Half-Life Calculator

Half-life is the time for half of a decaying quantity to disappear — radioactive nuclei, drug plasma levels, or carbon-14 in archaeological samples. Exponential decay means each equal time interval removes half of what remains, never quite reaching zero. Nuclear medicine, radiometric dating, and pharmacokinetics all depend on the same mathematics.

Exponential decay:

N = N₀ × (½)^(t / t½)

Equivalently N = N₀ × e^−λt with decay constant λ = ln(2) / t½ ≈ 0.693 / t½. Where N is remaining amount, N₀ is initial amount, t is elapsed time, and t½ is half-life. Solve for any unknown given the other three. After n half-lives, fraction remaining = (½)ⁿ.

Enter initial amount, half-life, and elapsed time for remaining quantity, or solve for time to reach a target fraction. Caffeine's half-life in adults is roughly 5 hours; iodine-131 for thyroid treatment is 8.02 days; carbon-14 is 5,730 years for radiocarbon dating. Multiple half-lives stack multiplicatively, not additively.

Worked example: A 80 mg drug dose with t½ = 6 h. After 18 h (three half-lives): N = 80 × (½)³ = 10 mg remains. Time to reach 5 mg (1/16 of original): 4 half-lives = 24 h. Technetium-99m (t½ = 6.01 h) decays to 25% in 12 h — two half-lives — standard for nuclear imaging dose planning.

Relate to dilution as conceptual inverse growth, molarity when tracking reacting species, and day-to-hour conversion for multi-scale half-lives. First-order chemical kinetics in reactors share identical math with different physical meaning.