Half-life is the time it takes for half of a decaying substance to disappear.
About this calculator
Half-life is the time it takes for half of a decaying substance to disappear. Carbon-14 dating, iodine-131 medical scans, and caffeine leaving your bloodstream all follow the same exponential pattern: every half-life period cuts the amount in half.
Enter the starting amount (N₀), the half-life, and how much time has passed. The calculator returns the remaining quantity, how much decayed, the percent left, and how many half-lives elapsed. Use the same time unit throughout — if half-life is in years, enter elapsed time in years too.
The formula N = N₀ × (½)^(t/t½) is equivalent to N = N₀ × e^(−λt) where λ = ln(2)/t½. After one half-life you have 50% left; after two, 25%; after ten, less than 0.1%.
For related math use the [[scientific-notation]] calculator for very small decay fractions, the [[percentage]] calculator for percent remaining, and the [[compound-interest]] calculator which uses the same exponential growth pattern in reverse.
Common uses
- Estimate remaining radioactivity after a known exposure time
- Check how much of a drug remains after several dosing intervals
- Solve chemistry homework on exponential decay
- Compare decay of isotopes with different half-lives
Frequently asked questions
What is the half-life formula?
N = N₀ × (½)^(t/t½). N₀ is the starting amount, t½ is the half-life, t is elapsed time, and N is what remains. Each full half-life multiplies the amount by 0.5.
How much remains after 3 half-lives?
After 3 half-lives, (½)³ = 1/8 of the original amount remains — 12.5%. Example: start with 80 g, half-life 2 hours, after 6 hours (3 half-lives) about 10 g remain.
Can half-life work for non-radioactive decay?
Yes. Any process where the decay rate is proportional to the current amount follows this model — drug metabolism, cooling, and some chemical reactions fit when conditions stay constant.
What units should I use for half-life and time?
They must match. If half-life is 5.27 years (cobalt-60), enter elapsed time in years. Mixing hours and days without converting gives a wrong answer.