Calculate remaining quantity, elapsed time, half-life, or initial quantity in radioactive or exponential decay using N(t) = N₀ × (½)^(t ÷ t½), with decay constant output.
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Remaining
50.0000 g
Remaining
50.00%
Decayed
50.00%
Half-lives elapsed
1.000
Decay constant (λ)
1.925e-4 /s
Also in Physics
Science — Physics
The half-life of a radioactive isotope — or any exponentially decaying quantity — is the time required for half the material to transform or decay. The decay equation N(t) = N₀ × (½)^(t ÷ t½) connects initial quantity, remaining quantity, elapsed time, and half-life.
N(t) = N₀ × (½)^(t/t½) = N₀ × e^(−λt), where λ = ln(2)/t½ is the decay constant. After n half-lives, the fraction remaining is (½)ⁿ: after 1 half-life 50% remains, after 2 half-lives 25%, after 10 half-lives less than 0.1%.
This calculator accepts any time unit from seconds to millions of years, making it suitable for medical isotopes (minutes to days) through geological dating (millions of years).
Common radioisotopes: Carbon-14 (5 730 years, used in radiocarbon dating), Iodine-131 (8 days, used in thyroid therapy), Uranium-238 (4.47 billion years, geological dating), Technetium-99m (6 hours, medical imaging).
Half-life also applies to drug pharmacokinetics: a drug with a 4-hour half-life reaches ~97% elimination after 5 half-lives (20 hours). The same principle governs capacitor discharge, population decline, and chemical reaction rates.
Frequently asked questions
Yes, conceptually. The same exponential decay equation applies. Enter the initial dose as initial quantity, the biological half-life as half-life, and elapsed time to estimate remaining drug concentration. Note that real pharmacokinetics involve multi-compartment models and individual variation.
The decay constant (λ) is the probability per unit time that a nucleus will decay. It relates to half-life by λ = ln(2) ÷ t½ ≈ 0.693 ÷ t½. A larger λ means faster decay.
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