Half-Life Calculator
Calculate remaining quantity, elapsed time, or number of half-lives for radioactive decay using N(t) = N₀ × (½)^(t/t½).
Results
What is it?
Radioactive decay is the spontaneous breakdown of an unstable atomic nucleus. The half-life (t½) is the time required for exactly half of a given quantity of a radioactive isotope to decay. The governing equation is N(t) = N₀ × (½)^(t/t½). After one half-life, 50% remains; after two, 25%; after ten, ~0.1%.
How to use
Enter the initial amount (in any unit — the result uses the same unit), the half-life period, and the elapsed time. Use the same time unit for half-life and elapsed time (e.g., both in years).
Example scenario
Carbon-14 has a half-life of 5,730 years. A fossil contains 25% of the original C-14. Enter initial = 100, half-life = 5730, elapsed = 11460 (two half-lives). Remaining = 25, confirming the sample is approximately 11,460 years old.
Pro tip
Common isotopes and their half-lives: Carbon-14 = 5,730 yr (archaeology), Uranium-238 = 4.47 billion yr (geology), Iodine-131 = 8 days (medical imaging), Technetium-99m = 6 hours (diagnostic imaging). In medicine, isotopes with short half-lives are preferred to minimise radiation dose to the patient.