Half-life Calculator
Enter an initial quantity, the half-life and the elapsed time to find how much remains: N = N₀ × (1/2)^(t/t½). Includes the number of half-lives elapsed, percent decayed, mean lifetime τ and the decay constant λ.
#half life#radioactive decay#exponential decay#carbon dating#decay constant
TheCalculators — Half-life Calculator
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Quantity remaining (Nₜ)
17.67767
2.5 half-lives elapsed · 17.68% remains
- Initial quantity (N₀)
- 100
- Remaining (Nₜ)
- 17.67767
- Decayed amount
- 82.32233
- % remaining
- 17.678%
- % decayed
- 82.322%
- Half-lives elapsed (t/t½)
- 2.5
- Mean lifetime τ = t½/ln2
- 14.42695
- Decay constant λ = ln2/t½
- 0.06931
Decay calculation
- 1Count the half-livest / t½ = 25 / 10 = 2.5
- 2Apply the decay formulaNₜ = N₀ × (1/2)^(t/t½) = 100 × (1/2)^2.5 = 100 × 0.176777
- 3ResultNₜ = 17.67767 (17.678% of the original amount)
Half-life by half-life
Exponential decay curve
023
Most useful next
Formula
N(t) = N₀ × (1/2)^(t / t½) · λ = ln2 / t½ · τ = t½ / ln2
Pro tips
- • After each half-life the remaining amount halves — 100 → 50 → 25 → 12.5 …
- • Carbon-14 has t½ ≈ 5,730 years, usable for dating up to ~50,000 years.
- • Ten half-lives leave about 0.1% of the original quantity.
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