Radioactive Decay Calculator
A Process That Never Speeds Up or Slows Down
Radioactive decay is one of the few processes in nature that runs on a perfectly fixed clock, unaffected by temperature, pressure, or chemical environment. Every unstable isotope has a characteristic half-life — the time for half of any sample to decay — and that half-life never changes no matter how much material remains. This predictability is what makes radiometric dating and nuclear medicine dosing possible.
The Formula
N0 is the initial amount, N(t) is the amount remaining after time t, and half-life is the isotope's characteristic decay constant, expressed in whatever time unit t is measured in. Because the exponent is a ratio of elapsed time to half-life, the formula works regardless of whether half-life is measured in seconds, days, or years, as long as t uses the same unit.
Where This Clock Is Put to Use
- Radiometric dating — carbon-14 (half-life ~5,730 years) and other isotopes let geologists and archaeologists date organic material and rock formations.
- Nuclear medicine — diagnostic and therapeutic radioisotopes are selected partly by half-life, balancing enough activity to be useful against minimizing a patient's total radiation exposure.
- Nuclear waste management — storage timelines for spent fuel are planned around how long it takes various isotopes to decay to safe activity levels.
- Smoke detectors — ionization detectors use a small americium-241 source, relying on its long, stable half-life for a consistent decades-long service life.
The Universal Decay Curve
Because the formula is expressed in half-lives, this curve looks identical for every radioactive isotope — only the time axis stretches or compresses depending on the specific half-life:
| Half-lives elapsed | Percent remaining |
|---|---|
| 0 | 100% |
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
| 5 | 3.125% |
By 5 half-lives, less than 5% of the original material remains — a useful rule of thumb for estimating when an isotope's activity has become negligible.
How to Use This Calculator
- Enter the Initial Amount (any unit, such as grams or activity).
- Enter the Half-Life of the isotope (e.g., in years).
- Enter the Elapsed Time, using the same time unit as the half-life.
- Select Calculate to see the amount remaining, along with the percentage remaining and the worked formula.
Related Calculations
For the energy released in decay-related photon emission, see the Photon Energy Calculator, or explore other exponential-style relationships with the Frequency Calculator.