Half-life calculator for radioactive decay

Free TutorAura tool · no sign-up · Updated 26 October 2026

Choose what to find and enter the other values. The calculator works out how many half-lives have passed and shows the working, using:

N = N_0 \times \left(\tfrac{1}{2}\right)^{t / T}

where $N_0$ is the starting amount, $N$ is the amount left, $t$ is the time passed and $T$ is the half-life. The "amount" can be a mass, a number of nuclei or an activity in becquerels (Bq).

Initial amountA mass, number of nuclei or activity (e.g. Bq).Time passedHalf-lifeSame time unit as the time passed.

Amount remaining

Working

1Equation: remaining = initial × (½)^(time ÷ half-life)
2Number of half-lives = 15 ÷ 5 = 3
3Remaining = 80 × (½)^3 = 10

Radioactivity questions? The AI tutor explains half-life graphs and decay step by step.Try it free

What half-life means

The half-life of a radioactive isotope is the time it takes for the number of unstable nuclei in a sample to halve, or for the activity (count rate) to fall to half. Decay is random, so we can't predict when one nucleus will decay, but a large sample halves in a predictable time.

Worked examples

Amount left: a sample has an activity of 80 Bq and a half-life of 5 days. After 15 days, that's $15 \div 5 = 3$ half-lives: $80 \to 40 \to 20 \to 10$ Bq.
Half-life: activity falls from 80 Bq to 20 Bq in 12 hours. That's 2 half-lives ( $80 \to 40 \to 20$ ), so the half-life is $12 \div 2 = 6$ hours.
Time: how long until 80 Bq falls to 10 Bq with a half-life of 5 days? 3 half-lives, so 15 days.

Reading half-life from a graph

On a graph of activity against time, find the starting activity, halve it, and read across to the curve and down to the time axis. Repeat from that point to check: each halving should take the same time. Exam questions often ask you to show this on the graph.

Real half-lives

Half-lives range from fractions of a second to billions of years. Carbon-14, used in radiocarbon dating, has a half-life of about 5,730 years. Iodine-131, used in medicine, has a half-life of about 8 days. Isotopes used inside the body are chosen with short half-lives so they don't stay radioactive for long.

Common mistakes

Subtracting half the original each time instead of halving what's left.
Mixing time units (days and hours).
Forgetting that the time and half-life must be in the same unit.

For background and exam questions, see half-life explained.

Frequently asked questions

Can I use this for drug half-lives?

The maths is the same for anything that halves at a steady rate, but this tool is designed for physics questions. Follow medical advice for medicines.

What is a becquerel?

The unit of activity: 1 becquerel (Bq) is one decay per second.

What is half-life?

The time it takes for the number of unstable nuclei in a sample, or its activity, to halve.

How much is left after 3 half-lives?

One eighth. Each half-life halves what's left: 1 → ½ → ¼ → ⅛.

Does half-life change over time?

No. The half-life of an isotope is constant: it always takes the same time for the amount to halve, whatever the starting amount.

Is anything I type sent to a server?

No. The calculation runs in your browser and nothing is stored.

Sources

GCSE Physics (8463) specification: subject content. AQA.
Cambridge IGCSE Physics 0625 syllabus for 2026, 2027 and 2028. Cambridge International.

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