Radioactive Decay Calculator Formula
Understand the math behind the radioactive decay calculator. Each variable explained with a worked example.
Formulas Used
Remaining Amount
remaining = initial_amount * pow(0.5, time_elapsed / half_life)Amount Decayed
decayed = initial_amount - initial_amount * pow(0.5, time_elapsed / half_life)Fraction Remaining
fraction_remaining = pow(0.5, time_elapsed / half_life)Variables
| Variable | Description | Default |
|---|---|---|
initial_amount | Initial Amount(g) | 100 |
half_life | Half-Life(years) | 5730 |
time_elapsed | Time Elapsed(years) | 11460 |
How It Works
Radioactive Decay
Radioactive materials decay at a rate characterized by the half-life.
Formula
N = N_0 * (1/2)^(t / t_half)
where N_0 is the initial amount, t is elapsed time, and t_half is the half-life. After each half-life, exactly half the material remains.
Worked Example
100 g of Carbon-14 (half-life 5730 years) after 11,460 years (2 half-lives).
- 01N = N0 * (1/2)^(t/t_half)
- 02N = 100 * (1/2)^(11460/5730)
- 03N = 100 * (1/2)^2
- 04N = 100 * 0.25 = 25 g
- 05Decayed: 100 - 25 = 75 g
Frequently Asked Questions
What is a half-life?
The time required for exactly half of a radioactive sample to decay. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on.
How is carbon dating done?
Living organisms absorb Carbon-14. After death, the C-14 decays (t_half = 5730 years). Measuring the remaining fraction reveals the age.
Can half-life be changed?
No. Radioactive decay is a nuclear process unaffected by temperature, pressure, chemical state, or any external conditions.
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 Radioactive Decay Calculator