How to use the half-life calculator
- Choose what to find: the amount remaining, the initial amount, the time elapsed or the half-life itself.
- Pick a substance to fill in its half-life, or choose "Enter my own half-life" and type it.
- Enter the amounts you know. Any unit works (grams, number of atoms, becquerels of activity or percent), as long as both amounts use the same one.
- Choose the time unit for the time and the half-life. Isotope half-lives are converted automatically, using a year of 365.25 days.
- Read the answer, the decay constant and mean lifetime, and a table of how the amount halves over eight half-lives.
The half-life formula
N₀ is the starting amount, N the amount left after time t, and T the half-life: the time it takes for half of any amount to decay. The ratio t ÷ T counts how many half-lives have passed, and each one multiplies the amount by 1/2. The same law is often written N = N₀e^(−λt), where the decay constant λ is the fraction decaying per unit of time. The mean lifetime τ is the average time an individual atom survives, about 1.44 half-lives.
Worked example
The calculator starts with 100 g of carbon-14 and asks how much is left after 10,000 years, using the 5,730-year half-life:
- Count the half-lives: 10,000 ÷ 5,730 = 1.74520.
- Fraction left: (1/2)^1.74520 = 0.298292.
- Amount left: N = 100 × 0.298292 = 29.83 g.
So about 29.8% survives and 70.17 g has decayed. The decay constant is ln 2 ÷ 5,730 = 0.000121 per year, and the mean lifetime is 5,730 ÷ 0.693147 = 8,267 years.
Going the other way, if only 25 g of the 100 g is left, then N₀ ÷ N = 4, which is 2², so exactly two half-lives have passed: t = 2 × 5,730 = 11,460 years.
Half-lives of common isotopes
| Isotope | Half-life | Where it matters |
|---|---|---|
| Fluorine-18 | 109.77 minutes | PET scans |
| Radon-222 | 3.8222 days | Indoor radon gas |
| Iodine-131 | 8.0252 days | Thyroid treatment, fallout |
| Cobalt-60 | 1,925.28 days (5.27 years) | Radiotherapy, sterilization |
| Tritium (H-3) | 12.32 years | Exit signs, fusion research |
| Strontium-90 | 28.91 years | Fission product |
| Cesium-137 | 30.08 years | Fission product, gauges |
| Radium-226 | 1,600 years | Historic luminous paint |
| Carbon-14 | 5,700 years (5,730 by convention) | Radiocarbon dating |
| Plutonium-239 | 24,110 years | Reactor fuel, weapons |
| Uranium-235 | 704 million years | Reactor fuel |
| Potassium-40 | 1.248 billion years | Potassium-argon dating |
| Uranium-238 | 4.468 billion years | Dating the age of the Earth |
Values are the evaluated half-lives from the IAEA Live Chart of Nuclides, which draws on the ENSDF nuclear data files, checked in 2026. For carbon-14 the evaluated value is 5,700 ± 30 years. Most textbooks and dating problems still use the older 5,730-year figure, so the calculator offers both.
Beyond radioactivity
Any process where a fixed fraction disappears in each equal stretch of time has a half-life. The same formula describes how long a medicine stays in your body (caffeine's half-life in adults is a few hours), how a charged capacitor discharges, and how the value of money shrinks under steady inflation. Steady growth follows the mirror-image rule, with a doubling time in place of a half-life; that is the same math behind the compound interest calculator.
Frequently asked questions
Does a substance ever decay completely?
Mathematically, no: every half-life leaves half of what was there, so the amount gets smaller forever without reaching zero. In practice, once only a few atoms remain, decay becomes a matter of chance for each atom. After 10 half-lives less than 0.1% is left, which is often treated as gone.
How is the half-life used in carbon dating?
Living things take in carbon-14 from the air, and the intake stops when they die. Measuring the fraction of carbon-14 left gives the time since death: t = T × log₂(N₀ ÷ N). A sample with 25% of the original level is about 11,460 years old. Real dating also corrects for past changes in the amount of carbon-14 in the atmosphere.
Can the amounts be in percent?
Yes. Use 100 for the initial amount and the remaining percentage for N. Any unit works as long as both amounts use the same one, because only the ratio N ÷ N₀ affects the time and the half-life.
What is the difference between half-life and mean lifetime?
The half-life is the time for half of a sample to decay. The mean lifetime is the average survival time of a single atom, and it is longer: τ = T ÷ ln 2 ≈ 1.443 × T. For carbon-14, that is 8,267 years against a half-life of 5,730 years.
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