Common Registration Assessment, Part 1
Clearance from half-life and volume of distribution
Three original questions linking half-life, volume and clearance, with the working shown and the usual traps pointed out.
Published 4 October 2026. Independent revision material, not GPhC questions, not for patient care.
For a drug with first-order elimination, clearance is the elimination rate constant multiplied by the volume of distribution: CL = k × Vd, where k = 0.693 ÷ half-life.
The exam moves in both directions: given half-life and volume to find clearance, or given clearance and volume to find half-life. Keep every unit in hours and litres until you convert at the end.
The method
- Write k = 0.693 ÷ t½ with the half-life in hours.
- Multiply k by the volume of distribution in litres to get clearance in L/h.
- If the volume is quoted per kg, multiply by the weight first.
- Convert L/h to mL/min only if the question asks for it: × 1,000 ÷ 60.
- For the reverse, k = CL ÷ Vd, then t½ = 0.693 ÷ k.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
Drug X has a half-life of 8 hours and a volume of distribution of 50 L. What is its clearance in L/h to two decimal places?
Show the answer
Answer: 4.33 L/h
Working: k = 0.693 ÷ 8 = 0.0866 per hour. CL = 0.0866 × 50 = 4.33 L/h.
Question 2
Drug Y has a half-life of 6 hours and a volume of distribution of 0.7 L/kg. For a 70 kg patient, what is the clearance in mL/min to the nearest whole number?
Show the answer
Answer: 94 mL/min
Working: Vd = 0.7 × 70 = 49 L. k = 0.693 ÷ 6 = 0.1155 per hour. CL = 0.1155 × 49 = 5.66 L/h. 5.66 × 1,000 ÷ 60 = 94 mL/min.
Question 3
Drug Z has a clearance of 6 L/h and a volume of distribution of 40 L. What is its half-life to one decimal place?
Show the answer
Answer: 4.6 hours
Working: k = CL ÷ Vd = 6 ÷ 40 = 0.15 per hour. t½ = 0.693 ÷ 0.15 = 4.62 hours, which rounds to 4.6 hours.
How this is examined
Questions often hide the volume behind a per-kg figure and a body weight. Resolve the actual volume in litres before applying CL = k × Vd.
Where marks are lost
- Using 0.7 instead of 0.693 for ln 2.
- Multiplying clearance by volume when the question asks for the rate constant: k = CL ÷ Vd.
- Converting to mL/min too early and carrying rounded figures through the rest of the working.
Frequently asked questions
Where does 0.693 come from?
It is the natural logarithm of 2. For first-order elimination the rate constant is ln 2 divided by the half-life.
Does clearance change with dose?
For first-order drugs clearance is constant regardless of dose or concentration, which is why the same value of k applies at every point in the decay.
Sources
- BNF, guidance on prescribing
- GPhC, Common Registration Assessment specification and permitted items for 2026
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Direct proportion and cross-multiplication
- Scientific notation and very small quantities
- Stock use and reorder quantities
- Parts per million and very dilute solutions
- Sodium chloride equivalents and isotonic solutions
- Density and specific gravity conversions
- Doses per day and hours between doses
- Finding the volume of diluent to add
- Capping a dose at a stated maximum
- Whole vials and ampoules to draw up
- Reading values from a provided graph
- Micrograms per kg per minute infusions
- Percentage composition of a compound preparation
- Suppository displacement values
- Isotonicity by freezing point depression
- Energy content of parenteral nutrition
- Syringe driver rate calculations
- Area under the curve calculations
- Renal dose adjustments using provided bands
- Insulin units and infusion calculations
- Working backwards from a stated dose
- Doses and days from multi-dose devices
- Combined additives in one infusion
- BMI calculations for the GPhC assessment
- Fewest tablets to make a dose
- Maintenance fluid requirements by weight
- Sodium load from effervescent tablets
- Ethanol content of liquid preparations
- Oxygen cylinder duration calculations
- Urine output and fluid balance calculations
- Quantities for titration packs
- Infusion line priming and dead space
See also the formula sheet, the eight sample questions and the approved calculator page.