Enter your initial quantity, remaining quantity, and time elapsed to calculate the half-life of a substance — or provide the half-life to find the remaining quantity after any time period. The Half-Life Calculator also derives the decay constant and mean lifetime so you get a complete picture of exponential decay in one calculation.
Half-Life (T½)
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Remaining Quantity N(t)
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Decay Constant (λ)
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Mean Lifetime (τ)
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Percent Remaining
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Number of Half-Lives
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Half-life is the time required for exactly half of a given quantity of a substance to decay or transform. It is most commonly used in nuclear physics to describe radioactive decay, but the concept applies to any process following exponential decay, including drug elimination from the body and certain chemical reactions.
The standard half-life formula is N(t) = N₀ × 0.5^(t/T½), where N(t) is the remaining quantity at time t, N₀ is the initial quantity, and T½ is the half-life. Rearranging this formula lets you solve for any one of the four variables given the other three.
Given the initial quantity N₀, remaining quantity N(t), and time elapsed t, the half-life is: T½ = t × ln(2) / ln(N₀/N(t)). This formula comes directly from rearranging the exponential decay equation and using natural logarithms.
All three describe the same decay process from different angles. The decay constant (λ) is the probability of decay per unit time: λ = ln(2) / T½. The mean lifetime (τ) is the average time a nucleus survives before decaying: τ = 1/λ = T½ / ln(2). They are all mathematically interchangeable.
Carbon-14 has a half-life of approximately 5,730 years. This relatively long and consistent half-life makes carbon-14 ideal for radiocarbon dating of organic materials, allowing scientists to reliably date samples up to roughly 50,000 years old.
Uranium-238 has an extraordinarily long half-life of approximately 4.468 billion years — roughly the age of Earth itself. This extreme stability means uranium-238 decays very slowly and is used in uranium-lead radiometric dating of ancient geological formations.
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation in the form of alpha particles, beta particles, or gamma rays. Over time, this transforms the original element (parent nuclide) into a different, more stable element (daughter nuclide). The rate of decay follows an exponential function governed by the decay constant.
Yes. The same exponential decay mathematics that governs radioactive decay also describes how drugs are eliminated from the body. Enter the initial drug dose as N₀, the desired remaining concentration as N(t), and the drug's known half-life to find how long it takes to reach that level — or vice versa.