16.1 Dosage Calculations

15.1 Dosage Calculations

Quick Answer: Dosage calculations convert a prescribed amount into a safe, measurable quantity for supply or administration. Master mass unit conversions (g ↔ mg ↔ micrograms), mg/kg body-weight dosing, liquid volume from concentration, day supply from directions, and basic infusion rates. On the APC Intern Written Examination, many calculation items are fill-in-the-blank (FIB)—you type a number, not pick a letter—so accuracy, SI units, and decimal discipline matter as much as knowing the formula.

Pharmaceutical calculations sit under Standard 3.4 (compound medicines) but appear whenever you check a prescription, prepare a dose, or counsel on how long a pack will last. Errors of a factor of ten (especially mg ↔ micrograms) are classic exam and practice traps.

Fill-in-the-blank exam technique (APC)

Unlike four-option MCQs, FIB calculation stems require a numeric entry. Practise as if every worked example below were blank:

1. Read the unit demanded in the stem (mg, mL, days, mg/h). Enter only the number the system expects—do not type “mg” unless instructed.
2. Respect decimal places. If the arithmetic yields a whole number (for example 270 mg), enter 270 not 270.0 unless the stem specifies format. If it yields 2.5 mL, enter 2.5 (leading zero before a decimal is good professional habit when writing; follow on-screen format rules in the centre).
3. Use SI consistently. Australian pharmacy uses milligrams, micrograms, millilitres, kilograms. Convert imperial or mixed units before calculating.
4. Show yourself the chain on scrap paper: write every conversion step so a missed ×1000 is visible.
5. Sanity-check magnitude. A paediatric amoxicillin dose of 27 000 mg is almost certainly a unit error; an adult tablet day-supply of 400 days for a 28-tablet pack is wrong.
6. Do not round mid-chain unless the stem or monographic practice requires it; round only the final answer to a clinically sensible precision (often nearest whole mg for solid doses, one decimal place for small liquid volumes when that is exact).

This study guide uses multiple-choice quizzes for self-check, but every worked example is written so you can cover the final number and re-derive it as if FIB.

Mass unit conversions (g ↔ mg ↔ micrograms)

Memorise and apply in one-thousand steps:

Worked example A — conversion chain

A label states 0.25 g. Express as mg and micrograms.

• 0.25 g × 1000 = 250 mg
• 250 mg × 1000 = 250 000 micrograms

Worked example B — microgram trap

Levothyroxine 100 micrograms is 0.1 mg, not 100 mg. Converting the wrong way multiplies risk of severe toxicity. Always write the unit beside each number on scrap paper.

Common unit traps

• Confusing micrograms with mg (factor of 1000)
• Reading 0.5 g as 0.5 mg
• Treating % or ratio strengths as mass doses without converting to mg first (see Section 16.2)
• Paediatric mg/kg applied to weight in grams instead of kilograms

Body-weight dosing (mg/kg)

$\text{Dose (mg)} = \text{Dose (mg/kg)} \times \text{Weight (kg)}$

If the regimen is mg/kg/day divided into several doses, calculate the daily total first, then divide by the number of doses—unless the stem already states mg/kg per dose.

Worked example C — single mg/kg dose

Child weight 18 kg. Amoxicillin 15 mg/kg/dose.

• Dose = 15 × 18 = 270 mg per dose

FIB entry: 270 (if asked in mg).

Worked example D — daily total then divided

Weight 20 kg. Dose 40 mg/kg/day in two divided doses.

• Daily total = 40 × 20 = 800 mg/day
• Per dose = 800 ÷ 2 = 400 mg

Always check whether a maximum dose applies (for example adult ceiling or monograph max mg/day). Weight-based arithmetic never overrides a stated maximum.

Body surface area (BSA) — high-level awareness

Some oncology and specialist paediatric regimens use mg/m² based on BSA rather than mg/kg. Intern Written level expects awareness: BSA dosing is specialised, requires a validated BSA value, and is not something you invent from height/weight without a reference method. If a stem gives BSA already (for example 1.2 m²) and a dose in mg/m², multiply:

• Dose = mg/m² × BSA (m²)

Example: 50 mg/m² × 1.2 m² = 60 mg. Do not confuse m² with kg.

Paediatric and adult liquid volumes from concentration

Labels often state mg per 5 mL (or mg/mL). Convert to a usable ratio:

$\text{Volume (mL)} = \frac{\text{Required dose (mg)}}{\text{Concentration (mg/mL)}}$

If labelled 125 mg/5 mL, concentration = 125 ÷ 5 = 25 mg/mL.

Worked example E — volume from mg/5 mL

Suspension 125 mg/5 mL. Required dose 250 mg.

• Method 1: 250 mg needs twice 125 mg → twice 5 mL = 10 mL
• Method 2: 25 mg/mL → 250 ÷ 25 = 10 mL

Worked example F — smaller dose

Same suspension 125 mg/5 mL. Required dose 62.5 mg.

• 62.5 is half of 125 → half of 5 mL = 2.5 mL

FIB: 2.5 (mL).

Worked example G — concentration given as mg/mL

Injection 10 mg/mL. Dose 35 mg.

• Volume = 35 ÷ 10 = 3.5 mL

Day supply from directions

$\text{Days' supply} = \frac{\text{Quantity of dose units supplied}}{\text{Number of dose units taken per day}}$

Read directions carefully: BD = 2/day, TDS = 3/day, QID = 4/day, mane = once daily morning, 1–2 QID requires a stated assumption (often maximum or prescribed exact dose).

Worked example H — solid oral

Supply 28 tablets, directions 1 tablet BD.

• Doses per day = 2 tablets
• Days = 28 ÷ 2 = 14 days

Worked example I — incomplete day

Supply 50 tablets, directions 1 TDS (3/day).

• 50 ÷ 3 = 16.666… → 16 full days with 2 tablets remaining (not a 17th full day)

Exam stems usually want the integer days the pack lasts at the stated rate, or the exact quotient if they ask how many days until empty—read the wording. If they ask how many days’ full dosing, use the integer full days; if they ask duration until quantity is exhausted, 50/3 may be expressed as a mixed number—APC FIB items typically seek a clear numeric convention stated in the stem.

Worked example J — liquid day supply

Bottle 100 mL, dose 5 mL TDS.

• Daily volume = 5 × 3 = 15 mL/day
• Days = 100 ÷ 15 ≈ 6.67 → 6 full days at full TDS (with 10 mL left), or 6.7 days if the stem wants one decimal—follow the question.

Continuous infusion rates (high-level)

When a volume is infused over a stated time:

$\text{Rate (mL/h)} = \frac{\text{Total volume (mL)}}{\text{Time (h)}}$

Worked example K

1000 mL over 8 hours → 1000 ÷ 8 = 125 mL/h.

If dose is in mg/h and concentration is known:

• Rate (mL/h) = dose (mg/h) ÷ concentration (mg/mL)

Example: need 4 mg/h, solution 2 mg/mL → 2 mL/h.

Intern level expects clean arithmetic and unit consistency, not advanced ICU pump programming detail.

Putting dosage calculations together

A typical multi-step stem: Child 16 kg; dose 7.5 mg/kg; suspension 50 mg/5 mL; what volume per dose?

1. Dose mg = 7.5 × 16 = 120 mg
2. Concentration = 50/5 = 10 mg/mL
3. Volume = 120 ÷ 10 = 12 mL

FIB answer: 12 (mL).

Always: convert units → calculate dose mass → convert to measurable volume or count → check against max dose and clinical sense. Dosage calculations are Standard 3.4 numeracy applied to safe supply—the same care you use at the bench and the counselling counter.