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
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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