Half-Life Calculator
Half-Life Formula
N₀
Initial quantity at time t = 0
t½
Half-life (time for half to decay)
Common Half-Lives
Related Calculators
Understanding Half-Life
What is Half-Life?
Half-life is the time required for half of a quantity to decay or transform. In nuclear physics, it's the time for half of a radioactive substance to decay. The concept also applies to medicine (drug elimination), chemistry (reaction rates), and other fields.
Decay Formula
Decay Over Time
| Half-Lives | % Remaining | % Decayed | Fraction |
|---|---|---|---|
| 0 | 100% | 0% | 1/1 |
| 1 | 50% | 50% | 1/2 |
| 2 | 25% | 75% | 1/4 |
| 3 | 12.5% | 87.5% | 1/8 |
| 4 | 6.25% | 93.75% | 1/16 |
| 5 | 3.125% | 96.875% | 1/32 |
| 10 | 0.098% | 99.9% | 1/1024 |
Applications
Carbon Dating
Carbon-14 has a half-life of 5,730 years. By measuring the ratio of C-14 to C-12 in organic materials, scientists can determine when an organism died, up to about 50,000 years ago.
Medicine
Drug half-life determines dosing schedules. A drug with a 4-hour half-life needs more frequent doses than one with a 24-hour half-life. After ~5 half-lives, a drug is effectively eliminated.
Nuclear Power
Understanding half-lives helps manage nuclear waste. Uranium-238 remains radioactive for billions of years, while some isotopes decay in days, requiring different handling procedures.
Medical Imaging
Technetium-99m (half-life 6 hours) is used in diagnostic imaging. Its short half-life means patients receive minimal radiation exposure while providing clear images.
Related Concepts
Decay Constant (λ)
λ = ln(2) / t½ ≈ 0.693 / t½
Probability of decay per unit time
Mean Lifetime (τ)
τ = 1/λ = t½ / ln(2) ≈ 1.443 × t½
Average time before decay
Key Points
- Half-life is constant for a given isotope—independent of initial amount
- Radioactive decay is probabilistic; we can only predict average behavior
- After 7 half-lives, less than 1% of the original material remains
- Half-life cannot be changed by temperature, pressure, or chemical reactions
Frequently Asked Questions
What is half-life in simple terms?
Half-life is the time it takes for half of a substance to decay or transform. For radioactive materials, it's the time for half of the atoms to undergo radioactive decay. For example, if you start with 100 grams and the half-life is 10 years, you'll have 50 grams after 10 years, 25 grams after 20 years, and so on.
Why is Carbon-14 used for dating ancient objects?
Carbon-14 has a half-life of about 5,730 years, making it ideal for dating organic materials up to ~50,000 years old. Living organisms constantly replenish C-14 from the atmosphere. When they die, the C-14 decays predictably, allowing scientists to calculate when the organism died by measuring remaining C-14.
How is half-life used in medicine?
Drug half-life determines how long a medication stays active in your body and affects dosing schedules. A drug with a 4-hour half-life needs more frequent doses than one with a 24-hour half-life. After about 5 half-lives, a drug is considered effectively eliminated from the body.
Can you change a radioactive element's half-life?
No, half-life is a constant property of each radioactive isotope and cannot be changed by temperature, pressure, chemical reactions, or any other external factors. This constancy makes radioactive dating methods reliable for scientific measurements.