Half-Life Calculator
Calculate remaining quantity, elapsed time, half-life, or initial quantity for exponential decay.
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Frequently Asked Questions
Clear answers to common questions to help you use this calculator confidently.
What is half-life?
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What is half-life?
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Half-life is the time for a quantity to reduce by half. After one half-life, 50% remains; after two, 25%; after n half-lives, (½)ⁿ remains.
How is half-life calculated?
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How is half-life calculated?
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t½ = ln(2)/k where k is the decay constant. From two measurements: k = ln(N₀/N) / t, then t½ = 0.693/k.
What is the decay constant (k)?
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What is the decay constant (k)?
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The decay constant is the fraction of a substance that decays per unit time. It relates to half-life by k = ln(2)/t½ ≈ 0.693/t½. A larger k means faster decay.
Does half-life apply to anything besides radioactivity?
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Does half-life apply to anything besides radioactivity?
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Yes. The same exponential decay math models drug elimination from the body (pharmacokinetics), capacitor discharge, and any process where the rate of decrease is proportional to the amount remaining.
Why does the quantity never reach exactly zero?
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Why does the quantity never reach exactly zero?
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Exponential decay is asymptotic — each half-life removes half of what's left, but never all of it. After 10 half-lives, less than 0.1% remains, which is why practical thresholds (not zero) are used for radioactive waste or drug clearance.
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