Calculation of Dosages
12 minute read
What you will learn
- Calculate the quantity of a medicine to supply for a given course
- Work out the volume or number of tablets that gives a required dose
- Use approximate and exact equivalents correctly
- Estimate children's doses using the common rules and weight-based dosing
- Solve miscellaneous dosage problems
Key points
- Total quantity = amount per dose × doses per day × number of days.
- Volume to give = (dose wanted ÷ amount of drug in the stock volume) × the stock volume.
- Number of tablets = dose wanted ÷ strength of one tablet.
- Use the exact equivalent when preparing or dispensing quantities. Approximate equivalents are for converting doses.
- Young's rule uses age, Clark's rule uses weight, Fried's rule is for infants, and body surface area is the most reliable of the rules.
- Dosing by milligrams per kilogram is the safest method for children. Always confirm a child's dose with the pharmacist.
- All the doses in this lesson are for practising arithmetic. They are not dosing advice.
A note before you start
The doses used in this lesson are made-up numbers for practising arithmetic. Real doses come from the prescriber and from approved references. Always confirm a dose with the pharmacist.
Dose terms
| Term | Meaning |
|---|---|
| Single dose | The amount taken at one time |
| Daily dose | The total amount taken in 24 hours |
| Total dose | The total for the whole course |
| Frequency | How often it is taken |
| Abbreviation | Meaning | Doses per day |
|---|---|---|
| od | once daily | 1 |
| bd | twice daily | 2 |
| tds | three times daily | 3 |
| qds | four times daily | 4 |
Quantity to supply
total quantity = amount per dose × doses per day × number of days
Example 1. Paracetamol 120 mg/5 mL, 10 mL qds for 3 days.
- 10 mL × 4 × 3 = 120 mL
Example 2. A tablet, one three times a day for 7 days.
- 1 × 3 × 7 = 21 tablets
How long does a supply last?
days = total quantity ÷ quantity used per day
- A 100 mL bottle at 5 mL twice a day: 5 × 2 = 10 mL a day, and 100 ÷ 10 = 10 days.
- A 150 mL bottle at 10 mL three times a day: 10 × 3 = 30 mL a day, and 150 ÷ 30 = 5 days.
- Number of 5 mL doses in a 150 mL bottle: 150 ÷ 5 = 30 doses.
Divided doses
The daily dose is 30 mg per kg, in 3 divided doses. The child weighs 20 kg.
- Daily dose = 30 × 20 = 600 mg
- Each dose = 600 ÷ 3 = 200 mg
Using the stock strength
Tablets and capsules
number of tablets = dose wanted ÷ strength of one tablet
The dose is 750 mg and the tablets are 250 mg. 750 ÷ 250 = 3 tablets.
Liquids
volume to give = (dose wanted ÷ drug in stock volume) × stock volume
Example 1. The dose is 250 mg. The stock suspension is 125 mg in 5 mL.
- (250 ÷ 125) × 5 = 2 × 5 = 10 mL
Example 2. The dose is 90 mg. The stock is 120 mg in 5 mL.
- (90 ÷ 120) × 5 = 0.75 × 5 = 3.75 mL
Round to a volume your oral syringe can measure, such as 3.8 mL, and check it with the pharmacist.
Example 3: drug in each dose from the total. A mixture contains 600 mg in 120 mL. How much is in each 5 mL dose?
- Strength = 600 ÷ 120 = 5 mg per mL
- 5 mL dose = 5 × 5 = 25 mg
Approximate and exact equivalents
| Item | Exact | Approximate |
|---|---|---|
| 1 grain | 64.8 mg | 65 mg |
| 1 minim | 0.0592 mL | 0.06 mL |
| 1 teaspoonful | 5 mL | |
| 1 kilogram | 2.205 lb | 2.2 lb |
- Use approximate equivalents for converting a dose written in older units into the metric dose that is actually given. A dose of 5 grains is taken as 325 mg (5 × 65).
- Use exact equivalents when you are calculating quantities to prepare or dispense. The exact value for 5 grains is 5 × 64.8 = 324 mg.
Children's doses
A child is not a small adult. Children differ in weight, in how their bodies handle medicines, and in how quickly they grow, so a dose is chosen carefully.
The safest method is to use a dose written per kilogram of body weight, or a dose banded by age or weight from an approved children's reference. The rules below give an estimate only. Use them when a weight-based dose is not available, and always have the result checked.
| Rule | Formula | For |
|---|---|---|
| Young's rule | age (years) ÷ (age + 12) × adult dose | Children 1 to 12 years |
| Clark's rule | weight (kg) ÷ 70 × adult dose | Children, by weight |
| Fried's rule | age (months) ÷ 150 × adult dose | Infants under 1 year |
| Body surface area | child's BSA (m²) ÷ 1.73 × adult dose | Most reliable of the rules |
Young's rule. Adult dose 500 mg. Child aged 4 years.
- 4 ÷ (4 + 12) = 4 ÷ 16 = 1/4
- 1/4 × 500 = 125 mg
Clark's rule. Adult dose 300 mg. Child weighs 21 kg.
- 21 ÷ 70 = 0.3
- 0.3 × 300 = 90 mg
Fried's rule. Adult dose 150 mg. Infant aged 10 months.
- 10 ÷ 150 × 150 = 10 mg
Body surface area. Adult dose 100 mg. Child's surface area 0.80 m².
- 0.80 ÷ 1.73 = 0.4624
- 0.4624 × 100 = 46.2 mg, which rounds to 46 mg
Dose per kilogram. The prescribed dose is 15 mg per kg. The child weighs 12 kg. The suspension is 120 mg in 5 mL.
- Dose = 15 × 12 = 180 mg
- Volume = (180 ÷ 120) × 5 = 1.5 × 5 = 7.5 mL
Miscellaneous dosage problems
How many tablets for a course? One tablet three times a day for 5 days. 1 × 3 × 5 = 15 tablets.
Working back from a total. You have 60 mL of a mixture and the dose is 10 mL three times a day. How many days will it last? 10 × 3 = 30 mL a day, and 60 ÷ 30 = 2 days.
Check every answer by estimating first, and make sure it is a volume or number of tablets that the patient can actually measure and take.
Exam focus
- Quantity to dispense: dose × frequency × days. Make sure you know od, bd, tds and qds.
- Stock strength problems: 'How many mL of a 125 mg/5 mL suspension give a 250 mg dose?'
- Children's dose rules: write the formula, put the numbers in, and show the working.
- Common mistake: using the adult formula for a child when a weight-based dose is available.
- Common mistake: forgetting that tds means 3 doses a day and qds means 4.
Quick check
Test yourself before you move on. Pick an answer to see the explanation.
1.A dose of 250 mg is needed. The stock suspension contains 125 mg in 5 mL. What volume is given?
2.The adult dose is 500 mg. Using Young's rule, what is the dose for a child of 4 years?
3.A 100 mL bottle of medicine is given at 5 mL twice a day. How long does it last?
4.The dose is 15 mg per kg. What is the dose for a child of 12 kg?
5.A mixture contains 600 mg of drug in 120 mL. How much drug is in each 5 mL dose?