Half-life calculator

How much is left after a given time, or how long until a target amount remains — with the decay constant and a halving schedule.

1 · The decay

Starting amount

Any unit — grams, milligrams, becquerels, percent.

Half-life

In whatever time unit you want the answer in.

2 · What do you want to know?

Time elapsed

Target amount remaining

Decay never reaches exactly zero, so the target must be above it.

0Remaining

0Percent left

0Half-lives

The halving schedule

Amount remaining after each half-life
Half-lives	Time	Remaining	Percent

Drug elimination follows this same arithmetic, but a plasma half-life on a label is a population average. Individual clearance varies with liver and kidney function, age, weight, genetics and other medicines. Use this to understand the shape of the curve, not to decide a dose.

What half-life means

A half-life is the time for half of something to decay. It is a property of the substance and does not depend on how much you started with: if half is gone in ten years, half of what remains goes in the next ten, and so on. That is why the amount left follows a curve rather than a straight line and never quite reaches zero.

The formula

The amount remaining is the starting amount times one half raised to the power of elapsed time divided by half-life. From that come two numbers physicists usually want: the decay constant, which is ln(2) divided by the half-life, and the mean lifetime, which is its reciprocal — the average time an individual atom survives, and always longer than the half-life.

Both directions

Enter a time and get the amount remaining, or enter a target amount and get the time to reach it. The second is usually the real question: when is it under 10 percent, or below a detectable level?

What it applies to

Anything decaying by a constant proportion per unit time: radioisotopes, drug plasma concentration, and by extension anything else with first-order kinetics. Carbon-14's half-life is 5,730 years, which is what makes radiocarbon dating work back to roughly ten half-lives.

Example

100 units with a half-life of 5,730 years: after 5,730 years, 50 remain; after 11,460, exactly 25. To reach 25 units from 100 with a ten-hour half-life takes twenty hours.

A note on drug half-life

Drug elimination follows this arithmetic, but a plasma half-life quoted on a label is a population average. Individual clearance varies with liver and kidney function, age, weight, genetics and other medicines. Use this to understand the shape of the curve, not to decide a dose.