Half-life decay calculator
Enter the starting amount, the half-life and the elapsed time, both times in the same unit, to see what remains.
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How to use it
- Enter initial amount n0, half-life t½ and elapsed time t (same unit as half-life).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
N = N0 × (1/2)^(t ÷ T½); decay constant λ = ln 2 ÷ T½.
Example
Inputs: Initial amount N0 = 100, Half-life T½ = 5,730, Elapsed time t (same unit as half-life) = 11,460. Result: Remaining amount N: 25; Fraction remaining: 25%; Number of half-lives: 2.
Limits and caveats
- Time and half-life must use the same unit, years, days or hours.
- Decay is random, so the result is an average that holds for large samples, not a handful of atoms.
Questions about this tool
How much is left after two half-lives?
A quarter, 25% of the original; after three half-lives, an eighth.
What is the half-life of carbon-14?
The commonly used value is about 5730 years, the basis of radiocarbon dating.
Can I use it for how long a drug stays in the body?
Roughly, when elimination is first-order, but always follow your doctor or pharmacist.