Half-Life Calculator
Work out how much of a substance remains after a time, or find the half-life or time from two amounts.
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Result
- Percent remaining
- Half-lives passed
- Decay constant (λ)
- Mean lifetime (τ)
- Work
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Half-Life Formulas
N(t) = N₀ × (½)^(t ÷ t½) = N₀ e^(−λt) λ = ln 2 ÷ t½ τ = 1 ÷ λ
t½ = t × ln 2 ÷ ln(N₀ ÷ N) t = t½ × ln(N₀ ÷ N) ÷ ln 2
Worked Example
Tips
Use the same time unit for half-life and elapsed time. Amounts can be grams, atoms, becquerels or percent. The same math covers drug elimination half-lives. Merged: this page also covers radioactive decay.