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.