Half-Life Calculator Calculate radioactive decay, remaining quantity, and decay time — with exponential decay visualizati...
Half-Life Calculator
Calculate radioactive decay, remaining quantity, and decay time — with exponential decay visualization and real-world examples.
| Half-Lives | Time | Remaining Amount | Percentage Remaining |
|---|---|---|---|
| 0 | 0 days | 100.00 g | 100.00% |
| 1 | 5 days | 50.00 g | 50.00% |
| 2 | 10 days | 25.00 g | 25.00% |
Half-life is the time required for half of the radioactive atoms in a sample to decay.
Key Concepts**:
- Exponential Decay**: The decay follows an exponential pattern, not linear
- Constant Rate**: Each isotope has a unique, unchanging half-life
- Independent of Amount**: Half-life is the same regardless of sample size
- Decay Constant**: Related to half-life by λ = ln(2) / T
Mathematical Formula**:
N(t) = N₀ × (1/2)^(t/T)
Where N(t) = amount at time t, N₀ = initial amount, T = half-life
✅ Example**: Carbon-14 has a half-life of 5,730 years. After 11,460 years (2 half-lives), 25% remains.
⚠️ Avoid these frequent errors:
- Linear vs Exponential**: Assuming decay is linear (50% after 1 half-life, 0% after 2) instead of exponential
- Unit consistency**: Mixing different time units (hours vs days vs years)
- Logarithm base**: Using common log instead of natural log or base-2 log
- Negative time**: Getting negative values due to incorrect formula application
- Infinite decay**: Forgetting that theoretically, radioactive material never completely disappears
✅ Best Practices**:
- Always use consistent units for time
- Verify that remaining amount is less than initial amount
- Use the correct logarithmic base for calculations
- Remember that after 10 half-lives, only about 0.1% remains
Half-life calculations are essential in:
- Archaeology**: Carbon-14 dating of organic materials
- Medicine**: Radioactive tracers and cancer treatment
- Nuclear Physics**: Reactor design and waste management
- Geology**: Dating rocks and geological formations
- Environmental Science**: Tracking pollutant decay
📊 Example Use Cases**:
- Carbon Dating**: Determine age of ancient artifacts using C-14 half-life (5,730 years)
- Medical Imaging**: Iodine-131 (8 days half-life) for thyroid diagnostics
- Nuclear Waste**: Plutonium-239 (24,000 years half-life) requires long-term storage
- Radiation Therapy**: Cobalt-60 (5.27 years half-life) for cancer treatment
➡️ Remaining Quantity
"100g initial, 5-day half-life, after 10 days" → 25.00g remaining
➡️ Decay Time
"100g to 25g with 5-day half-life" → 10.00 days elapsed
➡️ Find Half-Life
"100g to 50g in 5 days" → 5.00 days half-life
➡️ Common Isotopes
"Carbon-14, 100g, 10,000 years" → 29.87g remaining
Note: All calculations use the exponential decay formula N(t) = N₀ × (1/2)^(t/T). Results are rounded to 2 decimal places for clarity.