Half-Life Calculator
Calculate how much of a substance remains after a given time, based on its half-life.
The amount halves every 5 time units — over 12 units it decays from 100 down to 18.9465 (18.9% left).
- Percent Remaining18.95%
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N(t) = N₀ × 0.5^(t / half-life)
About the Half-Life Calculator
Half-life describes how long it takes for a quantity to fall to exactly half of its current value, and it shows up any time something decays at a rate proportional to how much of it is left — radioactive isotopes, the concentration of a drug in the bloodstream, or a hot cup of coffee cooling toward room temperature all follow the same underlying pattern.
It's a staple of chemistry and physics courses, where students compute how much of a radioactive sample remains after a given time, and it comes up just as often outside a classroom — carbon-14 dating an artifact, a pharmacist working out how long a medication stays active in the body, or an engineer estimating how long stored nuclear material stays hazardous.
The key thing that makes half-life math different from steady, linear decline is that the decay never actually stops — every half-life removes half of whatever's left, so the amount keeps shrinking but never technically reaches zero.
How it’s calculated
The formula is N(t) = N₀ × 0.5^(t / half-life), where N₀ is the starting amount, t is the elapsed time, and half-life is how long it takes to lose half the current amount. Every time t advances by one full half-life, the exponent increases by exactly 1, and the remaining amount gets cut in half again.
This is exponential decay, not linear decay — the substance doesn't lose a fixed amount per unit time, it loses a fixed fraction. That's why the amount drops fast at first (in absolute terms) and then tapers off, approaching but never quite touching zero.
Frequently asked questions
What does half-life actually mean?
It's the time it takes for a decaying quantity to drop to exactly half its current amount — and that same waiting period cuts whatever's left in half again, no matter how much or how little remains at that point.
Does the substance ever fully disappear?
Mathematically, no — each half-life only removes half of what's currently there, so the remaining amount keeps shrinking toward zero without ever technically reaching it, though after enough half-lives it becomes negligible.
How is half-life used in carbon dating?
Carbon-14 has a known half-life of about 5,730 years. By measuring how much carbon-14 remains in an organic sample relative to the original amount, scientists can work backward through this same formula to estimate the sample's age.
Can this calculator be used for drug elimination from the body?
Yes — many medications are eliminated from the bloodstream at a rate that closely follows the same exponential half-life pattern, so entering a drug's known half-life and elapsed time gives a reasonable estimate of how much remains active.
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