Calculator Inputs
Example Data Table
| Scenario | Isotope | Initial Amount | Half-Life | Elapsed Time | Remaining Amount |
|---|---|---|---|---|---|
| Sample A | Radium-226 | 100 g | 1600 Years | 800 Years | 70.7107 g |
| Sample B | Radium-226 | 100 g | 1600 Years | 1600 Years | 50 g |
| Sample C | Radium-226 | 100 g | 1600 Years | 3200 Years | 25 g |
| Sample D | Radium-228 | 80 g | 5.75 Years | 11.5 Years | 20 g |
Formula Used
This calculator applies exponential radioactive decay relationships for mass, activity, or any proportional quantity.
Remaining amount: N = N0 × (1/2)t / T1/2
Elapsed time: t = T1/2 × log(N0 / N) / log(2)
Half-life: T1/2 = t ÷ [log(N0 / N) / log(2)]
Decay constant: λ = ln(2) ÷ T1/2
When the quantity halves once, one half-life has passed. The graph extends the same rule across your selected time span.
How to Use This Calculator
- Choose the solving mode based on the unknown value.
- Pick a radium preset or switch to a custom half-life.
- Enter initial amount, remaining amount, or elapsed time as needed.
- Set consistent time units for half-life and elapsed time.
- Click calculate to show results above the form.
- Review the graph, percent decay, and decay constant.
- Use the export buttons to save a CSV or PDF report.
Frequently Asked Questions
1. What does this radium half-life calculator solve?
It solves remaining amount, initial amount, elapsed time, or half-life. It also shows percent decay, percent remaining, decay constant, and a decay curve.
2. Can I use mass or activity values?
Yes. The decay ratio works for grams, milligrams, curies, becquerels, or any proportional quantity. Just keep the same unit for initial and remaining values.
3. Why are isotope presets included?
Different radium isotopes decay at different speeds. Presets reduce manual entry errors and help you compare short and long half-life behavior quickly.
4. What happens if remaining amount exceeds initial amount?
That input violates simple decay behavior. The calculator stops and asks for correction because radioactive decay cannot increase the original amount in this model.
5. Is the graph based on measured data?
No. The chart is a theoretical decay curve built from your entries. It helps visualize the exponential trend and the position of your current result.
6. Can I estimate half-life from two measurements?
Yes. Choose the half-life mode, enter initial amount, remaining amount, and elapsed time, then calculate. The tool derives half-life from the observed decay ratio.
7. Why are time units important?
Time units must stay consistent during conversion. This file handles hours, days, and years automatically, then converts everything internally before solving.
8. When should engineers use this calculator?
It is useful for shielding studies, source aging checks, storage reviews, calibration planning, educational analysis, and quick scenario comparisons involving radium decay.