This half-life calculator solves the exponential decay equation in any direction: how much remains after a given time, how long decay takes, what the half-life is, or how much you started with. It works for radioactive isotopes, drug elimination, and anything else that halves on a schedule.
What Is Half-Life?
Half-life is the time it takes for half of a substance to decay or be eliminated. After one half-life 50% remains; after two, 25%; after three, 12.5% — always halving, never quite reaching zero. Each radioactive isotope has its own fixed half-life, from fractions of a second to billions of years, which makes it both a clock (radiocarbon dating) and a safety measure (how long waste stays dangerous). This calculator is part of our Chemistry Calculators collection.
The Half-Life Formula
N(t) = N₀ × (½)t/T½
Worked example (verified): 100 g of an isotope with a 5-day half-life, after 15 days: 15 ÷ 5 = 3 half-lives → 100 × (½)³ = 12.5 g remaining. Run it backwards: a carbon-14 sample at 25% of its original level has lived through 2 half-lives of 5,730 years → about 11,460 years old — the arithmetic behind radiocarbon dating. For very small remaining amounts, the Scientific Notation Calculator keeps the numbers readable.
Common Half-Lives
| Substance | Half-life | Used for |
|---|---|---|
| Carbon-14 | 5,730 years | Dating organic remains |
| Uranium-238 | 4.47 billion years | Dating rocks, Earth’s age |
| Iodine-131 | 8.02 days | Thyroid treatment & imaging |
| Technetium-99m | 6.01 hours | Medical scans |
| Caffeine (in the body) | ~5–6 hours | Pharmacology (elimination) |
| Radon-222 | 3.82 days | Home radon risk |
Half-Life Beyond Radioactivity
The same mathematics governs drug elimination (after ~5 half-lives a drug is ~97% cleared), caffeine fading through an afternoon, and even information relevance. Note the assumption: true exponential decay with a constant half-life. Drug levels in real bodies vary with metabolism, dose and other medications — clinical decisions need clinical tools, not this calculator.
Related Tools
- Scientific Notation Calculator — tiny and huge quantities
- pH Calculator — another logarithmic scale
- Chemistry Calculators — the full collection
Frequently Asked Questions
How do I calculate remaining amount after n half-lives?
Divide the starting amount by 2n. After 4 half-lives, 1/16 (6.25%) remains.
Can half-life change?
For radioactive decay, no — it is a nuclear property unaffected by temperature, pressure or chemistry. For drugs, “half-life” is an average that varies between people.
How long until a substance is completely gone?
Mathematically, exponential decay never reaches exact zero; practically, after 7 half-lives under 1% remains, and after 10, under 0.1%.
What is the decay constant?
λ = ln(2) ÷ T½ — the per-unit-time decay probability used in the form N = N₀e−λt. Both forms describe the same curve.
Why does carbon dating stop working after ~50,000 years?
After about 9 half-lives, so little carbon-14 remains (~0.2%) that measurement noise overwhelms the signal.
Is this half-life calculator free?
Yes — free, instant, no sign-up.