Calculate the remaining quantity of a substance after a given time, based on its half-life, using exponential decay.
Half-life and elapsed time must use the same time unit.
This tool calculates how much of a substance remains after a given time period, based on its half-life ā the time it takes for half of a substance to decay or be eliminated. It's used in nuclear physics, chemistry, pharmacology (drug elimination from the body), and radiometric dating.
N(t) = Nā Ć (1/2)^(t / T), where N(t) is the remaining quantity at time t, Nā is the initial quantity, and T is the half-life. Each time one full half-life passes, exactly half of the remaining substance decays away.
Enter the initial quantity, the half-life duration, and the elapsed time, and the calculator returns how much of the substance remains.
Example: Starting with 100 mg of a substance with a half-life of 5 hours, after 15 hours (3 half-lives) only 100 Ć (1/2)Ā³ = 12.5 mg remains.
Is half-life the same for every substance? No, half-life varies enormously ā from fractions of a second for some radioactive isotopes to billions of years for others like Uranium-238.
Does half-life apply to medications? Yes, a drug's biological half-life describes how long it takes the body to eliminate half of the drug from the bloodstream, which helps determine dosing schedules.
Does the substance ever reach exactly zero? Mathematically, no ā the exponential decay model means the remaining quantity approaches zero but never technically reaches it, though after about 7 half-lives less than 1% remains.
How is half-life used in radiometric dating? Scientists measure the remaining amount of a radioactive isotope (like Carbon-14) in a sample and use its known half-life to estimate how much time has passed since the material formed.
Can half-life be calculated backward, to find elapsed time? Yes, if you know the initial and remaining quantities along with the half-life, the formula can be rearranged to solve for elapsed time.