Calculator
Use N = N₀ × (1/2)^(t/t½). Time and half-life must use the same unit; the default values are unitless.
Formula and assumptions
N = N₀ × (1/2)^(t/t½)
This idealized model applies a constant half-life and is intended for learning and calculation checks. It does not assess radiation exposure, isotope handling or safety.
Assumption: The decay rate and half-life are constant over the interval.
Variables and units
Worked example
After two half-lives, 25% of the initial amount remains.
Fraction remaining after each half-life
| Half-lives elapsed | Fraction remaining | Percent remaining |
|---|---|---|
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
| 10 | 1/1024 | 0.098% |
Iodine-131, used in medicine, has a half-life of about 8 days: after 24 days (three half-lives) about 12.5% remains. Carbon-14 has a half-life of about 5,700 years, so a sample with a quarter of its original carbon-14 is roughly 11,400 years old. Decay never reaches exactly zero; after ten half-lives just under 0.1% remains.
Important limits
It is a learning model only and must not be used to assess radiation exposure, handling or safety.
Reference and related tools
OpenStax: Nuclear chemistry. Return to Chemistry Calculators for the other tools in this group.