About the Radioactive Decay Calculator
What is the Radioactive Decay Calculator?
Radioactive decay is exponential: in each half-life, half of the remaining atoms decay. This calculator finds how much is left after any time.
It works with grams, numbers of atoms or activity in becquerels, as long as the half-life and time use the same unit.
How to use the Radioactive Decay Calculator
- Initial Amount (g, atoms or Bq) (sample: 100)
- Half-Life (sample: 10)
- Time Elapsed (same unit as the half-life) (sample: 20)
- Press Calculate Remaining Amount (results also refresh as you type). The result card shows the Amount Remaining, along with Fraction remaining, Amount decayed, Half-lives elapsed and Decay constant λ.
Formula used
N = N₀ × (½)^(t ÷ t½)
- Decay constant = λ = ln 2 ÷ t½
- Mean lifetime = τ = t½ ÷ ln 2
Decay is random for individual atoms but predictable for large numbers.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Initial Amount (g, atoms or Bq) | 100 |
| Half-Life | 10 |
| Time Elapsed (same unit as the half-life) | 20 |
| Result | Value |
|---|---|
| Amount Remaining | 25 |
| Fraction remaining | 25% |
| Amount decayed | 75 |
| Half-lives elapsed | 2 |
| Decay constant λ | 0.069315 per time unit |
| Mean lifetime τ | 14.427 time units |
Tips for using the Radioactive Decay Calculator
- After 10 half-lives, less than 0.1% remains.
- Activity (Bq) decays with the same half-life as the amount.