Radioactive Decay (Half-Life) Calculator
Calculate radioactive decay, remaining material, and activity after a given time.
Supports common isotopes with known half-lives.
Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. The rate of decay is characterized by the half-life — the time it takes for half of the radioactive atoms to decay.
Decay formula:
N(t) = N₀ × (1/2)^(t / t½)
Where:
- N(t) = amount remaining after time t
- N₀ = initial amount
- t = elapsed time
- t½ = half-life of the isotope
Decay constant:
λ = ln(2) / t½ ≈ 0.693 / t½
Activity formula:
A(t) = A₀ × e^(-λt)
Activity is measured in becquerels (Bq) or curies (Ci). 1 Ci = 3.7 × 10¹⁰ Bq.
Common isotope half-lives:
| Isotope | Half-Life | Common Use |
|---|---|---|
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Iodine-131 | 8.02 days | Thyroid treatment |
| Cobalt-60 | 5.27 years | Cancer radiotherapy |
| Cesium-137 | 30.17 years | Industrial gauges |
| Uranium-238 | 4.47 billion years | Geology dating |
| Radon-222 | 3.82 days | Indoor air concern |
| Phosphorus-32 | 14.3 days | Lab research |
| Technetium-99m | 6.01 hours | Medical imaging |
Practical example: If you start with 100 grams of Iodine-131 (half-life = 8.02 days):
- After 8.02 days: 50 g remains
- After 16.04 days: 25 g remains
- After 24.06 days: 12.5 g remains
- After 80.2 days (~10 half-lives): only 0.098 g remains
Number of half-lives:
n = t / t½
After n half-lives, the fraction remaining is (1/2)^n.
Tip: After about 10 half-lives, less than 0.1% of the original material remains. This is often used as a practical threshold for when a radioactive source is considered “decayed away.”