Half-Life Calculator
Exponential decay for a single species. Leave exactly one of half-life, elapsed time, initial amount, and remaining amount blank so the page can solve it. Not medical or radiological guidance.
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How to use the half-life calculator
- Keep half-life and elapsed time in the same unit (seconds, years, or any shared unit).
- Enter three of the four fields: half-life, time, initial amount, remaining amount. Leave one blank.
- Read all four values plus how many half-lives have elapsed.
- Use any consistent amount unit (grams, becquerels, counts). The ratio is what matters.
Half-life
Time for half of a radioactive or decaying quantity to remain
| Symbol t½ | Half-life duration |
|---|---|
| Decay law | N = N0 × (1/2)^(t / t½) |
| N0 | Initial amount |
| N | Remaining amount after time t |
| Half-lives elapsed | t / t½ |
| Model | Single exponential, first-order decay |
What half-life means
Half-life is the time for a decaying quantity to fall to half its previous value. After one half-life, half remains. After three half-lives, one eighth remains. The default 80 units, t½ = 5, and t = 15 leaves 10 units.
Initial amount, remaining amount, and elapsed time
N0 is the starting quantity. N is what is left after elapsed time t. Both must use the same unit. Half-life and t must share a time unit. The page also reports how many half-lives fit into t.
How the solver picks the unknown
Leave exactly one field blank. The engine rearranges N = N0 × (1/2)^(t/t½) for that blank. Remaining amounts larger than the initial amount are rejected for decay solves.
Limits
Single-isotope exponential model only. Not medical dosing, not radiation protection, not multi-nuclide chains. See the disclaimer.