Calculate the amount remaining after a given time from the initial amount and the half-life, with the number of half-lives. Enter your values; the result updates as you type, with the method shown below.
About this calculator
Radioactive decay, drug elimination and many other processes halve at a constant rate. This calculator gives the amount remaining after a time, the percentage left, the number of half-lives and the decay constant.
Enter the initial amount, the half-life and the time elapsed, in the same time unit.
When to use it
- Carbon-14 dating exercises.
- Physics and chemistry homework.
- Understanding how long a substance lasts.
- Nuclear energy lessons.
How to read the result
N = N₀ × (1/2)^(t / T). 100 units of carbon-14 (half-life 5,730 years) leave about 29.8 after 10,000 years.
λ = ln 2 / T; after 10 half-lives less than 0.1% remains.
Mistakes to avoid
- Using different time units for half-life and elapsed time.
- Thinking the substance is gone after two half-lives.
- Using it for processes that are not exponential.
Formula
N = N₀ × (1/2)^(t / T½)
Worked example
100 g of carbon-14 (half-life 5,730 years) after 10,000 years: 29.8 g.
Frequently asked questions
What is a half-life?
The time for half of the substance to decay.
Which units?
Any, as long as half-life and time use the same one.
Does it ever reach zero?
In theory it keeps halving forever.
What is λ?
The decay constant, ln 2 divided by the half-life.
Can I use it for medicines?
As a rough guide; real elimination can be more complex.
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Results are estimates for information only. Check important figures with a professional.