Radioactive decay: remaining quantity, half-life, mean lifetime and decay constant.
How to use this calculator
Every field updates the result as you type — there is no submit step. The inputs below are pre-filled with a realistic example so you can see how the tool behaves before entering your own figures.
| Field | Unit | What it means |
|---|---|---|
| Initial quantity | — | Enter a numeric value. |
| Half-life | — | Enter a numeric value. |
| Elapsed time | — | Enter a numeric value. |
| Time unit label | — | Enter a numeric value. |
Formula
The calculation is based on the following relationship:
N(t) = N₀ · (1/2)^(t / t½)
Worked example
Using the default values loaded into the calculator above, the result is:
| Input | Value |
|---|---|
| Initial quantity | 100 |
| Half-life | 5730 |
| Elapsed time | 10000 |
| Time unit label | years |
| Output | Value |
|---|---|
| Remaining after 10,000 years | 29.82924364 |
| Fraction remaining | 29.829244% |
| Amount decayed | 70.17075636 |
| Half-lives elapsed | 1.745201 |
| Decay constant λ | 0.0001209681 per years |
| Mean lifetime τ | 8,266.642584 years |
| Time to 1% remaining | 38,069.296 years |
Precision and rounding
Calculations run in IEEE 754 double precision, giving about 15–17 significant decimal digits. Displayed values are rounded for readability while the full precision is retained internally, so intermediate rounding never accumulates into the final answer.
Very large or very small magnitudes switch automatically to scientific notation.
Sharing and saving a calculation
The "Copy link" button encodes every value you have entered into the page URL. Opening that link restores the calculation exactly, which makes it easy to bookmark a scenario, send it to someone else, or keep several variations side by side in separate tabs.
Frequently asked questions
What does the Half-Life Calculator do?
Radioactive decay: remaining quantity, half-life, mean lifetime and decay constant.
What result do the default values produce?
With the values pre-loaded in the calculator, remaining after 10,000 years comes to 29.82924364.
Is this calculator free to use?
Yes. It is free, requires no account, and runs entirely in your browser — nothing you enter is transmitted or stored on a server.
Can I save or share a calculation?
Yes. The "Copy link" button builds a URL containing all your entered values. Anyone opening that link sees the same calculation.
What formula does the Half-Life Calculator use?
N(t) = N₀ · (1/2)^(t / t½)
How accurate is the result?
Calculations use double-precision floating point, accurate to roughly 15 significant digits. Displayed values are rounded for readability only.