Pharmacokinetics
Drug Half-Life Calculator (Multiple Dose)
For a repeated dosing regimen, works out the elimination rate constant, how much the drug accumulates and how long it takes to reach steady state.
Time to steady state
Enter the half-life and the dose, then pick the dosing interval.
Inputs
From the drug monograph, e.g. 1–2 h for penicillins, 36 h for digoxin.
The amount given at every dose.
Time between doses.
Sets the length of the regimen and of the chart.
Try an example drug
Half-life interpretation guide
| Half-life range | Classification | Typical dosing |
|---|---|---|
| < 4 hours | Short | Multiple daily doses |
| 4-24 hours | Medium | Once or twice daily |
| 24-48 hours | Long | Once daily |
| > 48 hours | Very Long | Loading dose required |
kₑ = 0.693 / t½
Accumulation = 1 / (1 − e^(−kₑ × τ))
Steady State ≈ 4.32 × t½
Peak = Dose / (1 − e^(−kₑτ)) Trough = Dose × e^(−kₑτ) / (1 − e^(−kₑτ))
kₑ is the elimination rate constant (h⁻¹) and τ the dosing interval (h). kₑ is rounded to four decimal places before the other figures are worked out. The accumulation ratio is how many times higher a steady-state peak is than the peak after the first dose.
After 4.32 half-lives the drug is at about 95% of its steady-state level (1 − 0.5^4.32 ≈ 0.95). Peak and trough are amounts in the body; divide them by the volume of distribution to get concentrations.
Keep learning
References
- Rowland and Tozer's Clinical Pharmacokinetics and Pharmacodynamics: Concepts and Applications. 5th ed. Philadelphia: Wolters Kluwer; 2019.
- Ducharme MP, Shargel L, editors. Shargel and Yu's Applied Biopharmaceutics & Pharmacokinetics. 8th ed. New York: McGraw Hill; 2022.
Common questions
No. Time to steady state depends only on the half-life. A shorter interval makes the plateau higher and flatter (larger accumulation ratio, smaller swing between peak and trough), but it still takes about 4–5 half-lives to get there.
The accumulation ratio, peak and trough describe the eventual steady state, which does not depend on how many doses are given. The number of doses only sets how much of the build-up the chart shows.
When the half-life is long, reaching steady state by repeated dosing takes too long — digoxin (t½ ≈ 36 h) would take about a week. A loading dose reaches the target level at once, and maintenance doses then keep it there.
Almost nothing is left from one dose when the next is given, so the drug does not build up — each dose behaves like the first. That happens when the interval is many half-lives long, as with aspirin every 4 hours.
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