate the required drip rate in drops per minute.

You need to administer 500 mL of the drug:

 Total volume ordered (in mL) x drop factor = drops per minute (dpm) Time (in hours) 60

500 mL/12hrs x 20/60 = 41.66 X 0.33 = 13.88 = 14 drops per minute