Half-Life Calculator Formula
Understand the math behind the half-life calculator. Each variable explained with a worked example.
Formulas Used
Half-Life
half_life = -time_elapsed * log(2) / log(remaining_amount / initial_amount)Decay Constant
decay_constant = -log(remaining_amount / initial_amount) / time_elapsedVariables
| Variable | Description | Default |
|---|---|---|
initial_amount | Initial Amount | 100 |
remaining_amount | Remaining Amount | 25 |
time_elapsed | Time Elapsed(years) | 11460 |
How It Works
Half-Life Determination
The half-life can be computed from measured decay data.
Formula
t_half = -t * ln(2) / ln(N/N_0)
The decay constant is lambda = ln(2) / t_half. This connects the exponential decay rate to the half-life.
Worked Example
A sample starts at 100 units and has 25 remaining after 11,460 years.
- 01t_half = -t * ln(2) / ln(N/N0)
- 02t_half = -11460 * 0.6931 / ln(25/100)
- 03t_half = -11460 * 0.6931 / (-1.3863)
- 04t_half = 7940 / 1.3863
- 05t_half = 5730 years (Carbon-14)
Frequently Asked Questions
What are some common half-lives?
Uranium-238: 4.5 billion years. Carbon-14: 5,730 years. Iodine-131: 8 days. Radon-222: 3.8 days. Polonium-214: 164 microseconds.
What is the decay constant?
The probability of a single atom decaying per unit time: lambda = ln(2)/t_half. Higher lambda means faster decay.
Does every atom decay at the half-life?
No. Decay is probabilistic. Each atom has a constant probability of decaying per unit time. The half-life is a statistical measure for large populations.
Learn More
Guide
Understanding Radioactive Decay
A complete guide to radioactive decay. Learn about alpha, beta, and gamma decay, half-life calculations, decay chains, carbon dating, and nuclear stability.
Ready to run the numbers?
Open Half-Life Calculator