Radioactive Half-Life Remaining Calculator
Calculate remaining radioactive material after any elapsed time.
Enter initial amount and half-life to get remaining quantity and decay percentage.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. Half-life is the time required for exactly half of a radioactive substance to decay into another element or isotope. This concept is fundamental in nuclear physics, medicine, geology, and environmental science.
The Half-Life Formula
N(t) = N₀ × (½)^(t / t½)
Or equivalently using the natural exponential:
N(t) = N₀ × e^(−λt)
Where:
- N(t) = amount remaining after time t
- N₀ = initial amount
- t = elapsed time
- t½ = half-life period
- λ = decay constant = ln(2) / t½ ≈ 0.693 / t½
Common Radioactive Isotopes and Their Half-Lives
| Isotope | Use | Half-Life |
|---|---|---|
| Carbon-14 (¹⁴C) | Archaeological dating | 5,730 years |
| Iodine-131 (¹³¹I) | Thyroid cancer treatment | 8.02 days |
| Uranium-238 (²³⁸U) | Geological dating | 4.47 billion years |
| Radium-226 (²²⁶Ra) | Historical medical use | 1,600 years |
| Technetium-99m | Medical imaging | 6.01 hours |
| Cobalt-60 | Cancer radiation therapy | 5.27 years |
| Strontium-90 | Nuclear fallout | 28.8 years |
| Plutonium-239 | Nuclear weapons/fuel | 24,100 years |
Practical Applications
Radiocarbon Dating (C-14) Living organisms constantly replenish their carbon-14 from the atmosphere. After death, the C-14 decays at a known rate. By measuring the remaining C-14 ratio, scientists can date organic material up to ~50,000 years old.
Medical Isotopes Short-lived isotopes like Technetium-99m (6-hour half-life) are used in medical scans because they decay quickly, minimizing patient radiation exposure. After 48 hours (8 half-lives), only 1/256 of the original dose remains.
Decay Percentage
After n half-lives: Remaining = (½)ⁿ × 100% of original
After 1 half-life: 50% remains After 2 half-lives: 25% remains After 3 half-lives: 12.5% remains After 10 half-lives: ~0.1% remains