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Half-Life Calculator

Calculate remaining quantity after a number of half-lives, or solve for any one variable. Works for radioactive decay, drug elimination, or any exponential decay.

Inputs

Remaining amount
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Amount decayed
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Fraction remaining
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Decay constant (ฮป = ln2/T)
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Mean lifetime (1/ฮป)
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About Half-Life Calculator

Half-life formula

N(t) = Nโ‚€ ร— (1/2)^(t/T) where T is the half-life. Equivalently, N(t) = Nโ‚€ ร— e^(-ฮปt) where ฮป = ln(2)/T. Use whichever form is convenient.

Real-world examples

Caffeine half-life โ‰ˆ 5 hours. Iodine-131: 8 days. Carbon-14: 5,730 years (used in dating organic remains). Uranium-238: 4.5 billion years (โ‰ˆ age of Earth).

When does it run out?

Mathematically never โ€” only the model breaks down. In practice, after ~10 half-lives less than 0.1% remains, considered effectively zero.