This half-life calculator works out radioactive decay and any other exponential decay process. Find the amount remaining, the time elapsed, the half-life or the starting amount, and see the decay constant and mean lifetime.
Half-life formula
N(t) = N₀ × (1/2)t / t½
N₀ is the starting amount, N(t) the amount left after time t, and t½ the half-life. The same law can be written with the decay constant λ = ln 2 ÷ t½ as N(t) = N₀ × e−λt. The mean lifetime τ = t½ ÷ ln 2.
Common half-lives
| Isotope | Half-life | Used for |
|---|---|---|
| Carbon-14 | about 5,730 years | Radiocarbon dating |
| Iodine-131 | about 8 days | Thyroid treatment |
| Technetium-99m | about 6 hours | Medical imaging |
| Uranium-238 | about 4.5 billion years | Dating rocks |
Worked example
100 g of carbon-14 decays for 10,000 years. That is 10,000 ÷ 5,730 ≈ 1.745 half-lives, so about 29.83 g remains (29.8% of the original).
Frequently asked questions
What is half-life?
The time it takes for half of a quantity to decay. After two half-lives a quarter remains, after three an eighth, and so on.
Does the half-life change over time?
No. For radioactive decay it is constant, whatever the amount or age of the sample.
Can I use this for medicines?
Yes, as a simple model of how a drug’s level falls after a single dose. Real drug levels depend on dosing and how the body processes the drug, so follow medical advice.
What units should I use?
Any units, as long as the half-life and time use the same one (both in years, or both in hours, for example).
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Last reviewed: October 2026.