Calculator Inputs
This solver supports remaining quantity, elapsed time, half-life, and decay constant calculations in one page.
Example Data Table
| Scenario | Initial Quantity | Half-life | Elapsed Time | Remaining Quantity |
|---|---|---|---|---|
| Sample A | 100 g | 5 years | 10 years | 25 g |
| Sample B | 80 mg | 3 hours | 6 hours | 20 mg |
| Sample C | 250 counts/min | 12 days | 30 days | 44.19 counts/min |
| Sample D | 120 g | 4 hours | 12 hours | 15 g |
Formula Used
N(t) = N₀ × e^(−λt)N(t) = N₀ × (1/2)^(t / T½)t = ln(N₀ / N) / λT½ = ln(2) / λλ = ln(N₀ / N) / tThis calculator assumes single stage exponential decay. Keep time units consistent across elapsed time, half-life, and decay constant inputs.
How to Use This Calculator
- Select the unknown value you want to solve.
- Choose whether your known rate value is half-life or decay constant.
- Enter the initial quantity and any other required values.
- Add optional quantity and time units for cleaner results.
- Press calculate to show the result above the form.
- Review the stepwise solution, summary table, and graph.
- Use CSV or PDF export to save the result.
- Compare your values with the example table if needed.
Frequently Asked Questions
1. What equation does this calculator use?
It uses the standard exponential decay model. The core forms are N(t) = N₀e^(−λt) and N(t) = N₀(1/2)^(t/T½).
2. Can I use half-life or decay constant?
Yes. For remaining quantity and elapsed time, you can provide either half-life or decay constant. The calculator converts between them automatically.
3. Do time units matter?
Yes. All time-based values must use the same unit system. If time is in years, half-life must also be in years.
4. Why must remaining quantity be smaller than initial quantity?
Radioactive decay reduces the remaining amount over time. For positive elapsed time, the remaining quantity cannot exceed the initial quantity.
5. Can I use mass, atoms, activity, or counts?
Yes. Any proportional quantity works, as long as the same unit is used consistently for initial and remaining values.
6. What does the graph show?
The graph shows the decay curve from time zero forward. A marker highlights the solved point for your submitted scenario.
7. Why are some answers shown in scientific notation?
Very large or very small decay values are easier to read in scientific notation. This keeps the results accurate and compact.
8. Is this valid for every isotope?
It works when the isotope follows simple exponential decay. Multi-step chains and changing environmental conditions need more advanced modeling.