Calculators
Radioactive Decay and Half-life Calculator
Calculate the amount remaining after a given time from the half-life, the decay constant and mean life, and the time to decay to a target level.
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The tool
Enter your numbers below. Results update as you type, and nothing leaves your browser.
Everything you enter stays on your own machine. Nothing is sent to us or to anyone else, which you can confirm in your browser network tab.
What people use it for
- Physics and chemistry coursework
- Radiocarbon dating estimates
- Medical isotope planning
- Any first-order decay process
About this tool
What the Radioactive Decay and Half-life Calculator does
Radioactive decay is exponential: after each half-life, half of the remaining nuclei have decayed. The remaining amount is N₀ × (½)^(t ÷ T½). The decay constant λ = ln 2 ÷ T½, and the time to fall to any fraction f is T½ × log₂(1 ÷ f). The same maths applies to drug clearance, carbon dating and other first-order processes.
It also works as a radioactive decay calculator or a half-life calculator.
Formula
- N = N₀ × (½)^(t ÷ T½)
- λ = ln 2 ÷ T½; τ = 1 ÷ λ
- Time to target = T½ × log₂(N₀ ÷ N)
Worked example
Using the starting values in the calculator above:
| Input | Value |
|---|---|
| Initial amount | 100 |
| Half-life | 5,730 |
| Time elapsed (same unit as half-life) | 10,000 |
| Target amount remaining | 1 |
| Result | Value |
|---|---|
| Amount remaining | 29.8292 |
| Share remaining | 29.83% |
| Half-lives elapsed | 1.75 |
| Time to reach the target amount | 38,069.296 |
| Decay constant λ (per time unit) | 1.2097 × 10^−4 |
| Mean lifetime τ | 8,266.6426 |
How to read the result
After 10 half-lives, less than 0.1% of the original amount remains.
Keep time units consistent: if the half-life is in years, enter the elapsed time in years.
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Questions
Questions about this tool
The things clients actually want to know — costs, timelines, ownership and what happens after launch.
The time for half of a radioactive substance to decay.
One eighth, or 12.5%.
About 5,730 years.
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