Half-Life Calculator

Half-life is the time required for half of a radioactive sample, unstable particle population, medicine, or other exponentially decreasing quantity to remain. It does not mean every individual atom disappears at that moment. Decay is probabilistic at the particle level, but a large population follows a predictable exponential curve. This calculator uses the standard relationship N = N0 times one half raised to the ratio of elapsed time to half-life. N0 is the initial amount, N is the remaining amount, and both time values must use the same unit. Each complete half-life multiplies the amount by one half. After one half-life, 50 percent remains; after two, 25 percent remains; after three, 12.5 percent remains. Fractional half-lives work the same way. If 1.5 half-lives pass, the remaining fraction is approximately 35.36 percent. The model approaches zero continuously but never reaches exactly zero in its mathematical form. Real measurements may eventually report zero because instruments have detection limits or because the sample contains a finite number of atoms. The decay constant is another way to describe the same process. It is represented by lambda and equals the natural logarithm of two divided by the half-life. A larger decay constant indicates faster decay and therefore a shorter half-life. The exponential form N = N0 times exp(-lambda times t) is equivalent to the half-life form used here. The calculator displays both the remaining amount and lambda so results can be transferred into chemistry, nuclear physics, pharmacokinetics, and environmental models. Amounts may be entered as grams, kilograms, moles, atoms, activity counts, concentration, or any other consistent quantity. Because the formula calculates a proportion, the result keeps the same unit as the initial amount. Time can be seconds, minutes, days, years, or another unit, provided the half-life and elapsed time match. A half-life quoted in years cannot be combined directly with elapsed days without conversion. Half-life calculations support radiometric dating, medical dosing studies, isotope storage planning, tracer experiments, and classroom exercises. The ideal exponential model assumes one decay process with a constant probability over time. Decay chains, biological elimination with multiple compartments, changing environmental conditions, or mixtures of isotopes can require more detailed models. For safety-critical radiation work, use measured isotope data, include uncertainty, and follow qualified professional guidance rather than relying on a simple educational calculator alone.