Half-Life Decay Calculator

Every exponential decay process — radioactive isotopes, a drug clearing from your bloodstream, a capacitor discharging, even population die-off — follows the same equation: N(t) = N0 x (1/2)^(t / half-life), where N0 is the starting amount, N is what remains after time t, and half-life is how long it takes for half of whatever remains to disappear. This calculator solves that equation for any substance you name and for whichever of its four variables you don't already know — a genuinely general-purpose tool, unlike this site's caffeine half-life calculator, which models one specific substance at one fixed half-life.

Pick which variable is unknown — remaining amount, initial amount, elapsed time or the half-life itself — and enter the other three. If you're solving for the amount remaining or the original amount, the calculator applies the decay formula (or its inverse, N0 = N x 2^(t/half-life)) directly. Solving for elapsed time or for the half-life needs a logarithm: t = half-life x log2(N0/N), and since JavaScript's native logarithm is natural log (ln), the calculator performs — and displays — the standard change-of-base step, log2(x) = ln(x) / ln(2), so you see t = half-life x ln(N0/N) / ln(2) worked out with your own numbers rather than just a black-box answer.

The same equation shows up across very different fields under different names. Radiometric dating (carbon-14 for organic material, uranium-lead for rock) uses it to estimate age from how much of a radioactive isotope remains. Pharmacokinetics uses the identical math — often called first-order elimination — to describe how a single-compartment model of a drug clears from the body, which is exactly the model this site's caffeine calculator uses with a fixed 5-hour average half-life. This tool generalizes that idea: supply any half-life for any substance, drug or isotope, and it does the same algebra.

Keep the model's limits honest: it assumes a perfectly constant half-life and simple single-exponential decay. Real radioactive decay chains can branch into multiple products with different half-lives, and biological elimination isn't always perfectly first-order — so treat this as a mathematical model of ideal exponential decay, not a certified scientific or medical calculation for a specific real-world substance. Every number you enter is computed locally in your browser and never sent anywhere.