Drug Half-Life and Steady State Calculator
Drug Half-Life and Steady State Calculator
Calculate a drug's elimination half-life from two timed levels, and the time to reach steady state on the current regimen.
Drug Half-Life and Steady State
Half-life & steady stateFirst level 12.0, second level 3.0, 8 hours apart
Formula
- C1, C2
- two levels of the same drug, in the same units, with C1 the earlier sample
- hours
- time between the two samples
- 5 half-lives
- the point at which about 97% of the eventual steady-state concentration has accumulated
Worked example
First level 12.0, second level 3.0, 8 hours apart
ke = ln(12.0 ÷ 3.0) ÷ 8 = ln(4) ÷ 8 = 1.386 ÷ 8 = 0.173 per hour
half-life = 0.693 ÷ 0.173 = 4.0 hours
time to steady state = 4.0 × 5 = 20.0 hours
Accumulation toward steady state
| Half-lives elapsed | Fraction of steady-state concentration reached |
|---|---|
| 1 | 50% |
| 2 | 75% |
| 3 | 87.5% |
| 4 | 94% |
| 5 | 97% |
Why timing a level against steady state matters
Steady state is reached, for practical purposes, after about five half-lives of a fixed dosing regimen, at which point roughly 97% of the eventual concentration has accumulated. This holds regardless of the drug, the dose or the route, because it follows from the same exponential accumulation curve — each additional half-life closes half the remaining gap to steady state, so the fraction reached climbs from 50% after one half-life to 75%, 87.5%, 94% and 97% after two, three, four and five.
THE PRACTICAL CONSEQUENCE: a level drawn before steady state underestimates the eventual concentration on the current dose. Reading it as if it were the steady-state level and increasing the dose in response is a common and avoidable error — the level will keep climbing on the original dose alone, and the increase compounds on top of a rise that was already coming. The same arithmetic works in reverse for washout: after stopping a drug, about 97% of it has left the body once five half-lives have passed.
In the worked example, two levels eight hours apart give a calculated half-life of 4.0 hours, so steady state on the current regimen is reached at roughly 20 hours — just under a day. Reporting the half-life itself alongside the steady-state time is useful, because it lets the same figure be reused to judge how long any future dose change will take to fully express itself, and to plan the timing of the next level.
Frequently asked questions
How long does it take to reach steady state?
About five half-lives, at which point roughly 97% of the eventual concentration has accumulated. This is true for any drug given as a fixed regimen.
What happens if a level is drawn before steady state?
It underestimates the eventual concentration on the current dose. Increasing the dose in response to an apparently low early level is a common error, because the level would have kept rising anyway.
Does the same rule apply to stopping a drug?
Yes — washout follows the same curve in reverse. About 97% of the drug has been eliminated once five half-lives have passed since the last dose.
How is half-life calculated from two levels?
Take the natural log of the ratio of the two concentrations, divide by the time between them to get the elimination rate constant ke, then divide 0.693 by ke.
Related calculators
References
- Rowland M, Tozer TN. Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications, 4th ed. Lippincott Williams & Wilkins.
- Winter ME. Basic Clinical Pharmacokinetics, 6th ed. Lippincott Williams & Wilkins.