The formula
How it works
A half-life is the time it takes for half of a substance to decay away. Enter a starting amount, the half-life and how much time has passed to find how much is left — for radioactive decay, medicines and more.
FAQ
Does everything decay to nothing eventually?
In theory it keeps halving forever and never quite reaches zero, but in practice the amount becomes negligible after about ten half-lives, when less than 0.1% remains.
What has a half-life?
Radioactive isotopes are the classic example, but the same maths describes how a drug clears from your body, how a charged capacitor discharges, and any process where the rate of decay is proportional to how much is left.
How is half-life different from mean lifetime?
Half-life is the time for half the substance to decay, while mean lifetime is the average time a single particle survives; the two are related by a constant factor, with mean lifetime being about 1.44 times the half-life.
Can I work out the half-life from two measurements instead?
Yes — if you know the amount at two different times, you can rearrange the decay formula to solve for the half-life itself rather than the amount remaining, though this calculator is set up to solve for the remaining amount directly.
Why do different isotopes have such different half-lives?
Half-life depends on the stability of the atomic nucleus, which is governed by nuclear forces rather than external conditions, so it can range from a fraction of a second to billions of years depending on the isotope.
Does temperature or pressure change a half-life?
For radioactive decay, no — half-life is a nuclear property essentially unaffected by ordinary temperature, pressure or chemical state, unlike many chemical reaction rates.
What does the decay constant tell me?
The decay constant (λ) is the fraction of the remaining substance that decays per unit time, and it is simply another way of expressing the same half-life using the natural exponential form of the decay equation.
About the half-life calculator
This calculator works out how much of a substance remains after a period of decay, using its half-life — the time for the amount to halve. Half-life is the natural way to describe exponential decay, because no matter how much you start with, it always takes the same time to drop by half. From carbon dating to drug dosing, the same simple rule applies, and this tool makes it easy to apply.
How to use it
Enter the starting amount, the half-life, and how much time has passed — keeping the half-life and elapsed time in the same units (both in years, or both in hours, and so on). The calculator returns the amount remaining, the number of half-lives that have elapsed, and the percentage left. For example, 100 units with a half-life of 5 leaves 25 after 10 units of time, because that is two half-lives.
The formula
The amount remaining is , where is the starting amount, is the time elapsed and is the half-life. The exponent is simply how many half-lives have gone by. The related decay constant is , which lets you write the same decay as .
Where it is used
Half-life is central to nuclear physics and chemistry, where it dates ancient objects through carbon-14 and describes the decay of radioactive isotopes. In medicine it tells doctors how quickly a drug leaves the body, which sets dosing schedules. It also appears in pharmacology, environmental science tracking pollutants, and electronics, wherever something decays at a rate proportional to its current amount.