Calculate remaining quantity, decay constant, mean lifetime and activity of any radioactive isotope — with a visual decay curve.
Half-life is the time required for exactly one half of the atoms in a radioactive sample to undergo decay. After one half-life, 50% of the original substance remains. After two half-lives, 25% remains. After three, 12.5% — and so on. The decay is exponential, meaning the rate of decay is proportional to the current quantity.
Each radioactive isotope has its own fixed half-life. Carbon-14 has a half-life of 5,730 years, which makes it useful for dating organic materials up to roughly 50,000 years old. Uranium-238 has a half-life of 4.47 billion years — close to the age of Earth itself — which is why it's used in geological dating. On the other end, Technetium-99m has a half-life of just 6 hours, which makes it ideal for medical imaging because it decays quickly and leaves minimal radiation in the body.
The amount of substance remaining after a given time is calculated using the exponential decay equation:
The decay constant (λ) is related to the half-life by λ = ln(2) / t½, which equals approximately 0.693 / t½. The mean lifetime (τ) is the average time an atom survives before decaying, given by τ = 1 / λ. The mean lifetime is always longer than the half-life by a factor of about 1.443.
Half-life calculations are used across many fields. In nuclear medicine, they determine how long a radioactive tracer stays active in the body. In archaeology, carbon dating relies entirely on the half-life of C-14. In nuclear engineering, understanding half-lives is essential for managing reactor fuel cycles and nuclear waste storage. In environmental science, they help model the decay of radioactive contaminants in soil and water.