How exponential decay works
A half-life is the time it takes for half of whatever you started with to disappear — through radioactive decay, a chemical reaction, or a drug clearing from the body. The defining feature is that the same fraction vanishes in each equal stretch of time, not the same amount. After one half-life you have 50% left, after two 25%, after three 12.5%, and so on.
Because the rate depends on how much is currently present, the amount never quite reaches zero; it just keeps halving. This calculator raises one-half to the power of however many half-lives have elapsed, which works for whole and fractional numbers of half-lives alike.
Reading the decay curve
The remaining amount is what is left after the elapsed time, the percent remaining expresses that as a share of the original, and the half-lives elapsed counts how many halvings have passed. The chart traces the amount falling over time, showing the characteristic steep early drop that flattens into a long, slow tail.
A useful rule of thumb: after about seven half-lives less than 1% remains, which is why people often treat seven to ten half-lives as "effectively gone".
Getting the units right
The only thing to watch is consistency: the half-life and the elapsed time must use the same unit. If the half-life is in days, enter the elapsed time in days too. The initial amount can be in any unit you like — grams, becquerels, milligrams, atoms — and the result comes back in that same unit. This idealised model assumes a single, constant half-life and is not a substitute for medical or radiological dosing guidance.
Formula
remaining = initial · 0.5^(elapsed / halfLife)Frequently asked questions
- What units should I use?
- Any unit works as long as the half-life and elapsed time use the same one (both in years, both in days, etc.).