Calculator Inputs
Example Data Table
| Isotope | Basis | Start | Half-life | Elapsed / Target | Result |
|---|---|---|---|---|---|
| Carbon-14 | Mass | 100 g | 5730 years | 11460 years elapsed | 25 g remaining |
| Iodine-131 | Activity | 20 MBq | 8.02 days | 24.06 days elapsed | 2.5 MBq remaining |
| Cobalt-60 | Mass | 5 g | 5.27 years | 50% remaining target | 5.27 years required |
| Unknown sample | Atoms | 1.00e8 atoms | Estimated | 1.00e8 to 5.00e7 in 12 hours | 12-hour half-life |
Formula Used
General decay law: N(t) = N0e-λt
Quantity falls exponentially with time when the decay constant stays fixed.
Decay constant from half-life: λ = ln(2) / T1/2
A shorter half-life creates a larger decay constant and faster decline.
Activity relation: A = λN
Activity is directly proportional to the number of undecayed nuclei.
Mean life: τ = 1 / λ
Mean life is the average lifetime of a nucleus in the sample.
Time to a target fraction: t = -ln(f) / λ
Here, f is the remaining fraction, such as 0.25 for 25%.
Half-life from two measurements: T1/2 = Δt × ln(2) / ln(N1/N2)
Use consistent units for both measurements, then apply the measured interval.
How to Use This Calculator
- Choose a solve mode: predict quantity, find target time, or estimate half-life.
- Select the quantity basis: mass, atoms, or activity.
- Enter the sample name and atomic mass if conversion support is needed.
- Fill in half-life, elapsed time, target quantity, or measured values as required.
- Set the graph span in half-lives to control the plotted timeline.
- Press the calculate button to view results above the form.
- Use the CSV button for spreadsheets and the PDF button for printable reports.
Frequently Asked Questions
1) What does this calculator solve?
It predicts remaining quantity, finds time to reach a target, or estimates half-life from two measured values. It also reports decay constant, mean life, activity, and helpful conversions.
2) Can I use mass, atoms, or activity?
Yes. You can work directly with mass, number of atoms, or radioactive activity. The decay fraction is the same for all three because each follows the same exponential law.
3) Why is atomic mass optional?
Atomic mass is only needed when you want mass-to-atoms or activity-to-mass conversions. Pure decay timing still works without it because half-life and decay constant alone determine the fraction remaining.
4) What happens if I enter the half-life in years and time in days?
That is fine. The calculator converts everything into a common base internally, then reports the result in the units tied to your chosen input fields.
5) Why does the graph curve drop quickly at first?
Exponential decay always drops fastest in absolute terms when the sample is largest. As the quantity shrinks, the same fractional loss produces a smaller absolute change.
6) Can I use activity data to estimate half-life?
Yes. Because activity is proportional to the number of undecayed nuclei, the same ratio method used for mass or atoms also works for activity measurements.
7) Why can’t the second measurement exceed the first?
For a simple decay estimate, the later value must be smaller than the earlier value. A larger reading suggests growth, background effects, or measurement issues outside this model.
8) Are the exports useful for reports or lab notes?
Yes. The CSV export works well for spreadsheets, while the PDF export captures the result summary and graph for reports, coursework, handouts, or documentation.