justyourcalculatorHalf-Life Calculator
Fill in three values of the decay formula and solve the fourth.
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Half-Life Calculator
Radioactive decay: remaining amount, time or half-life
Leave one box empty to solve for it.
Use the same time unit as t.
Quantity remaining (Nₜ)
25
- Half-lives elapsed
- 2
- Fraction remaining
- 25%
- Decay constant (λ)per time unit
- 0.13862944
- Mean lifetime (τ)
- 7.2134752
- Remaining
How it was calculated
- Nₜ = N₀ × (1/2)^(t / t½)
- Nₜ = 100 × 0.5^(10 / 5) = 100 × 0.5^2
- Nₜ = 25
| Half-lives | Time | Remaining | Percent left |
|---|---|---|---|
| 0 | 0 | 100 | 100% |
| 1 | 5 | 50 | 50% |
| 2 | 10 | 25 | 25% |
| 3 | 15 | 12.5 | 12.5% |
| 4 | 20 | 6.25 | 6.25% |
| 5 | 25 | 3.125 | 3.125% |
| 6 | 30 | 1.5625 | 1.5625% |
| 7 | 35 | 0.78125 | 0.78125% |
| 8 | 40 | 0.390625 | 0.390625% |
| 9 | 45 | 0.195313 | 0.195313% |
| 10 | 50 | 0.097656 | 0.097656% |
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How the half-life calculator works
Half-life is the time it takes for half of a decaying quantity to disappear. After one half-life 50% remains, after two 25%, after three 12.5%, and so on: Nₜ = N₀ × (1/2)^(t / t½).
The same decay can be described by the decay constant λ (the fraction lost per unit of time, in the limit) or the mean lifetime τ (the average time a single atom survives). They're linked by t½ = ln(2) / λ = τ × ln(2).
Use any unit of time you like (seconds, days, years), as long as t and the half-life use the same one. The formula works for any exponential decay: radioactive isotopes, drug elimination, or discharging capacitors.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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