Drug Accumulation and Steady-State Calculator

Drug half-life is the time required for the concentration of a drug in the body to decrease by 50%. It governs dosing frequency, how quickly a drug reaches steady-state concentration, and how long it takes to clear the system after the last dose.

This page is about the repeat-dose side of that: put a dosing interval in the fourth box and it returns the accumulation factor, the steady-state peak and trough, and how long the drug takes to level off. That is the question behind “why did this build up on me in week two”.
If you took a single dose and only want to know when it is out of your system, the drug half-life in body calculator answers that one and lets you give the half-life in minutes or days rather than hours. Both pages use the same first-order model and return the same remaining amount for the same inputs.

Half-life formula: C(t) = C₀ × (1/2)^(t / t½)

Or equivalently: C(t) = C₀ × e^(−0.693 × t / t½)

Where:

• C(t) = concentration at time t
• C₀ = initial concentration
• t½ = half-life of the drug
• t = elapsed time

Time to steady state: Steady-state concentration is reached after approximately 4–5 half-lives of continuous dosing at fixed intervals. Time to steady state ≈ 4 × t½

Drug accumulation factor (at steady state): Accumulation = 1 / (1 − (1/2)^(τ/t½)) Where τ = dosing interval

Fraction of drug eliminated after n half-lives: Remaining = (1/2)^n × 100%

• After 1 half-life: 50% remains
• After 3 half-lives: 12.5% remains
• After 5 half-lives: 3.1% remains (considered “cleared”)
• After 7 half-lives: 0.78% remains

Common drug half-lives:

Worked example: Diazepam with t½ = 48 hours. Initial dose: 10 mg at time zero. After 48 hours: 5 mg remains After 96 hours: 2.5 mg remains After 240 hours (10 days): 10 × (0.5)^5 = 0.31 mg (3.1% of original dose) Considered clinically cleared after ~10 days (5 half-lives).

Clinical implication: Drugs with long half-lives (days to weeks) accumulate to high levels with daily dosing and linger long after discontinuation, which matters for drug interactions and for tapering protocols.

Fluoxetine is the standard illustration. Its own half-life is 1 to 4 days and its active metabolite norfluoxetine runs 7 to 15 days, so it takes over a month to clear. That is why it is one of the few antidepressants that can often be stopped without a taper: the drug tapers itself on the way out.