Half-Life Calculator (Radioactive Decay)
Half-life calculator: remaining amount after radioactive decay, elapsed time, or half-life itself.
N = N0 · (½)t / T½
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
After each half-life, half of what is left decays: N = N₀·(½)^(t/T½).
It also works for drug elimination and any other exponential decay. Carbon-14 has a half-life of about 5 730 years.
Formula
N = N0 · (½)t / T½
| Symbol | Quantity | Units |
|---|---|---|
| N0 | Initial amount | — |
| t | Elapsed time | s, ms, µs, ns, min, h, d, wk, yr |
| T½ | Half-life | s, ms, µs, ns, min, h, d, wk, yr |
| N | Remaining amount | — |
Worked example
Given: N0 = 100 · t = 6.33762 × 10-8 yr · T½ = 3.16881 × 10-8 yr
N = N0 (½)t/T½
Result: N = 25
Frequently asked questions
How much remains after two half-lives?
25 % of the initial amount.