Half-Life Calculator
| Isotope | Half-life | Known for |
|---|---|---|
| Carbon-14 | 5,730 years | radiocarbon dating archaeology |
| Iodine-131 | 8.02 days | thyroid treatment and diagnostics |
| Technetium-99m | 6.01 hours | the workhorse of medical imaging |
| Cobalt-60 | 5.27 years | cancer radiotherapy sources |
| Cesium-137 | 30.17 years | Chernobyl and Fukushima fallout |
| Strontium-90 | 28.79 years | bone-seeking fallout product |
| Radium-226 | 1,600 years | the Curies’ original element |
| Plutonium-239 | 24,110 years | weapons and reactor fuel |
| Americium-241 | 432 years | smoke detector ionization sources |
| Potassium-40 | 1.25 billion years | dating rocks, and bananas |
| Uranium-238 | 4.47 billion years | the Earth’s dating clock |
| Thorium-232 | 14.0 billion years | older than most of the universe’s stars |
Radioactive decay follows one line of math: after each half-life, half of what remained is gone - so the remainder is 2^(-t/T), never zero. This calculator runs that exponent for twelve common isotopes (half-lives from the Brookhaven NNDC data) or any custom value, and answers in percent and fraction.
The same law reads backward as dating: Carbon-14’s 5,730-year half-life turns a measured ratio into an age, which is how archaeology dates charcoal and how the Uranium-238 clock dates rocks a billion years old.
How to use
- Pick an isotope (the half-life fills itself) or choose custom and type a half-life with matching units.
- Enter elapsed time; the chips load the classic cases - two Carbon-14 half-lives, one Iodine-131, four Cobalt-60 quarter-lives.
- Read the fraction line for the exact multiplier and how many half-lives the elapsed time represents.
Frequently asked questions
Why does radioactive material never fully disappear?
Because the decay removes half per half-life, the remainder is a geometric sequence: 1/2, 1/4, 1/8... approaching but never reaching zero. That is why regulations use practical targets - ten half-lives leaves 0.1%, the standard rule of thumb for when a source is stored rather than feared.
How does carbon dating use this calculator?
Living things exchange carbon constantly, holding a steady Carbon-14 ratio with the atmosphere. At death the exchange stops and the ratio decays on a 5,730-year clock: a wooden artifact showing 25% of the living ratio is two half-lives old - about 11,460 years. The calculator’s C-14 chip runs exactly this.
What is the decay constant lambda?
The exponent’s other face: lambda = ln(2) / T½, about 0.693 divided by the half-life, so N(t) = N₀ · e^(-λt). Same curve, different spelling - textbooks use lambda, this calculator uses the 2^(-t/T) form because half-lives are what tables publish.
Why do medical isotopes have such short half-lives?
By design: Technetium-99m’s 6 hours means the imaging dose fades before the patient leaves the hospital, while Iodine-131’s 8 days is long enough to concentrate in the thyroid and short enough to stop soon after. The therapeutic window is half-life selection.