Half-Life Calculator
Decay That Never Quite Reaches Zero
Radioactive decay, drug elimination, and even the fading of a chemical reagent all share the same mathematical signature: whatever amount remains, half of it disappears in a fixed interval, no matter how much or how little was there to start. That interval is the half-life, and it lets you predict remaining quantity at any point in time — or work backward from measurements to find the half-life itself.
The Formula
N0 is the starting amount, t is the elapsed time, and t_half is the half-life in the same time units as t. Given a starting and ending amount instead, the calculator rearranges this to solve for the half-life directly: t_half = t × ln(2) ÷ ln(N0 / N).
Where This Calculation Matters
- Radiometric dating — measuring the remaining fraction of a radioactive isotope reveals the age of a sample.
- Nuclear medicine dosing — radioactive tracers and treatments are timed around their half-life to balance diagnostic signal against radiation exposure.
- Pharmacokinetics — many drugs clear the body following the same exponential decay pattern, which determines dosing intervals.
- Radioactive waste management — storage timelines are planned around how many half-lives are needed to reach a safe activity level.
Fraction Remaining After Successive Half-Lives
| Half-Lives Elapsed | Fraction Remaining |
|---|---|
| 0 | 100% |
| 1 | 50% |
| 2 | 25% |
| 3 | 12.5% |
| 4 | 6.25% |
| 5 | 3.125% |
| 7 | 0.7812% |
By 5 half-lives, less than 5% of the original quantity remains — a common rule of thumb for when a decaying substance is considered practically gone.
How to Use This Calculator
- Choose whether you're solving for the amount remaining or for the half-life itself.
- To find remaining amount, enter Initial Amount (N0), Elapsed Time, and Half-Life in matching time units.
- To find the half-life, enter Initial Amount (N0), Final Amount (N), and Elapsed Time instead.
- Select Calculate to get the result.
Related Calculations
Working with population growth instead of decay? The biology section's Population Growth Calculator uses the same exponential math in the opposite direction. For simple mole-to-mass conversions of a decaying isotope, see the Moles Calculator.