Half-Life Calculator - Radioactive Decay & Remaining Amount

How to use this tool

1. Enter an initial quantity and choose a typical isotope half-life or enter a custom value.
2. Enter elapsed time in the same unit and leave exactly one field blank to solve it.
3. Use the conversion panel to relate half-life, mean lifetime, and decay constant.

Half-life formula

N(t) = N₀ × (½)^(t / t½)

• N₀ - initial quantity
• t½ - half-life (any time unit, consistent with t)
• t - elapsed time
• N(t) - remaining quantity at time t

Common half-lives

• Carbon-14: 5,730 years (radiocarbon dating)
• Uranium-238: 4.47 billion years
• Iodine-131: 8.02 days (medical isotope)
• Radon-222: 3.82 days

Half-life reference table

Applications

• Radiocarbon dating: Carbon-14 in organic materials decays at a known rate; comparing remaining C-14 to the atmospheric ratio gives the age of the sample up to ~50,000 years.
• Nuclear medicine: Tc-99m's 6-hour half-life means it is nearly gone within 2 days, minimizing patient radiation exposure while still enabling imaging.
• Reactor design: reactor designers must account for hundreds of different fission products, each with a different half-life, to plan cooling and waste handling.

Exponential decay intuition

After each half-life, exactly half the remaining quantity decays. After 10 half-lives, approximately 0.1% of the original quantity remains. After 20 half-lives, approximately 0.0001%. This is why nuclear waste with short half-lives (like Cs-137 at 30 years) is more intensely radioactive in the short term but becomes less dangerous much sooner than long-lived isotopes.