Half-Life Calculator
Calculate remaining quantity after radioactive or exponential decay from half-life and elapsed time, plus decay constant and mean lifetime.
Last reviewed by the Radiatus Cloud team
N(t) = N₀ × (1/2)t / t½. Common half-lives: Carbon-14 ≈ 5,730 years, Iodine-131 ≈ 8.02 days, Caesium-137 ≈ 30.1 years.
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How much is left after a given time
Half-life is the time for a quantity to halve through exponential decay, and it describes radioactive materials, drug concentrations in the body, and any process that decays at a rate proportional to what remains. This calculator finds the remaining quantity after a given time from the half-life and the starting amount.
Why halving is not linear
The counter-intuitive thing about half-life is that the quantity never simply runs out on a schedule. After one half-life, half remains; after two, a quarter; after three, an eighth. It approaches zero but by ever-smaller steps, which is why a substance with a short half-life still leaves a trace long after, and why the number of half-lives elapsed, not the raw time, is what determines how much is left.
Across physics, medicine and more
The same mathematics governs carbon dating, nuclear safety, medication dosing intervals and the decay of many natural processes. Being able to compute the remaining fraction from the half-life makes those problems concrete. The calculation runs in your browser, so your figures are not uploaded.
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Frequently Asked Questions
What is a half-life?
The time it takes for a quantity to halve through exponential decay. It is constant, so the substance halves again in each successive half-life period.
Why does the quantity never reach zero?
Because each half-life removes only half of what remains, so it approaches zero by ever-smaller steps rather than running out on a fixed schedule.
What determines how much is left?
The number of half-lives that have elapsed, not the raw time. After n half-lives, the fraction remaining is one over two to the power n.
Where does half-life apply?
Radioactive decay, carbon dating, drug concentrations in the body, and any process that decays proportionally to what remains.
Is my input uploaded?
No. The calculation runs entirely in your browser.
Privacy & Security
Runs entirely in your browser. No data is sent to any server.
How to Use
Enter the initial quantity, the half-life and the elapsed time in the same unit. Results update as you type.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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