Half-Life Calculator
Enter the initial quantity, half-life T and elapsed time t — get the remaining amount from N = N₀ · (1/2)^(t/T), plus percent left and half-lives passed.
Reviewed by the OmniCalc teamMethod verified 2026-07-01
Any unit — grams, atoms…
Any time unit
Same unit as T
25
= 25% remaining= 2 half-lives
Remaining amount 25 — 25%Show steps
- Half-lives elapsed: n = t ÷ T = 20 ÷ 10 = 2.
- Remaining fraction: (1/2)ⁿ = 0.5^2 = 0.25, i.e. 25%.
- Remaining amount: N = N₀ × (1/2)^(t/T) = 100 × 0.25 = 25.
How to use the half-life calculator
- 1Enter the initial quantity N₀ — the unit is up to you: grams, atoms, becquerels…
- 2Enter the half-life T and the elapsed time t in the same time unit.
- 3Read the remaining amount, the percent left and the half-lives passed — with the working under Show steps.
The rule of ten half-lives
After 10 half-lives only 1/1024 of the original amount — about 0.1%— is left. That’s why ten half-lives is often treated as the point where a radioactive source is effectively gone.
Frequently asked questions
What is the half-life formula?
N = N₀ × (1/2)^(t/T), where N₀ is the initial quantity, T is the half-life and t is the elapsed time. Every full half-life cuts the remaining amount in half: after one half-life 50% is left, after two 25%, after three 12.5%.
What units should I use?
Any units work as long as they are consistent: the half-life and the elapsed time must share one time unit (seconds, days, years…), and the result comes out in the same unit as the initial quantity — grams, atoms, becquerels or anything else.
Does the elapsed time have to be a whole number of half-lives?
No. The exponent t ÷ T can be fractional, so after half of one half-life about 70.7% remains. Decay is a smooth exponential curve, not a series of sudden halvings.