About this calculator
Use it to find the amount remaining after some time, the time taken to decay to a given amount, or the half-life itself.
Use the same unit of time throughout (years, days, seconds) and the same unit for amounts (grams, atoms, percent).
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Carbon-14 after 11,460 years
- Amount remaining
- 25
- Fraction remaining
- 25%
- Half-lives elapsed
- 2
- Amount decayed
- 75
After 11,460 (2 half-lives), 25 of the original 100 remains (25%).
Show the working
- Number of half-lives = time ÷ half-life = 11,460 ÷ 5,730 = 2.
- Remaining = start × (½)^half-lives = 100 × 0.5^2 = 25.
100 g decaying to 25 g with an 8-day half-life
- Time elapsed
- 16
- Half-lives elapsed
- 2
It takes 16 (2 half-lives) for 100 to decay to 25.
Show the working
- Half-lives = log₂(start ÷ now) = log₂(100 ÷ 25) = 2.
- Time = half-lives × half-life = 2 × 8 = 16.
100 becomes 12.5 in 30 days
- Half-life
- 10
- Half-lives elapsed
- 3
If 100 decays to 12.5 in 30, the half-life is 10.
Show the working
- Half-lives elapsed = log₂(100 ÷ 12.5) = 3.
- Half-life = time ÷ half-lives = 30 ÷ 3 = 10.
What a half-life is
The half-life is the time it takes for half of a radioactive substance (or any exponentially decaying quantity) to disappear. After one half-life, half is left; after two, a quarter; after three, an eighth. The formula is remaining = start × (½)^(time ÷ half-life).
Finding time or half-life
Turn the formula round with logarithms: the number of half-lives that have passed is log₂(start ÷ now), and time = half-lives × half-life. Knowing the start, the amount now and the elapsed time gives the half-life the same way.
Not only radioactivity
The same maths describes a drug clearing from the body, caffeine wearing off, or a cooling difference in temperature, wherever a quantity falls by the same fraction in equal times.
Frequently asked questions
What is the half-life formula?
Remaining = starting amount × (½) raised to the power (time ÷ half-life).
How many half-lives until less than 1% remains?
Seven: after 7 half-lives about 0.78% is left.
What is the half-life of carbon-14?
About 5,730 years, which is why it is used to date ancient organic material.
Does the unit of time matter?
Only that the half-life and the time use the same unit.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.