Calculate how much of a substance remains after radioactive decay, or how long until a specific amount remains. Covers physics, chemistry, pharmacology, and carbon dating.
Half-life is the time it takes for exactly half of a radioactive substance to decay. After one half-life, 50% remains. After two half-lives, 25% remains. After ten half-lives, less than 0.1% remains.
N(t) = N₀ × (1/2)^(t/t½), where N(t) is the remaining amount, N₀ is the initial amount, t is elapsed time, and t½ is the half-life. This calculator solves for any of these variables.
Carbon-14 has a half-life of 5,730 years. This is why radiocarbon dating works for organic materials up to about 50,000 years old — after 9 half-lives, less than 0.2% remains.
Drug half-life determines dosing intervals. Aspirin has a half-life of about 20 minutes. Ibuprofen is 2 hours. Fluoxetine (Prozac) is 1-4 days. A drug is considered eliminated after 5 half-lives.
The decay constant (λ) is the probability per second that any given atom will decay. It relates to half-life by: λ = ln(2) / t½ ≈ 0.693 / t½.
The hazard period of nuclear waste is approximately 10 half-lives, after which less than 0.1% remains. Plutonium-239 has a half-life of 24,100 years, meaning it remains hazardous for hundreds of thousands of years.
Tc-99m is used in medical imaging (nuclear medicine scans). Its 6-hour half-life is ideal — long enough to image the body but short enough that 99.6% decays within 48 hours, minimising patient radiation exposure.