Calculator
Choose a mode, enter values, and calculate isotope decay behavior.
Example data table
These sample rows show how half-life changes remaining quantity over time.
| Isotope | Initial quantity | Half-life | Elapsed time | Remaining quantity |
|---|---|---|---|---|
| Carbon-14 | 100 g | 5730 years | 5730 years | 50 g |
| Iodine-131 | 80 MBq | 8.02 days | 16.04 days | 20 MBq |
| Technetium-99m | 12 mCi | 6.01 hours | 12.02 hours | 3 mCi |
| Cobalt-60 | 25 g | 5.27 years | 21.08 years | 1.5625 g |
Formula used
Core decay equation
N = N₀ × e-λt
N is remaining quantity. N₀ is initial quantity. λ is decay constant. t is elapsed time.
Half-life relation
λ = ln(2) / t1/2
The decay constant comes directly from the isotope half-life.
Elapsed time from two quantities
t = ln(N₀ / N) / λ
Use this when you know the starting amount and the remaining amount.
Half-life from measured decay
t1/2 = t × ln(2) / ln(N₀ / N)
This rearrangement estimates half-life from experimental data.
Activity relation
A = A₀ × e-λt
Activity drops with the same exponential pattern as quantity.
How to use this calculator
- Select the calculation mode that matches your chemistry task.
- Choose a preset isotope or type your own isotope label.
- Enter the half-life and choose the correct time unit.
- Add elapsed time, initial quantity, or remaining quantity as needed.
- Optionally enter activity if you also want activity output.
- Press calculate to show results, graph, and export options.
Frequently asked questions
1. What does this isotope decay calculator measure?
It estimates remaining quantity, initial quantity, elapsed time, half-life, or decay constant. It also shows activity decay when you enter an initial activity value.
2. Can I use grams, moles, or atoms here?
Yes. The calculator works with any consistent quantity unit. Enter the unit label you prefer, then keep all quantity inputs in that same unit.
3. Does activity decay differently from mass?
No. Activity follows the same exponential decay pattern as the number of unstable nuclei. That is why the same decay equation can estimate both.
4. Why must remaining quantity be smaller than initial quantity?
For a normal decay calculation, radioactive material decreases over time. A remaining amount equal to or larger than the initial value would not match standard decay behavior.
5. What is the decay constant λ?
The decay constant is the probability rate of decay per time unit. Larger λ values mean faster decay and a shorter half-life.
6. Can this tool estimate half-life from lab observations?
Yes. Use the half-life mode, then provide elapsed time, initial quantity, and remaining quantity. The calculator rearranges the decay equation to estimate half-life.
7. Are preset isotope values fixed?
They are convenience defaults for common isotopes. You can replace them with your own half-life value whenever your reference source uses different rounded data.
8. What does the graph show?
The graph plots remaining quantity over time and also shows remaining percentage. When available, your current calculated result is marked on the curve.