Half-Life Calculator

This half-life calculator works out how much of a substance remains after a period of radioactive or exponential decay, and also tells you the percentage remaining and how many half-lives have elapsed. A half-life is the time it takes for exactly half of a quantity to decay or transform into another form. After one half-life, 50% of the original amount is left; after two half-lives, 25%; after three, 12.5%, and so on indefinitely. The amount follows an exponential curve that gets closer and closer to zero but never quite reaches it. The formula is N(t) = N0 x (1/2)^(t / t_half), where N0 is the starting amount, t is the elapsed time, and t_half is the half-life. The exponent is simply the number of half-lives that have passed. You enter the starting amount, the half-life of the substance, and the elapsed time, making sure both the half-life and the elapsed time use the same unit (years, days, hours, or seconds), and the calculator returns the remaining amount, the percentage still present, and the number of half-lives that have gone by. Half-lives are most famous in nuclear physics and radioactive decay, where they span an enormous range from microseconds for unstable isotopes to billions of years for others. Carbon-14 has a half-life of 5,730 years, which underlies radiocarbon dating. However, the same maths applies to pharmacokinetics (drug clearance), electronics (capacitor discharge), and any other process that decays exponentially at a constant rate. The default example uses carbon-14 with a starting amount of 100 g and an elapsed time of 11,460 years, which is exactly two half-lives. Results assume constant decay rate and ideal conditions.

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Use the same time unit for the half-life and the elapsed time: both in years, days, hours, or seconds. The starting amount can be in any unit (grams, atoms, becquerels) as long as you are consistent.