Half-life calculator
How much of a substance remains after a time, or the half-life or time from the amounts.
About this calculator
This half-life calculator works out how much of a substance is left after a given time, for radioactive isotopes, medicines or anything that decays exponentially.
It can also find the half-life, the time taken or the starting amount, and shows the decay constant and mean lifetime.
How it works
Each half-life cuts the amount in half: N = N₀ × (1/2)^(t ÷ T), where T is the half-life. Rearranged, the time is T × log₂(N₀ ÷ N) and the half-life is t × ln 2 ÷ ln(N₀ ÷ N).
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Worked example
- Find: Amount remaining
- Starting amount: 100
- Half-life: 5,730
- Time elapsed: 10,000
Amount remaining: 29.8292436424
Common questions
What is half-life?
The time it takes for half of a substance to decay or be removed. After two half-lives a quarter is left, and after three an eighth.
How much is left after 5 half-lives?
1/32 of the starting amount, about 3.1%. After 10 half-lives, less than 0.1% remains.
Does half-life apply to medicines?
Yes. A drug's half-life is how long the body takes to clear half of it. Most drugs are largely gone after about 4 to 5 half-lives.
Sources and further reading
The story behind it
Where the idea came from: The term half-life was coined by Ernest Rutherford in 1907, from his work on radioactive decay.
In the late 1940s Willard Libby used the steady decay of carbon-14 to date ancient remains, winning the Nobel Prize in Chemistry in 1960. Carbon-14's half-life is about 5,730 years.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
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