Half-Life Calculator

What It Does

This page solves one relation — N(t) = N₀ · (1/2)^(t / t½) — in whichever direction you choose. Amount left after a time takes the starting quantity, the half-life and the elapsed time and returns what remains. Time to reach a target takes the starting quantity, the target and the half-life and returns how long it takes. Half-life from two readings takes two amounts and the time between them and returns the half-life. Beside the answer it reports the fraction remaining and how many half-lives the case spans.

Real-World Usage

Use it for radioactive decay — how much of a sample is left after a number of half-lives, or how old a sample is from the fraction that remains; for the clearance of a medicine from the body, where the half-life is the figure a dose schedule is built on; for radiocarbon dating, where the half-life of carbon-14 is what turns a remaining fraction into an age; and for any other process that halves in every interval of the same length.

Local Context

A half-life is a property of the substance and not of the country, so nothing here changes with your location and one page serves all nine countries with the same arithmetic. Two conventions are worth knowing. The decimal separator in the input fields is the point, as in 1.5 and 0.25, whatever separator your language uses in ordinary prose; the answer is formatted in your language’s own convention, so the same figure reads 1,5 in German and 1.5 in English. And the time unit is yours to choose — hours, days or years — as long as the half-life and the elapsed time are written in the same one.

What is a half-life?

It is the time a quantity takes to fall to half its value. If a substance has a half-life of five days, then after five days half of it remains, after ten days a quarter, and after fifteen days an eighth — whatever amount you started with. The relation is N(t) = N₀ · (1/2)^(t / t½), and the starting amount only scales the answer; it never changes the half-life.

How do I work out the half-life from two measurements?

Divide the second reading by the first to get the fraction left, then ask how many halvings that took: a quarter left means two halvings, because 1/2 × 1/2 = 1/4. The half-life is the time between the two readings divided by that number. The page does exactly this: choose Half-life from two readings, enter both amounts and the time between them.

Why does the elapsed time have to be greater than zero?

Because a half-life measures how fast a quantity changes with time, and the time in this relation is a duration. A time of zero would mean both readings were taken at the same instant, which says nothing about how fast the decay is. Enter the time that actually passed between the two measurements.

Does the page work in hours, days or years?

Any of them, as long as the unit is consistent. The half-life and the elapsed time must be written in the same unit — both in hours, both in days or both in years — and the answer comes back in that unit. The amounts can be in grams, moles, becquerels or atoms: only the ratio between them enters the arithmetic.