Half-Life Calculator
Calculate how much of a radioactive substance remains after elapsed time using N(t) = N₀ × (½)^(t÷t½).
How to use this half-life calculator
- Enter the initial amount.
- Enter the half-life and elapsed time in the same unit (both years, both days, etc.).
- Example — Carbon-14: t½=5730 yr, elapsed=11460 yr → 2 half-lives → 25% remains.
- After 10 half-lives, only ~0.098% of the original amount remains.
Formula
N(t) = N₀ × (½)^(t÷t½). Decay constant λ = ln2 ÷ t½. Percent remaining = 100 × 0.5^(t÷t½).
About the Half-Life Calculator
Radioactive decay follows first-order kinetics: the rate is always proportional to the amount remaining. This gives the characteristic exponential decay curve.
Carbon-14 dating works because living organisms continuously exchange CO₂ with the atmosphere, maintaining a constant ¹⁴C/¹²C ratio. At death, exchange stops and ¹⁴C decays at its known rate (t½=5730 yr), allowing age determination from the remaining ratio.
Frequently asked questions
+What is a half-life?
The time for exactly half a sample to decay. After 1 half-life: 50% remains. After 2: 25%. After 10: 0.098%.
+Carbon-14 half-life?
5,730 years. This is the basis of radiocarbon dating — used to date organic materials up to ~50,000 years old.
+Can half-life apply to non-radioactive processes?
Yes — any first-order process has a half-life: drug elimination, first-order chemical reactions, population decay. The mathematics is identical.