Physics & Chemistry
Half-Life
Calculator
Calculate remaining quantity, elapsed time, number of half-lives, and decay constant. Includes mean lifetime, decay constant converter, and exponential decay chart.
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Remaining (Nt)
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% Remaining
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Half-Lives (n)
Radioactive Decay Calculator
units
t
t½
units
☢️ Leave the field you want to solve for empty. Formula: Nt = N₀ × (½)^(t/t½)
Remaining Quantity (Nt)
25
of 100 initial units
25% remaining
Half-Lives n
2
Decayed
75%
Remaining
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Half-Lives
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λ (decay const)
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Mean Lifetime τ
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Understanding Radioactive Half-Life
The half-life (t½) is the time required for exactly half of the radioactive nuclei in a sample to decay. It is a constant specific to each radioactive isotope — independent of temperature, pressure, or chemical state.
Half-Life Formulas
Remaining quantity: Nt = N₀ × (1/2)^(t/t½)
Nt = N₀ × e^(−λt)
Number of half-lives: n = t / t½
Decay constant: λ = ln(2) / t½ ≈ 0.693 / t½
Mean lifetime: τ = 1 / λ = t½ / ln(2) ≈ 1.4427 × t½
Find time: t = t½ × log₂(N₀/Nt)
t = −ln(Nt/N₀) / λ
What is the difference between half-life and mean lifetime?
The half-life (t½) is when 50% has decayed. The mean lifetime (τ) is the average time a single nucleus survives before decaying — it equals t½/ln(2) ≈ 1.443 × t½. So mean lifetime is about 44% longer than half-life. After one mean lifetime, ~63.2% has decayed (1/e remains).
Does temperature affect radioactive half-life?
No. Radioactive decay is a quantum nuclear process unaffected by chemical or physical conditions — temperature, pressure, chemical bonding, or magnetic fields. This makes half-life a reliable dating tool in geology and archaeology (radiocarbon dating uses Carbon-14 with t½ = 5,730 years).
What are some common isotopes and their half-lives?
Carbon-14: 5,730 years (used in radiocarbon dating). Uranium-238: 4.47 billion years (geological dating). Iodine-131: 8.02 days (medical therapy). Polonium-210: 138 days. Radon-222: 3.82 days. Technetium-99m: 6 hours (medical imaging). Francium-223: 22 minutes.