Half-Life Calculator
Calculate remaining quantity, half-life, or time elapsed for radioactive decay and other exponential processes.
About Half-Life
The half-life of a substance is the time required for half of it to decay or transform. The governing equation is N(t) = N₀ × (½)^(t/t½), where N₀ is the initial quantity, t is elapsed time, and t½ is the half-life. After one half-life, 50% remains. After two, 25%. After ten, about 0.1%. This exponential decay applies to radioactive isotopes, drug concentrations in the body, and many other natural processes.
The decay constant λ = ln(2)/t½ characterizes how quickly a substance decays — a higher λ means faster decay. The relationship between half-life and decay constant is fundamental to nuclear physics and pharmacokinetics. Carbon-14, with a half-life of 5,730 years, enables radiocarbon dating of ancient organic materials.
Half-life calculations are closely related to exponential functions. Our Log Calculator and Exponent Calculator cover the underlying mathematical tools. For probability of decay events, see the Probability Calculator.
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For the underlying method, read How to Use a Scientific Calculator: Functions, Angles, and Expression Order or Binary and Hexadecimal Explained: A Beginner's Guide.