☢️ Half-Life Calculator

Half-Life Calculator

Solve for remaining quantity, initial quantity, half-life, or elapsed time in any radioactive or exponential decay process.

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Half-Life Calculator
N(t) = N₀ × (½)^(t / half-life) — solve for any variable
Applies to both half-life and elapsed time below
Any unit — grams, atoms, activity, etc.
Result
Remaining Quantity
Percent Remaining
Half-Lives Elapsed
Decay Constant (λ)
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The Half-Life Formula

Half-life decay follows N(t) = N₀ × (½)^(t / half-life), where N₀ is the starting quantity, N(t) is what remains after time t, and the half-life is how long it takes for exactly half the quantity to decay. Pick which value you want to solve for and enter the other three.

Common Half-Lives

Carbon-14, used in archaeological dating, has a half-life of about 5,730 years. Iodine-131, used in some medical treatments, decays with a half-life of roughly 8 days. Caffeine in the human body has a biological half-life of around 5 hours, and Uranium-238 decays with a half-life of about 4.5 billion years.

The Decay Constant

The decay constant λ (lambda) relates to half-life by λ = ln(2) ÷ half-life, and describes the fraction of the remaining quantity that decays per unit of time in the underlying exponential decay equation N(t) = N₀ × e^(−λt).

Does half-life mean a substance is half gone, then completely gone after two half-lives?

No — decay is exponential, not linear. After one half-life, 50% remains; after two, 25% remains; after three, 12.5% remains, and so on. In theory a small fraction always remains mathematically, though it eventually becomes negligible.

Is half-life the same as the time something becomes "safe"?

Not necessarily. Radioactive material is generally considered to have decayed to background-level safety after roughly 10 half-lives, when less than 0.1% of the original activity remains, but the exact safety threshold depends on the specific isotope and its initial activity.

Can this calculator be used for things other than radioactivity?

Yes — the same exponential decay math applies to drug elimination from the body, capacitor discharge, and any other process where a quantity decreases by a fixed proportion over a fixed time interval.