Half-Life Calculator

Half-life decay formula

The decay formula is N = N₀ × (1/2)^t/T, where N is the remaining amount, N₀ is the initial amount, t is elapsed time, and T is half-life.

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What half-life describes

Half-life is the time it takes for a quantity undergoing exponential decay to drop to exactly half its value — it applies to radioactive isotopes, drug concentrations in the body, and any process where the rate of decrease is proportional to the current amount. Because the decay is exponential, the same fraction (one half) is lost during each successive half-life period, regardless of the starting amount.

Frequently asked questions

Why does it never reach exactly zero? Exponential decay approaches zero asymptotically — each half-life reduces the remaining amount by half, so mathematically some (eventually negligible) amount always technically remains, even though it becomes practically undetectable after enough half-lives.

Can I use this for medication dosing? This calculator demonstrates the general mathematical model used in pharmacokinetics (drug half-life), but real medication clearance can be affected by many biological factors — always follow a healthcare provider's dosing guidance rather than a generic decay calculation.

Why does solving for half-life require the remaining amount to be less than the initial amount? Half-life describes decay (a decreasing quantity) — if the "remaining" amount isn't actually smaller than the "initial" amount, the scenario doesn't represent decay and the formula has no valid solution.