Half-Life Calculator
Calculate the remaining amount of a substance after radioactive or exponential decay.
Try an example
78.5106
About this calculator
How This Half-Life Calculator Works
Enter an initial amount, a half-life, and an elapsed time (in matching units), and the calculator returns how much remains after exponential decay.
Worked Example
100 units of carbon-14 (half-life 5,730 years), after 2,000 years, decays to about 78.51 units remaining — 78.5% of the original amount.
The Formula
Remaining = Initial × 0.5^(Elapsed time ÷ Half-life). Every time the elapsed time equals exactly one half-life, the remaining amount is cut exactly in half — this compounding halving is what makes decay exponential rather than linear.
Why Decay Never Fully Reaches Zero
Since each half-life only removes half of whatever remains, the formula mathematically approaches zero but never technically reaches it — in practice, after enough half-lives the remaining amount becomes negligible or undetectable, which is why fields like radiocarbon dating have a practical limit (roughly 50,000 years for carbon-14) beyond which too little remains to measure reliably.
Beyond Radioactive Decay
The same exponential decay math describes any process where a constant fraction is lost over a fixed time period — including how the body eliminates certain medications (a drug's "half-life" is a standard pharmacology measure), and other natural decay processes.
Worked example
100 units of carbon-14 (half-life 5,730 years), after 2,000 years, decays to about 78.51 units remaining — 78.5% of the original amount.
Frequently asked questions
What is a half-life?
The time it takes for exactly half of a decaying substance to break down or be eliminated. It's a constant for a given substance — it doesn't speed up or slow down as the amount decreases.
Why does the amount never reach exactly zero?
Exponential decay approaches zero but never technically reaches it in the formula — each half-life removes half of whatever remains, so a tiny fraction always remains mathematically, even if it becomes practically undetectable.
Does this apply to things other than radioactive decay?
Yes — the same math describes any exponential decay process, including how the body eliminates certain medications, or how a drug's concentration decreases over time.