Drug Half-Life 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.

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–weeks) accumulate to high levels with daily dosing and linger long after discontinuation — important for drug interactions and tapering protocols.