Half-Life Calculator

A half-life is the time it takes for a quantity to fall to half its starting value. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. It applies to radioactive decay, drug elimination in the body, and any process of exponential decay.

Use N = N₀ × (½)^(t / t½), where N₀ is the initial amount, t is the elapsed time, and t½ is the half-life. Divide the elapsed time by the half-life to get the number of half-lives, then multiply the starting amount by one-half raised to that power.

The decay constant (λ) is the probability per unit time that a given particle decays, related to the half-life by λ = ln(2) ÷ t½ ≈ 0.693 ÷ t½. It appears in the continuous decay formula N = N₀ × e^(−λt), which is mathematically identical to the half-life formula.

The mean lifetime (τ) is the average time a particle survives before decaying, equal to 1 ÷ λ, or about 1.44 times the half-life. It is longer than the half-life because a few long-lived particles pull the average up.

Yes. Enter the drug half-life and the time since the dose to estimate how much remains in the body. For example, a drug with a 6-hour half-life will have about 25% left after 12 hours (two half-lives). Most drugs are considered cleared after about 4–5 half-lives.