Accumulation & Steady-State Helper
Calculate first-order accumulation factor and steady-state milestones from half-life and dosing interval.
Accumulation & steady-state results
Enter half-life and dosing interval in the same time unit.
Theoretical values assume linear, time-invariant one-compartment first-order elimination, identical instantaneous repeat doses, and superposition. Verify actual AUC/Cmax accumulation ratios with multiple-dose data. Absorption rate, infusion, multicompartment, nonlinear or time-dependent PK, active metabolites, and loading doses are excluded.
Basis: FDA review equation R=1/(1−e^(−kτ)) and the EMA PK-guideline definition of observed accumulation.
Tool Guide
Definition
Accumulation & Steady-State Helper — Under linear, time-invariant one-compartment first-order elimination and superposition of identical instantaneous repeat doses, calculates k=ln2/t½, interval remaining fraction e^(−kτ), theoretical R=1/(1−e^(−kτ)), and 90/95/99% steady-state milestones.
Purpose
(1) Cross-check theoretical remaining fraction and accumulation for a half-life/interval pair (2) Approximate continuous time to 90/95/99% steady state (3) Identify the first scheduled dose exceeding each target fraction (4) Prepare simple reference values before multiple-dose PK design
How to Use
① Enter terminal half-life and dosing interval in the same time unit. ② Review interval remaining fraction and theoretical accumulation factor. ③ Distinguish the continuous-time milestone from the discrete scheduled-dose milestone. ④ Compare with observed multiple-dose AUCτ, Cmax, and Cmin ratios to assess linearity and time dependence. Do not automatically multiply an observed Cmax or AUC by the theoretical factor; absorption, infusion, and distribution phases can change the result.
Examples
Example) t½=24 h and τ=12 h → 70.7107% remains at the next dose; 29.2893% is eliminated → theoretical R=3.4142; instantaneous-input peak/trough=1.4142 → continuous 95% approximation=103.73 h=4.3219 half-lives → on a 12 h schedule, 95.5806% just after dose 9 (96 h after the first dose) Report observed accumulation with an explicit endpoint such as AUCss/AUCsingle or Cmax,ss/Cmax,single.