Calculator Input
Choose a target variable, enter the known values, and submit the form. Results appear above the form and the graph updates automatically.
Decay Curve Visualization
The graph plots quantity decay over time using the solved or entered decay constant. When initial activity is supplied, activity values decay proportionally.
Example Data Table
| Sample | Initial Quantity | Half-Life | Elapsed Time | Final Quantity | Remaining % |
|---|---|---|---|---|---|
| Carbon-14 Example | 1000 atoms | 5730 years | 5730 years | 500 atoms | 50% |
| Iodine-131 Example | 800 mg | 8 days | 16 days | 200 mg | 25% |
| Generic Lab Sample | 2500 counts | 12 hours | 36 hours | 312.5 counts | 12.5% |
Formula Used
Primary decay equation: N(t) = N₀e-λt
Half-life relation: T1/2 = ln(2) / λ
Decay constant from known values: λ = ln(N₀ / N) / t
Elapsed time: t = ln(N₀ / N) / λ
Remaining percentage: Remaining % = (N / N₀) × 100
Activity model: A(t) = A₀e-λt
These equations assume ideal exponential decay with a constant decay rate. They are widely used in physics, archaeology, medicine, and laboratory quality checks.
How to Use This Calculator
- Select the target variable from the Solve For list.
- Enter the known decay values. You may provide either decay constant or half-life.
- Choose consistent time, quantity, and activity units before calculating.
- Press Calculate Now to place the result summary above the form.
- Review the graph to see how quantity changes across the time range.
- Use the CSV or PDF buttons to export the results.
Frequently Asked Questions
1. What does this solver calculate?
It can solve final quantity, initial quantity, decay constant, half-life, elapsed time, remaining percentage, and final activity from the values you already know.
2. Can I enter half-life instead of decay constant?
Yes. The calculator automatically converts half-life into the decay constant using ln(2) divided by half-life, then uses that value in every related equation.
3. Why must final quantity be lower than initial quantity?
For normal radioactive decay, the remaining amount decreases over time. A larger final value would contradict the decay model unless additional production or measurement issues exist.
4. What units should I use?
Use any units you want, but stay consistent. If half-life uses years, elapsed time should also use years for correct results.
5. Does the activity graph follow the same decay pattern?
Yes. Activity decreases exponentially at the same fractional rate as quantity, so its curve has the same shape when you provide an initial activity.
6. Can this tool help with archaeology or radiometric dating?
Yes. The same exponential model supports age estimation and remaining fraction analysis in dating work, provided the input assumptions and isotope data are valid.
7. Why does the solver reject negative time?
Negative elapsed time would imply moving backward from the reference state. Standard decay problems treat time as zero or greater for meaningful interpretation.
8. What do the export buttons save?
The CSV button saves the computed result table. The PDF button creates a simple report containing the same result summary for sharing or recordkeeping.