Radioactive decay
Pick a cited isotope or enter a custom half-life, then calculate the percentage and optional mass remaining after an elapsed time.
Remaining after 5,730 years
50%
Half-life: 5,730 years (C-14). Decay constant lambda = 3.8332e-12 s^-1.
For C-14, 5,730 years elapsed leaves 50% remaining; 11,460 years leaves 25% remaining.
| Isotope | Half-life | Use | Source |
|---|---|---|---|
| C-14 | 5,730 years | radiocarbon dating | IUPAC |
| U-235 | 7.04e8 years | nuclear fuel | NIST |
| U-238 | 4.47e9 years | uranium series dating | NIST |
| Pu-239 | 24,110 years | reactor and weapons material | NIST |
| Ra-226 | 1,600 years | uranium decay-series reference | IAEA |
| Tc-99m | 6.01 hours | medical imaging | IAEA |
| I-131 | 8.02 days | nuclear medicine | IAEA |
| K-40 | 1.25e9 years | potassium-argon dating | IUPAC |
Half-life is the time required for a sample to fall to half of its starting amount. The calculator uses the standard exponential model: remaining fraction = (1/2)^(elapsed time / half-life). That same model works for radioactive decay and any process where a quantity shrinks by a fixed percentage over equal intervals.
Radiocarbon dating is the familiar C-14 example. Carbon-14 has a half-life of about 5,730 years, so one half-life leaves 50% and two half-lives, 11,460 years, leave 25%. In practice, radiocarbon dating becomes difficult beyond roughly 50,000 years because so little C-14 remains that contamination, background counts, and calibration uncertainty dominate the signal.
Nuclear waste planning uses half-life differently. A common storage rule of thumb is to consider about 10 half-lives, not one. After 10 half-lives, the parent isotope is down to about 0.098% of its starting amount, which is roughly a thousand-fold reduction. That does not make every material harmless: dose also depends on decay products, radiation type, chemistry, shielding, and exposure route. But the 10x half-life yardstick gives engineers a quick first pass for how long the dominant radionuclide remains relevant.
First, two half-lives is not complete decay. Each halving applies to whatever is left, so two half-lives leave 25%, three leave 12.5%, and the curve approaches zero without mathematically reaching it. Second, the half-life does not depend on how much material you start with: a kilogram and a milligram of the same isotope halve on exactly the same schedule, because decay is a fixed per-atom probability. Third, a half-life is not an expiry date for individual atoms. Any single atom may decay in the next second or outlast a thousand half-lives; the half-life only describes the statistical behaviour of large populations.
Technetium-99m, the workhorse of diagnostic imaging, has a half-life of 6.01 hours (IAEA). A dose prepared in the morning has passed just under four half-lives by the same time the next day, since 24 divided by 6.01 is about 3.99, and 0.5 raised to that power leaves roughly 6.3% of the starting activity. This is why imaging departments run on same-day schedules: the tracer decays to near-uselessness overnight, which is also what makes it safe to send patients home within hours.
At the other end of the scale sits plutonium-239 at 24,110 years (NIST). Applying the ten-half-life planning yardstick gives 241,100 years before the parent isotope falls to about 0.098% of its starting amount. Enter Pu-239 in the calculator with 241,100 years elapsed and you can confirm the figure directly. The contrast between a 6-hour tracer and a 24-millennium fuel isotope is the whole reason the same formula serves both hospital schedulers and repository engineers.
When you know the remaining fraction and want the elapsed time, rearrange the model: elapsed time equals the half-life multiplied by log(remaining fraction) divided by log(0.5). A carbon-14 sample measured at 12.5% of its original activity is exactly three half-lives old, which is 3 times 5,730, or 17,190 years. Awkward fractions work the same way: 10% remaining corresponds to about 3.32 half-lives, because 0.5 raised to 3.32 is roughly 0.1. This reverse form is the core of every radiometric dating method, from radiocarbon on bone and charcoal to potassium-argon on volcanic rock.
A common engineering yardstick is ten half-lives, which leaves about 0.098% of the original atoms, a thousand-fold reduction. Whether that is safe still depends on the decay products, the radiation type, and how a person is exposed, so ten half-lives is a first pass, not a clearance rule.
Yes. Switch to the custom half-life mode and enter any value in years, days, or hours. Keep in mind that biological half-lives are averages that vary between individuals, unlike nuclear half-lives, which are fixed physical constants.
Lambda equals the natural log of 2 divided by the half-life, expressed per second. For carbon-14, with a 5,730-year half-life, that works out to about 3.83 x 10^-12 per second. It is the same information as the half-life, just written as a rate.
Half-lives are measured quantities with experimental uncertainty, and reference bodies update their evaluations over time. Each isotope in this tool is labeled with the body it was taken from: IUPAC, NIST, or IAEA.
For practical purposes, no. Heat, pressure, and chemical bonding leave nuclear half-lives essentially untouched, which is exactly why radiometric dating works: a rock's thermal history does not reset the clock.