Half-Life Calculator
Half-life is the time required for half of a substance to undergo decay or be eliminated. It applies to radioactive decay, drug metabolism, and chemical reactions. After n half-lives, the remaining fraction is (1/2)ⁿ.
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Tip: In medicine, it takes about 4–5 half-lives for a drug to reach steady state in the body, and 4–5 half-lives to be substantially eliminated. This guides dosing frequency.
- 1Remaining quantity: N(t) = N₀ × (1/2)^(t/t½)
- 2N₀ = initial amount, t = elapsed time, t½ = half-life
- 3Equivalently: N(t) = N₀ × e^(−λt) where λ = ln(2)/t½
- 4After 10 half-lives: only ~0.1% of the original remains
Carbon-14 (t½=5,730yr), 1,000 atoms, 11,460 years=250 atoms remaining2 half-lives: 1000→500→250
Drug half-life 8 hours, dose 500mg, after 24 hours=62.5 mg remaining3 half-lives: 500→250→125→62.5
| Substance | Half-life | Application |
|---|---|---|
| Carbon-14 | 5,730 years | Archaeological dating |
| Uranium-238 | 4.47 billion years | Geological dating |
| Iodine-131 | 8.02 days | Medical imaging / therapy |
| Caffeine (in body) | 5–6 hours | Drug metabolism |
| Alcohol | ~1 drink/hour | BAC reduction |
| Aspirin | 15–20 minutes | Drug metabolism |
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Fun Fact
Radiocarbon dating (carbon-14) can only date materials up to ~50,000 years old — about 9 half-lives. Beyond that, too little C-14 remains to measure accurately. For older materials, potassium-40 (half-life 1.25 billion years) is used.
References
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