This calculator gives general estimates for information only. It does not replace advice from your doctor, pharmacist or another qualified health professional.
What half-life means
The elimination half-life of a drug is the time it takes for its concentration in the blood to fall by half. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. Most drugs follow this first-order, exponential pattern, because the body clears a fixed fraction rather than a fixed amount per hour. Half-lives range from minutes (adrenaline) to hours (caffeine, ibuprofen) and days (some antidepressants).
The formulas
- Amount remaining = initial dose × 0.5^(time ÷ half-life)
- Number of half-lives = time ÷ half-life
- Time to reach a fraction f = half-life × log₂(1 ÷ f); below 10% takes 3.32 half-lives
- Elimination constant k = ln 2 ÷ half-life
- Rule of thumb: after 5 half-lives, about 3% remains, and the drug is considered practically eliminated.
Worked example: 200 mg of caffeine, half-life 5 hours
- After 10 hours, 2 half-lives have passed: 200 × 0.5² = 50 mg remain, 25% of the dose.
- It takes 5 × 3.32 = 16.6 hours to fall below 20 mg (10%).
- After 5 half-lives, or 25 hours, about 6 mg remain.
- The elimination constant is 0.693 ÷ 5 = 0.1386 per hour: about 13% of the caffeine present is cleared each hour.
A coffee at 4 p.m. still leaves a quarter of its caffeine in your body at 2 a.m., which is why afternoon coffee can disturb sleep.
Amount remaining over time (200 mg, half-life 5 h)
| Time | Remaining | Share |
|---|---|---|
| 1 h | 174.1 mg | 87.1% |
| 5 h | 100.0 mg | 50.0% |
| 10 h | 50.0 mg | 25.0% |
| 15 h | 25.0 mg | 12.5% |
| 20 h | 12.5 mg | 6.3% |
| 25 h | 6.3 mg | 3.1% |
Repeated doses and steady state
When you take a drug regularly, each dose adds to what remains from the previous ones. The level rises until intake and elimination balance: this steady state is reached after about 4 to 5 half-lives, whatever the dose. It explains why some medicines take a week or more to work fully, and why their effects take as long to wear off after stopping.
What changes the half-life
- Liver and kidney function: reduced function lengthens the half-life of drugs they clear, which may require a lower dose.
- Age: older adults often eliminate drugs more slowly.
- Pregnancy, smoking and other medicines: smoking speeds up caffeine clearance, while pregnancy and some drugs slow it down a lot.
Published half-lives are averages; individual values can be half or double. Never change a dosing schedule based on this calculator alone.