Time to Steady State Calculator
Estimate how long a drug takes to reach steady state from its half-life (about 5 half-lives), the number of doses needed, the accumulation factor and the peak-to-trough ratio for a dosing interval.
How it works
fraction of steady state after time t = 1 − e^(−ke·t) = 1 − 0.5^(t ÷ t½) · ~97% after 5 t½, 90% after 3.32 t½ · ke = 0.693 ÷ t½ · accumulation factor R = 1 ÷ (1 − e^(−ke·τ)) · peak ÷ trough = e^(ke·τ)
With regular dosing (or a constant infusion) a drug accumulates until the amount eliminated per interval equals the amount given. The approach to that plateau depends only on the half-life: 50% of steady state after one half-life, 75% after two, 87.5% after three, and about 97% after five, which is the usual clinical rule. Dose size and frequency change the height of the plateau, not how fast it is reached — that is what loading doses are for. The accumulation factor compares a steady-state level with the level after the first dose, and the peak-to-trough ratio shows how much levels swing within each interval.
Worked example
A drug with an 8-hour half-life reaches steady state after about 5 × 8 = 40.0 h (1.67 days) and 90% of it after 26.6 h. Dosed every 12 hours, that is 4 doses; ke = 0.0866 /h, the accumulation factor is 1 ÷ (1 − e^(−0.0866 × 12)) = 1.55 and the peak is 2.83 times the trough.
Sources: StatPearls — Steady State Concentration · StatPearls — Physiology, Zero- and First-Order Kinetics
Frequently asked questions
Why does steady state take 5 half-lives?
Each half-life closes half of the remaining gap to the plateau: 50%, 75%, 87.5%, 93.75% and 96.9% after five. Clinically, about 97% is treated as steady state; some references use 4 half-lives (94%).
Does a higher dose reach steady state faster?
No. A higher dose gives a higher plateau but takes the same number of half-lives to reach it. Only a loading dose, or a shorter half-life, gets there sooner.
When should I check a drug level?
Usually at steady state (after 4–5 half-lives on a stable regimen), and as a trough just before the next dose unless the drug’s monitoring guideline says otherwise.
What is the accumulation factor?
R = 1 ÷ (1 − e^(−ke·τ)): how many times higher the steady-state levels are than after the first dose. Dosing once every half-life gives R = 2.
Related calculators
Educational pharmacokinetic estimate for health professionals only — not medical advice or a prescription. Population parameters vary widely between patients; base real dosing on the product label, measured drug levels, local protocols and a clinical pharmacist.