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Radioactive Activity after Half-Lives Calculator — result sheet
Estimate remaining activity, undecayed fraction, decay constant, and activity lost after a chosen elapsed time and half-life.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: λ = ln(2)/half-life; remaining activity A = A₀e^(−λt); remaining fraction = A/A₀.
Radioactive activity falls exponentially because the decay constant is fixed for the nuclide. Two half-lives leave one quarter of the initial activity, but the same relation also works for fractional half-lives.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Initial activity — Bq; minimum 1.0E-6; maximum 1.0E+30
- Half-life — years; minimum 1.0E-6; maximum 1000000000
- Elapsed time — years; minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Initial activity | 100000 |
| Half-life | 5 |
| Elapsed time | 10 |
Decay constant ≈ 0.13863 per year; remaining activity = 25,000 Bq and 25% remains.
Assumptions and limits
- Half-life and elapsed time use the same time unit, here years.
- The source is treated as a single nuclide with constant decay behavior and no replenishment.
- Shielding, detector response, daughter-product ingrowth, biological dose, and safety decisions are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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