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A half-life is the time it takes for half of a quantity to decay away — used for radioactive isotopes, medications leaving the body, and any process with exponential decay. Enter the starting amount, the half-life and the elapsed time, and this tool works out how much remains.
How is it calculated?
Exponential decay
remaining = initial × 0.5^(elapsed ÷ half-life)
Each half-life halves what’s left, so decay is exponential, not linear:
| Half-lives passed | Fraction remaining |
|---|---|
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
Same units for time
The elapsed time and the half-life must be in the same unit — seconds, hours, years, whatever fits — because only their ratio matters. That ratio is the number of half-lives, and the tool reports it alongside the amount.
Where it applies
Radioactive dating and safety, the clearance of drugs and caffeine from the body, the decay of a signal, and charge or heat loss with a characteristic decay time.
Worked example
Caffeine has a half-life of about 5 hours. Start with 200 mg from a strong coffee: after 5 hours (one half-life) 100 mg remains, after 10 hours 50 mg, after 15 hours 25 mg. That’s 0.5^(15 ÷ 5) = 0.5³ = 12.5% of the original — which is why an afternoon coffee can still affect sleep.
FAQ
What is a half-life?+
The time it takes for half of a quantity to decay or be eliminated. After one half-life, 50% remains; after two, 25%; after three, 12.5%. It applies to radioactive isotopes, drugs in the body and any exponential-decay process.
How do I calculate how much remains?+
Multiply the starting amount by one-half raised to the number of half-lives elapsed: remaining = initial × 0.5^(elapsed ÷ half-life). The calculator does this from the three values you enter.
Why is decay exponential and not steady?+
Because each period removes a fixed fraction of what’s currently left, not a fixed amount. Halving 100 gives 50, halving 50 gives 25 — the absolute loss shrinks each time, producing a curve that approaches zero without ever quite reaching it.
Do the time units matter?+
Only that they match. The elapsed time and the half-life must use the same unit, since the calculation depends on their ratio. Mixing hours and days would give a wrong number of half-lives.
Can I use it for medications?+
Yes — drug elimination often follows first-order (exponential) kinetics with a characteristic half-life, so the same formula estimates how much of a dose remains over time. For medical decisions, always rely on a clinician rather than an estimate.