Science & Engineering
Half-Life Calculator - Radioactive Decay & Remaining Amount
Calculate remaining quantity, elapsed time, or half-life for radioactive decay using N(t)=N₀×(½)^(t/t½).
Leave exactly one field blank - it will be calculated from the other three.
Half-life formula
N(t) = N₀ × (½)^(t / t½)
- N₀ - initial quantity
- t½ - half-life (any time unit, consistent with t)
- t - elapsed time
- N(t) - remaining quantity at time t
Common half-lives
- Carbon-14: 5,730 years (radiocarbon dating)
- Uranium-238: 4.47 billion years
- Iodine-131: 8.02 days (medical isotope)
- Radon-222: 3.82 days
Half-life reference table
| Isotope | Half-life | Significance |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating of organic materials |
| Plutonium-239 | 24,100 years | Nuclear waste requiring long-term storage |
| Uranium-238 | 4.47 billion years | Uranium-lead dating of rocks |
| Technetium-99m | 6 hours | Most common nuclear medicine diagnostic isotope |
| Iodine-131 | 8 days | Thyroid cancer treatment |
| Radon-222 | 3.82 days | Indoor air quality concern in basements |
Applications
- Radiocarbon dating: Carbon-14 in organic materials decays at a known rate; comparing remaining C-14 to the atmospheric ratio gives the age of the sample up to ~50,000 years.
- Nuclear medicine: Tc-99m's 6-hour half-life means it is nearly gone within 2 days, minimizing patient radiation exposure while still enabling imaging.
- Reactor design: reactor designers must account for hundreds of different fission products, each with a different half-life, to plan cooling and waste handling.
Exponential decay intuition
After each half-life, exactly half the remaining quantity decays. After 10 half-lives, approximately 0.1% of the original quantity remains. After 20 half-lives, approximately 0.0001%. This is why nuclear waste with short half-lives (like Cs-137 at 30 years) is more intensely radioactive in the short term but becomes less dangerous much sooner than long-lived isotopes.