☢️ Half-Life Calculator

What This Calculator Does

This tool calculates how much of a substance remains after a certain amount of time, based on its half-life — the time it takes for half of a decaying quantity to disappear. It applies to radioactive isotopes, drug elimination from the body, and any process that follows exponential decay.

The Formula

The remaining amount is found using the exponential decay equation: N(t) = N₀ × (1/2)^{t / t_1/2}, where N₀ is the initial amount, t is the elapsed time, and t_1/2 is the half-life. The decay constant λ (lambda), which describes the fractional rate of decay per unit time, is related to the half-life by λ = ln(2) ÷ t_1/2.

A Few Notes

• Time units for elapsed time and half-life must match (both in hours, both in years, etc.) for the result to be correct.
• This model assumes a constant, single-step decay process, which is the standard model for radioactive decay and many first-order chemical or pharmacological processes.
• This calculator is provided for general educational and planning purposes and is not a substitute for professional radiological, pharmacological, or laboratory guidance.