Radioactive Decay Half-Life Calculator
Calculate remaining radioactive material after any time period.
☢️ Science📐 N(t) = N₀ × (½)^(t/t½)
Initial amount
Half-life (any time unit)
Time elapsed (same unit)
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Radioactive Decay Half-Life Calculator | N(t) = N₀ × (½)^(t/t½) | % remaining |
Step-by-Step Examples
Example 1
Carbon-14 Dating
100 initial, t½ = 5730 yr, elapsed 11460 yr.
- 2 half-lives | Remaining: 100×(½)² = 25
✓ 25% remaining
Example 2
Medical I-131
100 units, t½ = 8 days, elapsed 24 days.
- 3 half-lives | Remaining: 12.5%
✓ 12.5%
Example 3
Uranium-238
100, t½ = 4.47e9 yr, elapsed 1e9 yr.
- 0.224 half-lives | Remaining: 85.7%
✓ 85.7%
Real-World Applications
Nuclear Scientists
Calculate radioactive decay for any isotope.
Medical Physicists
Calculate radiation timing for nuclear medicine.
Chemistry Students
Learn radioactive decay with real data.
Archaeologists
Understand carbon-14 dating principles.
Common Mistakes to Avoid
⚠️
Half-life vs mean lifetime
Mean lifetime τ = t½/ln(2) ≈ 1.443×t½. After one mean lifetime 36.8% remains (not 50%).
⚠️
Time units
Half-life and elapsed time must use same units.
Frequently Asked Questions
Carbon-14 dating? ▾
t½ = 5,730 yr. Living organisms maintain C-14/C-12 ratio; after death C-14 decreases.
When is a substance safe? ▾
~10 half-lives → 0.1% remaining. Iodine-131: 80 days. Cesium-137: 300 years.
Decay constant? ▾
λ = ln(2)/t½. Activity A = λN atoms.