Drug Half-Life Calculator
Calculate medication remaining from dose, half-life in hours, and time elapsed.
Returns concentration at each interval and time to reach 1% of original dose.
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:
| Drug | Half-life |
|---|---|
| Ibuprofen | 2 hours |
| Amoxicillin | 1–1.5 hours |
| Aspirin (acetylsalicylate) | 15–20 minutes |
| Diazepam (Valium) | 20–100 hours |
| Fluoxetine (Prozac) | 1–4 days |
| Levothyroxine | 6–7 days |
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.