Half-Life Calculator
Solve exponential decay for the remaining amount, the half-life, or the elapsed time (with the decay constant and mean lifetime).
Details
Any consistent unit: grams, atoms, becquerels.
Remaining amount (N)
25
After 2 half-lives
Started with
100
Left at the end
25
Half-life (years)
5
Time passed (years)
10
This works out how much of a substance is left after a given time, how long it takes to decay to a given amount, or what the half-life must be.
Enter any three of the four values — starting amount, remaining amount, elapsed time and half-life — and it finds the fourth.
What a half-life is
A half-life is the time it takes for half of something to disappear. Not half of the original every time, but half of whatever is left.
That distinction is what makes decay curve rather than fall in a straight line. After one half-life you have 50%, after two 25%, after three 12.5%. Each step halves the remainder.
It never quite reaches zero mathematically, which is why decay is described this way rather than as a countdown to nothing. In practice, after about five half-lives only around 3% remains and the substance is usually considered gone.
Each step halves what remains, not what you started with. That is why the drop is dramatic at first and then flattens out into a long tail.
What to enter
- Solve for
- The remaining amount, the elapsed time, or the half-life itself.
- Initial amount (N₀)
- How much you started with. Units do not matter as long as both amounts use the same one, since only the ratio is used.
- Remaining amount (N)
- How much is left. Must be less than the starting amount.
- Elapsed time (t) and half-life (t½)
- Both must be in the same unit. Mixing hours and days here is the main source of wrong answers.
Half-lives worth knowing
- Carbon-14
- 5,730 years. The basis of radiocarbon dating, useful back to roughly 50,000 years.
- Iodine-131
- 8 days. Short enough to be used medically and then clear quickly.
- Uranium-238
- 4.5 billion years, roughly the age of the Earth.
- Caffeine
- About 5 hours in a typical adult. A 4pm coffee still has a quarter of its caffeine in you at 2am.
- Five half-lives
- About 3% left. The common rule of thumb for a drug being effectively cleared.
What this assumes
Decay is exponential and the half-life is constant, which holds precisely for radioactive isotopes.
Biological half-lives vary between people, with age, liver function and other medications all shifting them.
How to calculate half-life decay
Count how many half-lives have passed, then halve repeatedly. Fractional half-lives need the formula.
- t ÷ t½
- How many half-lives have elapsed
- (1/2)^
- Halving that many times
Count the half-lives. Divide the elapsed time by the half-life. 11,460 years of carbon-14 at 5,730 years each is exactly 2.
Halve that many times. Two half-lives means 100% → 50% → 25%.
For fractions, use the power. 1.5 half-lives means (1/2)^1.5 = 0.354, so about 35.4% remains.
To find the time instead. Work backwards with a logarithm: t = t½ × log(N ÷ N₀) ÷ log(0.5).
See a worked example: dating a sample with 25% of its carbon-14 left
- Remaining
- 25% of the original
- Half-life
- 5,730 years
25% means two halvings: 100% → 50% → 25%.
So two half-lives have passed.
2 × 5,730 = 11,460 years.
Note how the precision falls away with age. By 50,000 years so little carbon-14 remains that the method stops working.
About 11,460 years old
Frequently asked questions
Because each half-life halves what is left, not the original amount. Two half-lives leave 25%, not zero.
Mathematically it never reaches zero, only ever halving again. Practically, after five half-lives about 3% remains and most fields treat that as gone.
How long your body takes to clear half the drug. It sets how often a dose is needed and how long effects last.
Caffeine's is around 5 hours, so a 4pm coffee still leaves about a quarter of the caffeine in your system at 2am. That is why afternoon coffee affects sleep more than people expect.
Living things take in carbon-14 continuously. When they die that stops, and the carbon-14 already in them decays with a half-life of 5,730 years.
Measuring what fraction is left gives the time since death. It works well to roughly 50,000 years, after which too little remains to measure reliably.
For radioactive decay, essentially no. It is a property of the nucleus and is not affected by temperature, pressure or chemistry, which is what makes it reliable for dating.
Biological half-lives absolutely do change. Age, liver and kidney function, genetics and other medications all shift how fast a drug clears.
The same idea running the other way: how long something takes to double rather than halve. It applies to population growth, compound interest and bacteria.
The Rule of 72 gives a quick estimate: divide 72 by the growth rate. At 6% growth, doubling takes roughly 12 years.
Problems people actually run into
Assuming decay is linear
If half is gone in 5 hours, it is tempting to think it is all gone in 10. It is not — 25% is still there, and 12.5% after 15 hours.
This matters with medication. People assume a drug has cleared because two half-lives have passed, when a quarter of the dose is still active.
Mixing time units
The elapsed time and the half-life must be in the same unit. Entering a half-life in hours and an elapsed time in days gives an answer wrong by a factor of 24.
Convert first. It is the single most common error here, and the answer usually looks plausible enough to go unnoticed.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026