Pharmaceutical calculations

The nine calculations worth being fast at

Calculation marks are the most reliable in the degree: the method never changes, only the numbers. These are the nine that recur, each with the formula and one worked example.

Every answer below is rounded only at the final step. Rounding part-way through is the single most common way to lose these marks.

1. Concentration as percentage

Three different percentages, and the exam will not tell you which it means — the units do.

Notation	Means	Example
% w/v	g of solute in 100 mL of product	5% w/v = 5 g in 100 mL
% w/w	g of solute in 100 g of product	1% w/w cream = 1 g in 100 g
% v/v	mL of liquid in 100 mL of product	70% v/v alcohol

Worked example

How much sodium chloride is in 250 mL of 0.9% w/v saline?

0.9% w/v means 0.9 g in 100 mL.
250 mL is 2.5 × 100 mL.
0.9 × 2.5 = 2.25 g

2. Molarity

moles = mass (g) ÷ molar mass (g/mol) molarity (mol/L) = moles ÷ volume (L)

Worked example

What is the molarity of 0.9% w/v sodium chloride? (M_r NaCl = 58.44)

0.9% w/v = 9 g/L.
moles = 9 ÷ 58.44 = 0.154 mol.
In 1 L, so molarity = 0.154 mol/L — which is why saline is called 154 mmol/L.

3. Dilutions

C₁V₁ = C₂V₂

Works with any consistent concentration unit. The trap is being asked for the diluent volume rather than the final volume.

Worked example

How much water must be added to 50 mL of 20% w/v to make 5% w/v?

C₁V₁ = C₂V₂ → 20 × 50 = 5 × V₂
V₂ = 1000 ÷ 5 = 200 mL final volume.
Water to add = 200 − 50 = 150 mL

4. Parts and ratio strengths

A 1 in 1000 solution is 1 g in 1000 mL, which is 0.1% w/v. Adrenaline is the example everyone is expected to know.

Ratio	% w/v	mg/mL
1 in 1000	0.1%	1 mg/mL
1 in 10 000	0.01%	0.1 mg/mL
1 in 200	0.5%	5 mg/mL

5. Doses by body weight

dose = dose per kg × weight (kg) volume = dose ÷ concentration

Worked example

A child weighing 18 kg needs paracetamol 15 mg/kg. The suspension is 120 mg/5 mL. What volume?

Dose = 15 × 18 = 270 mg.
Concentration = 120 ÷ 5 = 24 mg/mL.
Volume = 270 ÷ 24 = 11.25 mL, measured as 11.25 mL.

6. Body surface area dosing

Used for cytotoxics. The Mosteller formula is the one to memorise.

BSA (m²) = √( height (cm) × weight (kg) ÷ 3600 )

Worked example

170 cm, 70 kg, dose 375 mg/m².

BSA = √(170 × 70 ÷ 3600) = √3.306 = 1.818 m².
Dose = 375 × 1.818 = 682 mg

7. Infusion rates

rate (mL/h) = volume (mL) ÷ time (h) drops/min = (volume × drop factor) ÷ (time in minutes)

Standard giving sets are 20 drops/mL for clear fluids and 15 drops/mL for blood.

Worked example

1 L of sodium chloride 0.9% over 8 hours, giving set 20 drops/mL.

Rate = 1000 ÷ 8 = 125 mL/h.
Per minute = 125 ÷ 60 = 2.083 mL/min.
Drops/min = 2.083 × 20 = 42 drops/min

8. Dose-rate infusions

rate (mL/h) = (dose µg/kg/min × weight kg × 60) ÷ concentration µg/mL

Worked example

Dopamine 5 µg/kg/min for a 70 kg patient. Bag is 800 mg in 500 mL.

Concentration = 800 mg ÷ 500 mL = 1.6 mg/mL = 1600 µg/mL.
Dose per minute = 5 × 70 = 350 µg/min.
Per hour = 350 × 60 = 21 000 µg/h.
Rate = 21 000 ÷ 1600 = 13.1 mL/h

9. Loading and maintenance doses

loading dose = (V_d × target concentration) ÷ bioavailability maintenance dose rate = (target concentration × clearance) ÷ bioavailability

Worked example

Theophylline, V_d 0.5 L/kg, 70 kg patient, target 15 mg/L, given intravenously (F = 1).

V_d = 0.5 × 70 = 35 L.
Loading dose = 35 × 15 = 525 mg

Units worth never confusing

From	To	Multiply by
g	mg	1000
mg	µg	1000
L	mL	1000
mmol	µmol	1000

In an exam, write the units on every line. Most lost calculation marks are unit errors, not arithmetic errors.

← Back to the overview