Solve any half-life problem: how much remains after a given time, how long until a sample decays to a level, the original amount, or the half-life itself. This free radioactive decay calculator also gives the decay constant and plots the curve, and works for drug elimination and first-order reactions too.
Half-life formulas
Worked example: carbon dating
Carbon-14 has a half-life of 5,730 years. After 11,460 years (two half-lives), 100 g of C-14 has decayed to 100 × ½ × ½ = 25 g. Working backwards, a bone with 25% of the original C-14 is about 11,460 years old.
Half-lives of common isotopes
| Isotope | Half-life | Use |
|---|---|---|
| Technetium-99m | 6.0 hours | Medical imaging |
| Iodine-131 | 8.0 days | Thyroid treatment |
| Cobalt-60 | 5.27 years | Radiotherapy, sterilisation |
| Carbon-14 | 5,730 years | Radiocarbon dating |
| Uranium-238 | 4.47 billion years | Dating rocks |
Frequently asked questions
What is half-life?
The time it takes for half of a radioactive sample (or a drug, or a reactant in a first-order reaction) to decay. After each half-life, half of what remained is gone.
How do I calculate the amount remaining?
Use N = N₀ × (½)^(t/T½). Enter the initial amount, the time and the half-life, and leave N empty.
How do I find how long it takes to decay?
Leave the time box empty and enter the initial amount, remaining amount and half-life. The calculator uses t = T½ × log(N/N₀) / log(½).
Does half-life work for medicines?
Yes. Most drugs are eliminated by first-order kinetics, so after about 5 half-lives roughly 97% of a dose is gone.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.