Half-Life Calculator
Enter any three of the starting amount, the amount left, the time and the half-life. You get the fourth, with the decay constant.
Fill in three of the four values and leave the one you want to find empty. The answer appears as you type, in the unit shown next to its box. The amounts can be grams, atoms, becquerels or anything proportional.
Worked examples
Carbon-14
100 g, half-life 5,730 years, 11,460 years passed
25 g remains
Two half-lives.
Time to reach 12.5%
Half-life 8 days, 100 reduced to 12.5
24 days
Three half-lives.
About Half-Life Calculator
The half-life of a radioactive substance is the time it takes for half of the atoms to decay. After one half-life half remains, after two a quarter, after three an eighth, and so on. The amount left is the starting amount multiplied by one half raised to the power of the time divided by the half-life. The same law describes drugs clearing from the body, the discharge of some circuits and any process of exponential decay.
Enter any three of the four values and the page finds the other one. You can work out how much of a sample remains, how long it takes to fall to a given level, what the half-life is from two measurements, or what the amount was to begin with. The decay constant and the mean lifetime are shown too. Carbon-14, used in dating, has a half-life of 5,730 years, so a sample with a quarter of its original carbon-14 is about 11,460 years old.
How to use Half-Life Calculator
- Enter the starting amount and the amount left in the same unit, or leave one empty.
- Enter the time passed and the half-life, choosing a time unit for each.
- Leave the value you want to find empty.
- Read the result, the number of half-lives and the decay constant.
Common uses
- Radiocarbon dating questions
- Working out how long a medicine stays active in the body
- Estimating the activity left in a radioactive source
- Chemistry and physics exam practice on decay
Frequently asked questions
What is the half-life formula?
N = N0 x (1/2) raised to the power of t / T, where N0 is the starting amount, t the time passed and T the half-life.
How many half-lives until it is gone?
It never quite reaches zero. After 10 half-lives about 0.1% remains, and after 20 about one millionth.
Can I use any unit for the amounts?
Yes. Grams, atoms, becquerels or percentages all work, because only the ratio matters. The time units are converted for you.
What is the decay constant?
It is the probability of decay per unit time, equal to ln 2 divided by the half-life. The mean lifetime is its reciprocal, about 1.44 half-lives.