Half-Life Calculator
Solve exponential decay problems for remaining amount, initial amount, elapsed time, half-life, and decay constant. Includes a decay curve and same-unit time inputs.
Enter t and T1/2 in the same units: seconds, minutes, hours, days, or years.
Half-life T1/2 is the time it takes for an amount, activity, or concentration to decrease by half. The model applies to radioactive isotopes, first-order reactions, and simple elimination models, but it does not replace reference nuclide data, radiation-dose calculations, or medical guidance.
What this half-life calculator solves
English search results for half-life calculator pages focus on a practical exponential decay solver: enter the known values, choose what is missing, and calculate the remaining amount, elapsed time, half-life, initial amount, or decay constant.
- Find remaining amount N(t) from an initial amount, half-life, and elapsed time.
- Find when the starting amount, remaining amount, and elapsed time are known.
- Find elapsed time t for a substance to decay from N0 to N.
- Find the original amount N0 from the remaining amount, half-life, and time.
Half-life formulas
N(t) is the remaining amount, N0 is the initial amount, t is elapsed time, and T1/2 is the half-life.
lambda is the decay constant in the selected inverse time unit.
The decay constant is larger when the half-life is shorter.
Use this rearranged form when N0, N, and t are known.
Use this rearranged form to find elapsed time.
How to read the result
| Output | Meaning |
|---|---|
| Remaining N(t) | Amount, activity, concentration, or percent left after the selected time |
| Half-lives elapsed | How many half-life intervals have passed |
| Decay constant lambda | First-order decay rate per selected time unit |
| Decay curve | Graph of the same exponential model across time |
Common half-life examples
The default values use a carbon-14 style example:, years, and years gives 25 remaining, or two half-lives elapsed.
| Example | Typical use |
|---|---|
| Carbon-14 | Radiocarbon dating and classroom decay problems |
| Technetium-99m | Nuclear medicine activity estimates |
| First-order chemical reactions | Concentration decay over time |
| Drug elimination models | Simple educational clearance estimates |
Important limits
- The calculator assumes one first-order exponential decay process.
- It does not model decay chains, branching ratios, daughter products, shielding, dose, exposure, or detector response.
- For specific radionuclides, verify the half-life in an authoritative nuclide database before using the result.
- For drugs or biological half-life, the result is only a simple mathematical estimate and must not be used for dosing or medical decisions.
Frequently Asked Questions
Sources and References
- Half-lifeU.S. Nuclear Regulatory Commission
- Properties of Radioactive Isotopes: An OverviewCDC
- LiveChart of Nuclides - Advanced versionIAEA
Calculations are based on the listed reference sources. Links open in a new tab.
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