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Half-Life Calculator
Half-Life Calculator
Radioactive decay — find remaining quantity, elapsed time, or half-life t½
N(t) = N₀ × (½)t / t½
Please fill in all required fields.
Enter values and hit Calculate
to see the decay curve & results.
Remaining Quantity
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Decay Constant (λ)
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Mean Lifetime (τ)
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Amount Decayed
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% Remaining
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Step-by-Step
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About the Half-Life Calculator
Calculate radioactive decay: the quantity remaining after some time, the time taken, or the half-life itself.
How to use the Half-Life Calculator
- Enter three of Initial Quantity (N₀), Remaining Quantity N(t), Time Elapsed (t) and Half-Life (t½).
- Choose the units and press the matching Find button or Calculate.
Formula and method
N(t) = N₀ × (½)^(t ÷ t½). To find time: t = t½ × log₂(N₀ ÷ N(t)).
Worked example
100 g of a substance with a 12-hour half-life leaves 25 g after 24 hours (two half-lives).
Three half-lives. Starting with 80 g of a substance, after 3 half-lives (80 → 40 → 20 → 10) 10 g remains.
When to use the Half-Life Calculator
- Working out how much of a radioactive substance remains after a given time.
- Estimating the age of materials with radiocarbon dating.
- Understanding how medicines decay in the body.
Common mistakes to avoid
- Assuming that after two half-lives everything is gone. Half remains after one, a quarter after two.
- Mixing time units.
Tips
- Time and half-life must use the same unit.
- After 10 half-lives about 0.1% remains.
Frequently Asked Questions
The time it takes for half of a radioactive sample to decay.
The time it takes for half of the atoms in a sample to decay.