Half-Life Calculator
Calculate how much of a substance remains after a given time, based on its half-life.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter an initial quantity, half-life, and elapsed time to find the remaining quantity.
Use the same time unit as "elapsed time" below (e.g. both in years, or both in days).
Your result
12.5
Remaining quantity
Number of half-lives elapsed3
AI explanation
Formula
N(t) = N₀ × (1/2)^(t ÷ half-life)Worked example
100 units, half-life of 10, after 30 units of time
| Field | Value |
|---|---|
| Initial quantity | 100 |
| Half-life | 10 |
| Elapsed time | 30 |
| Remaining quantity | 12.5 |
| Number of half-lives elapsed | 3 |
Assumptions
- Elapsed time and half-life must be entered in the same unit — the calculator doesn't convert between units automatically.
Frequently asked questions
What is half-life?
The time it takes for a quantity to reduce to half its initial value — commonly used for radioactive decay, but also applicable to drug elimination and other exponential decay processes.
Why must time and half-life be in the same unit?
The formula divides time by half-life to find the number of half-lives elapsed — if they're in different units (like years vs. days), the result will be wrong.
Does the substance ever completely disappear?
Mathematically, no — exponential decay approaches zero but never quite reaches it, though after many half-lives the remaining amount becomes negligible.