Half-Life Calculator
Track radioactive decay: solve for the amount remaining, the time elapsed, or the half-life itself.
Radioactive decay follows remaining = initial × (½)^(t / half-life). Pick what you want to find, then fill in the rest. Keep the time and half-life in the same units — seconds, years, whatever fits your isotope.
Remaining amount
25
Fraction remaining
25%
How it works
A half-life is the time it takes for half of a radioactive sample to decay. It's a fixed property of each isotope — carbon-14's is about 5,730 years, while some medical isotopes vanish in hours. After one half-life you have 50% left, after two you have 25%, after three 12.5%, and so on down the curve.
The math behind it is remaining = initial × (½) raised to the number of half-lives elapsed, where that number is just time divided by the half-life. Start with 100 grams and wait two half-lives and you're left with 25 grams. Because the decay is exponential, the sample never quite reaches zero — it just keeps halving.
Switch what you're solving for depending on what you know. Have the half-life and want the leftover amount? Solve for remaining. Know how much decayed and want to date the sample? Solve for time — that's the idea behind radiocarbon dating. Keep your time and half-life in the same units and the answer comes out in those units too.
Frequently asked questions
Does the starting amount change the half-life?
No. Half-life is independent of how much you start with — a gram and a kilogram of the same isotope both lose half their atoms in the same span. That's what makes it such a reliable clock for dating.
How is this used for carbon dating?
Living things absorb carbon-14, which stops when they die and then decays with a 5,730-year half-life. By measuring how much is left compared to a living sample, you solve for elapsed time — exactly the 'solve for time' mode here.
Why can't the sample fully disappear?
Because each half-life removes only half of what remains, not a fixed amount. Mathematically you keep halving forever, so the curve approaches zero without ever touching it — though in practice the count eventually becomes negligible.