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Half-Life Remaining Quantity — result sheet
What remains of a decaying sample after a given elapsed time.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: N = N₀ × (1/2)^(t / T½).
Each half-life halves the remainder: after 3 half-lives one eighth survives. Zero elapsed time returns the full sample.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Initial quantity — minimum 0; maximum 1000000000
- Half-life — time units; Must be greater than zero.; minimum 1.0E-6; maximum 1000000000
- Elapsed time — time units; Same units as the half-life.; minimum 0; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Initial quantity | 100 |
| Half-life | 5 |
| Elapsed time | 15 |
12.5 remaining after 3 half-lives (1/8 of sample).
Assumptions and limits
- Single constant half-life; no replenishment or competing decay paths.
- Half-life positive; elapsed time zero or positive in matching units.
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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