Half-life Calculator — Exponential Decay
Compute how much of a substance remains after a given time using exponential decay. Enter the initial amount, the time elapsed, and the half-life — using the same time unit for both — to get the remaining quantity.
Enter the initial amount, time elapsed, and half-life to see the remaining amount.
How it works
What is half-life?
Half-life is the time it takes for a quantity to fall to half of its starting value. It describes exponential decay in radioactive isotopes, chemical reactions, and drug elimination.
The remaining amount is found with remaining = initial × 0.5^(time_elapsed / half_life). After one half-life, half remains; after two, a quarter remains, and so on.
Using consistent units
Always express the time elapsed and the half-life in the same unit — seconds, hours, days, or years. The calculator only divides the two values, so mixed units give wrong results.
The initial amount can be in any unit (grams, moles, milligrams) and the result is returned in that same unit.
Frequently asked questions
›What formula does this use?
It uses remaining = initial × 0.5^(time_elapsed / half_life), the standard exponential decay equation.
›Do the time units need to match?
Yes. The time elapsed and the half-life must use the same unit, since only their ratio matters.
›Can I use it for medication?
Yes. It estimates how much of a drug remains in the body based on its biological half-life.
›What happens after several half-lives?
Each half-life halves the amount: 50%, then 25%, then 12.5%, and so on toward zero.
›Does the substance ever fully disappear?
Mathematically it approaches zero but never reaches exactly zero, though it becomes negligible quickly.
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