Half-Life Decay Calculator
Solve first-order exponential decay from initial amount, remaining amount, half-life, or elapsed time with a step schedule.
At a glance
- Computes
- First-order decay solved for initial amount, remaining amount, half-life, or elapsed time.
- You supply
- Any three of initial amount, remaining amount, half-life, and elapsed time.
- Use when
- A quantity decays in proportion to what remains, at a constant half-life.
- Not for
- A rate constant that varies with temperature. Activation Energy Calculator
Remaining quantity (example) against Elapsed time (seconds), logarithmic vertical axis
Decay result
Enter three values
First-order exponential decay.
| Step | Elapsed | Remaining | Percent |
|---|
N(t) = N0 * (1 / 2)^(t / h); lambda = ln(2) / h
How?
How this is calculated
The solver uses first-order exponential decay with a constant half-life. The schedule lists whole half-life steps from the solved initial amount.
Formula: N(t) = N0 * (1 / 2)^(t / h); lambda = ln(2) / h
Radioactive decay
Radioactive decay is first order: the number of decays per second is proportional to how many nuclei remain. The proportionality constant is lambda, the natural logarithm of 2 divided by the half-life. Mean lifetime is its reciprocal, so it equals the half-life divided by ln 2 and is longer than the half-life because the surviving tail is long.
Activity
Activity is lambda times the number of nuclei and is reported in becquerels, one decay per second. Enter a nuclei count or an amount in moles to calculate it. The curie equivalent uses the exact definition 1 Ci = 3.7e10 Bq. The tool bundles no isotope table: you supply both the half-life and amount, so the calculation never guesses a nuclide.
Which carbon-14 half-life to use
The measured carbon-14 half-life is 5,730 years. Conventional radiocarbon ages use the older Libby half-life of 5,568 years so published ages remain comparable, then calibration curves convert that conventional age to calendar time. Enter the value used by your source. This page performs exponential decay only and does not perform archaeological calibration, contamination correction, or reservoir correction.
Sources
- OpenStax College Physics 2e, Half-Life and Activity. OpenStax. Retrieved .
- Wikipedia, Half-life. Wikipedia. Retrieved .
- Wikipedia, Exponential decay. Wikipedia. Retrieved .
Method last reviewed