Common Registration Assessment, Part 1
Accumulation towards steady state
Calculate the fraction of steady state reached after whole half-lives in a simple constant-infusion model.
Published 7 October 2026. Independent revision material, not GPhC questions, not for patient care.
For a constant infusion started with no drug present, a first-order model approaches steady state in stages. After one half-life, it has reached 50% of its eventual concentration; after two, 75%; after three, 87.5%. Each stage closes half the remaining gap.
The fraction reached after n whole half-lives is 1 − (0.5)^n. You do not need an exponent key: halve the remaining gap once for each stage. This model assumes constant input and unchanged clearance. A loading dose or non-linear kinetics changes the picture.
The method
- Divide elapsed time by half-life to find the number of stages.
- Start with a gap of 100% to steady state.
- Halve the gap for each whole half-life.
- Subtract the remaining gap from 100%.
- Multiply the fraction reached by the eventual concentration if requested.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
A constant infusion starts with no drug present. Half-life is 4 hours. What percentage of steady state has been reached after 12 hours in the stated model?
Show the answer
Answer: 87.5%
Working: 12 ÷ 4 = 3 half-lives. Remaining gap: 100%, 50%, 25%, 12.5%. Fraction reached = 100 − 12.5 = 87.5%.
Question 2
The eventual steady-state concentration is 16 mg/L. Half-life is 6 hours and the infusion starts with no drug present. What concentration is predicted at 12 hours?
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Answer: 12 mg/L
Working: 12 ÷ 6 = 2 half-lives. Fraction reached = 75% = 0.75. Concentration = 16 × 0.75 = 12 mg/L.
Question 3
In the same model, half-life is 5 hours. After how many hours is 96.875% of steady state reached?
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Answer: 25 hours
Working: Fractions reached are 50%, 75%, 87.5%, 93.75% and 96.875% after 1, 2, 3, 4 and 5 half-lives. Time = 5 × 5 = 25 hours.
Two different half-life questions
After two half-lives, a single amount undergoing elimination has 25% remaining. A constant infusion approaching steady state from zero has reached 75%. Read whether drug is being removed, added, or both.
Where marks are lost
- Using the fraction remaining rather than the fraction accumulated.
- Calling five half-lives exactly 100%.
- Applying this no-loading-dose model after a loading dose.
Frequently asked questions
Is steady state reached exactly after five half-lives?
Not exactly in this model. Five half-lives gives 96.875%, close to the eventual value.
Can I use this table for a changing infusion rate?
Not without a model accounting for the change. These exercises keep the rate constant.
Sources
- The Pharmaceutical Journal, back to basics: pharmacokinetics
- 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
- Elimination rate constant and half-life
- 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.