Half-Life Decay Calculator

Decay is the clearest example of an exponential: each half-life removes half of what is left, so the amount falls fast at first and then keeps falling forever without reaching zero. This computes what remains after any elapsed time, lists the first eight half-lives, and then solves the equation back for time — which must return the elapsed time exactly if the exponential and its logarithm are being used correctly.

Half-life

In whatever time unit you like — years, days, seconds. The answer uses the same one.

Starting amount

Grams, atoms or becquerels; only the ratio matters to the arithmetic.

Time elapsed

In the same unit as the half-life. Try a few multiples of it.

Your result will appear here.

What this generator does

Raises a half to the power of the number of half-lives elapsed and multiplies by the starting amount, then inverts the equation using a base-two logarithm to recover the elapsed time and compares the two.

How to use this tool

Enter the half-life in any time unit.
Enter the starting amount and the time elapsed.
Read what remains, and how many half-lives that represents.
Check the solved-back time against the one you entered.

Understanding the controls

Half-life: In any time unit — years for carbon-14, seconds for a short-lived isotope. The answer uses the same unit throughout.
Starting amount: Grams, atoms or becquerels. Only the ratio matters to the arithmetic, so the unit is yours to choose.
Time elapsed: In the same unit as the half-life. Try exact multiples first, then something in between.

Common use cases

Working out remaining activity after a given time
Teaching exponential decay with the inverse shown
Producing half-life problems with verified answers
Understanding the arithmetic behind carbon dating
Seeing why decay never quite reaches zero

How this generator works

The amount remaining is the starting amount times a half raised to the elapsed time over the half-life. Inverting that gives time as the half-life times the base-two logarithm of the ratio between the starting and remaining amounts. Before display the remaining amount is recomputed, the equation is solved back and must return the elapsed time, and every row of the half-life table is confirmed to be exactly half the row before it.

Randomness and fairness

Nothing here is random. A half-life, an amount and a time give exactly one answer.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

This models a large sample where the average behaviour is smooth; individual atoms decay randomly, and a handful of atoms behaves nothing like the curve.
Decay chains are not modelled, so a daughter isotope that decays in turn is outside this.
Very long elapsed times leave remainders too small for a computer's floating point to represent exactly.
The unit is whatever you choose, so mixing years and days will give a wrong answer without any warning.

Privacy and your data

The decay is computed in your browser. The half-life and amounts you enter are never transmitted, stored or included in analytics.