Common Registration Assessment, Part 1
Elimination rate constant and half-life
Use supplied equations to calculate rate constants and half-lives without logarithms or a scientific calculator.
Published 7 October 2026. Independent revision material, not GPhC questions, not for patient care.
The elimination rate constant k links clearance to apparent volume of distribution: k = Cl ÷ V. In the first-order model, half-life = 0.693 ÷ k. The number 0.693 is supplied here, so you can use an ordinary calculator.
Keep clearance and volume in matching units. A clearance of 120 mL/min is not 120 L/hour. Read the requested time unit before calculating. These answers describe a simplified model, not how to choose a dosing interval for a real patient.
The method
- Write the supplied equation and identify the missing term.
- Convert clearance to the same volume unit as V.
- Calculate k, retaining enough digits for the next step.
- Divide 0.693 by k if half-life is requested.
- State the time unit and round at the end.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
Use k = Cl ÷ V and half-life = 0.693 ÷ k. Cl = 6 L/hour and V = 30 L. Calculate half-life to 2 decimal places.
Show the answer
Answer: 3.47 hours
Working: k = 6 ÷ 30 = 0.2 per hour. Half-life = 0.693 ÷ 0.2 = 3.465 hours, rounded to 3.47 hours.
Question 2
Cl = 100 mL/min and V = 24 L. Calculate k in units per hour.
Show the answer
Answer: 0.25 per hour
Working: 100 mL/min = 0.1 L/min = 6 L/hour. k = 6 ÷ 24 = 0.25 per hour.
Question 3
Use V = Cl × half-life ÷ 0.693. Cl is 3 L/hour and half-life is 6.93 hours. Find V.
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Answer: 30 L
Working: V = 3 × 6.93 ÷ 0.693 = 30 L.
A direction check
With V fixed, increasing clearance increases k and shortens half-life. With clearance fixed, increasing V lengthens half-life. If your result moves in the opposite direction, inspect the division and units.
Where marks are lost
- Using mL/min against a volume in litres.
- Rounding k too early.
- Giving a half-life with no time unit.
Frequently asked questions
Do I need logarithms for these questions?
No. These exercises supply equations using 0.693. Follow the ordinary calculator operations shown.
What does per hour mean?
It is the unit of the rate constant, often written h⁻¹. It is not a volume or a dose.
Sources
- The Pharmaceutical Journal, back to basics: pharmacokinetics
- The Pharmaceutical Journal, using provided formula
- GPhC, 2026 assessment specification and permitted items
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
- 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
See also the formula sheet, the eight sample questions and the approved calculator page.