Give it a starting amount and either a half-life or a decay constant, and it works out what is left after any stretch of time, from a coffee's caffeine to a vial of iodine-131.
Exponential decay describes anything that loses a constant fraction of itself per unit of time, not a constant amount. A quantity that drops by half every fixed stretch, whether that stretch is five hours or five thousand years, is running on the same equation.
That single rule covers a wider range of situations than most people expect:
| Substance or system | Half-life | Field |
|---|---|---|
| Iodine-131 (physical decay) | 8.02 days | Nuclear medicine |
| Caffeine, average adult | 3 to 7 hours | Pharmacology |
| Carbon-14 | 5,730 years | Archaeological dating |
| Tritium | 12.3 years | Nuclear physics |
| A discharging RC circuit | 0.693 × RC | Electronics |
The equation behind every row is N(t) = N₀ × e−kt, where N₀ is the starting amount, k is the decay constant, and t is elapsed time. After one half-life, 50 percent remains. After two, 25 percent. After three, 12.5 percent. Each additional half-life cuts what is left in half again, and the amount never technically reaches zero, only closer to it.
Physical decay constants, like iodine-131's 8.02-day half-life, come from measured nuclear physics and barely change between sources. Biological and behavioral ones swing hard.
Caffeine's half-life runs from about three hours to seven, depending on liver enzyme activity, pregnancy, smoking, and even other medications. A calculator built for one person's metabolism will be wrong for the next. Iodine-131 in a person's thyroid clears faster than its 8.02-day physical half-life too, because the body also excretes it, so doctors track a shorter "biological" half-life instead of the textbook number.
Pick the half-life or decay constant that matches the actual situation, not the first search result. When two sources disagree, the calculation is only as trustworthy as the weaker of the two inputs.
First-order decay shows up anywhere the rate of loss depends on how much is left:
Growth runs the same equation with the sign flipped. The Compound Interest Calculator solves that mirror image, where a balance gains a constant fraction of itself instead of losing one.
The details that change what "remaining amount" means.
They describe the same rate two different ways. Half-life is a duration, the time for half the amount to disappear. The decay constant k is a rate, the fraction lost per unit of time. They convert through k = ln(2) divided by the half-life. This calculator only needs one of the two.
Check that the starting amount and the half-life or decay constant are both positive numbers, and that elapsed time is zero or higher. A half-life or decay constant of zero has no defined answer, since the amount would either never change or vanish instantly.
Yes, for drugs cleared through first-order kinetics, which covers most medications. It will not work for the small group cleared through zero-order kinetics, like ethanol at typical drinking levels, where a fixed amount leaves per hour instead of a fixed percentage.
Yes. If the half-life is in days, enter elapsed time in days too. Mixing hours with a half-life given in days will produce a number that looks plausible but is wrong by whatever factor separates the two units.
No. A decay chain needs a separate equation for each isotope in the sequence, since a daughter product is being created and decaying at the same time. This calculator solves a single, independent decay step.
No. Every calculation runs in your browser, and nothing is logged, stored, or uploaded.
