Half-life calculator
Remaining amount from a half-life, or the time to reach a given remainder.
Fill in the fields and the result will appear here automatically.
Both modes use one exponential decay model: the remaining parent component after a time, or the time to a chosen remainder. Enter the component’s mass in grams and half-life in years. The output includes remaining and decayed mass, remaining share, elapsed half-lives and mean lifetime. The model assumes constant half-life and no replenishment; decay products and their subsequent decay are not calculated.
How it works
Formula and logic
N = N₀·(1/2)^(t/T); the inverse mode gives t = T·ln(N₀/N)/ln 2; mean lifetime τ = T/ln 2.
Example
For an entered half-life of 5730 years, after 11460 years 100 g of the parent component leaves 25 g:100·(1/2)²=25.
Fields and units
- What to find — list option
- Initial amount — g
- Half-life — years
- Time elapsed — years
- Remainder wanted — g
How to use
- — Use years in both modes. Convert a half-life given in days and the elapsed time to years first; units do not switch automatically. In the inverse mode 0<N≤N₀: N=N₀ gives zero time, while N=0 cannot be reached in finite model time.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §10.3: exponential decay model and half-life
- Limitation
- The model assumes constant half-life and no replenishment; decay products and their subsequent decay are not calculated.
FAQ
Why does the model never reach exactly zero?
At constant half-life, the exponential mean is positive at every finite time. It models an expected amount for an ensemble, not each atom’s decay schedule. After 10 half-lives the share is 1/1024≈0.09765625%; whether it may be neglected depends on the task.
How does mean lifetime differ from half-life?
The mean lifetime is the half-life divided by the natural logarithm of two, about 1.44 times longer. It is easy to confuse the two, and the activity formula uses the mean lifetime.
Why can the remainder not exceed the initial amount?
Because decay only removes material. Such a pair of numbers means a typo, and a negative time in the answer would be worse than a refusal.
Can I enter another time unit?
The equation depends on t/T, but the interface labels and outputs use years. Convert the original time units to years before entry so the numbers and labels agree.
What does a numerical range message mean?
A mathematically positive remainder can be smaller than the smallest representable number. The page then shows a range message instead of a zero mass. A very small remaining fraction may separately be unrepresentable while the mass still fits.