Half-Life Calculator
Exponential decay: amount left, time, half-life or start, with isotopes.
About this tool
Choose what to solve for: the amount remaining, the starting amount, the elapsed time or the half-life. Then fill in the other three, using any time unit as long as it is consistent. Presets load half-lives for carbon-14, uranium-238, plutonium-239, radium-226, caesium-137, tritium, iodine-131, technetium-99m, radon-222 and caffeine. The results include the fraction left, the decay constant and the mean lifetime, with a decay curve.
How half-life works
Radioactive isotopes decay at random, but in a large sample the amount falls by half in each half-life, whatever the starting amount. The amount left is N = N₀ × (½)^(t ÷ T½). After one half-life, 50% remains, after two, 25%, after three, 12.5%, and after ten, about 0.1%. Carbon-14 has a half-life of 5,730 years, so a sample falls from 100 to 25 units in 11,460 years. Radiocarbon dating runs that calculation backwards to estimate the age of once-living material. The decay constant λ = ln 2 ÷ T½ is the fraction decaying per unit time over short intervals. The mean lifetime τ = 1 ÷ λ is the average time an atom survives, about 1.44 half-lives. The same maths describes other first-order processes, such as a drug being cleared from the body. Caffeine's half-life is commonly around five hours in adults but varies widely between people, so the preset is an illustration, not medical advice. The logarithm calculator solves the exponents, the scientific notation converter handles huge half-lives and the compound interest calculator shows exponential growth. Compound interest, explained with real numbers explains the shared maths.
Frequently asked questions
How do I calculate half-life?
T½ = t × ln(0.5) ÷ ln(N ÷ N₀). If 100 units fall to 25 in 11,460 years, the half-life is 5,730 years.
How much is left after 3 half-lives?
One-eighth, or 12.5%: half of a half of a half.
Does half-life depend on the amount?
No. For first-order decay the half-life is constant, whether you start with a gram or a tonne.
Is my data saved?
No. Everything runs in your browser and nothing is stored or sent.