Half-Life Calculator
How much of a decaying quantity remains after a time, or the half-life, elapsed time or starting amount, with the decay constant and mean lifetime.
Result
Amount remaining: 29.829244
Exponential decay exactly. Biological half-lives vary between people and are not given here.
- Half-life
- 5,730
- Time elapsed
- 10,000
- Starting amount
- 100
- Half-lives elapsed
- 1.7452
- Share remaining
- 29.8292%
- Decay constant, per unit of time
- 0.000121
- Mean lifetime
- 8,267
https://calcgallery.com/chemistry/half-life-calculator/
Results come from the published equations applied to the values you enter. They are not electrical design, conductor sizing, laboratory safety or medical guidance. Weather indices describe a standard person in standard conditions and are not a forecast. Where codes apply, local rules vary and must be checked. Read the full disclaimer
How to use the Half-Life Calculator
- Choose what to solve for, the amount remaining, the half-life, the time elapsed or the starting amount.
- Enter the other three, with the half-life and the time in the same unit, whatever it is.
- Read the answer, the number of half-lives that have passed, and the mean lifetime.
The formulas
remaining N = N0 × (1/2)^(t ÷ T½)half-life T½ = t × ln 2 ÷ ln(N0 ÷ N)time t = T½ × ln(N0 ÷ N) ÷ ln 2start N0 = N × 2^(t ÷ T½)The decay constant, λ = ln 2 ÷ T½, is the fraction decaying per unit of time for small times. The mean lifetime is 1 ÷ λ.
Only for decay
Solving for the half-life or the time takes the logarithm of the starting amount over the remaining amount, which only makes sense if the amount has fallen. If the remaining amount is equal to or larger than the start, the page says it is not decay instead of returning a meaningless number.
With your numbers
- N = 100 × (1/2)^(10,000 ÷ 5,730) = 29.829244
- 1.7452 half-lives; mean lifetime 8,266.64
Quick reference
Exponential decay exactly. Biological half-lives vary between people and are not given here.
| Example | Result |
|---|---|
| 100 after one half-life of 5,730 years | Amount remaining: 50 |
| 100 after two half-lives | Amount remaining: 25 |
| 100 after 10,000 years | Amount remaining: 29.829244 |
| Half-life if 25 of 100 is left after 11,460 years | Half-life: 5,730 |
| Time to fall from 100 to 6.25 | Time elapsed: 22,920 |
| Starting amount if 10 is left after 3 half-lives | Starting amount: 80 |
Common questions about the Half-Life Calculator
- What is a half-life?
- The time it takes for half of a decaying quantity to go. After one half-life, half remains; after two, a quarter; after three, an eighth. It is the same whether you start with a gram or a tonne.
- How is the mean lifetime different?
- The mean lifetime is the average time a single atom, or molecule, survives before it decays. It is the half-life divided by ln 2, about 1.44 times longer. For carbon-14, with a half-life of 5,730 years, it is about 8,267 years. The two are often confused.
- Can I use this for medicines?
- The arithmetic is the same for anything that falls by a steady fraction per unit of time, including many drugs in the body. But a biological half-life depends on the person, their kidneys and liver, and other medicines, and it is not a fixed constant like a radioactive one. This page stores no drug half-lives; ask a pharmacist or doctor about any medicine.
- What units should I use?
- Any, as long as the half-life and the elapsed time use the same one. Amounts can be grams, atoms, becquerels or a percentage, as long as the starting and remaining amounts match.