numvana

Half-Life Decay Calculator

Calculate how much of a substance remains after a given time, from its half-life — for radioactive decay, drug elimination, or any first-order decay process.

Amount remaining
25
Amount decayed
75
Fraction remaining
25%
Number of half-lives elapsed
2
Decay constant (λ, per time unit)
0.115525

How it works

This models any first-order exponential decay process — radioactive isotopes, a drug or caffeine clearing from the body, a charged capacitor discharging — using the standard half-life formula: N(t) = N₀ · (1/2)^(t ÷ half-life), where N₀ is the starting amount and t is elapsed time. Every half-life that passes cuts the remaining amount by exactly half, regardless of how much is left.

This is mathematically the same relationship as the continuous decay-constant form N(t) = N₀ · e^(−λt), with the decay constant λ = ln(2) ÷ half-life — both are shown, since some fields (physics, pharmacology) conventionally use one form or the other for the identical decay curve.

Elapsed time and half-life just need to share the same time unit (both in hours, or both in days, etc.) — the formula itself is unit-agnostic, so enter whichever unit fits your situation rather than a fixed one.

FAQ

Does this only work for radioactive decay?

No — half-life decay is a general mathematical pattern for anything that loses a fixed fraction of what remains per unit time, not just radioactivity. It's the same math behind how long caffeine or a medication stays in your system, how a capacitor discharges, and how carbon-14 dating works — you just supply the half-life for whatever you're modeling.

Why is the amount never exactly zero?

Exponential decay approaches zero but never mathematically reaches it — each half-life only removes half of what's currently left, so however small the remaining amount gets, half of it is always still a positive number. In practice, once the remaining amount is negligible compared to what you started with, it's treated as effectively gone.

Related calculators