Half-Life Calculator
Find how much of a substance remains after a given time from its half-life and starting amount.
How it works
N = N₀ × (1/2)^(t / t½) · half-lives elapsed = t / t½
A half-life is the time it takes for half of a decaying substance to disappear. After one half-life, 50% remains; after two, 25%; after three, 12.5%, and so on. The remaining amount equals the starting amount times one-half raised to the number of half-lives that have passed.
Worked example
Starting with 100 units and a 5-minute half-life, after 15 minutes three half-lives have passed, so 100 × (1/2)³ = 12.5 units remain.
Frequently asked questions
Does the elapsed time have to be a whole number of half-lives?
No. The formula uses t ÷ t½ as a continuous exponent, so it works for any elapsed time, whole or fractional.
What kinds of things follow half-life decay?
Radioactive isotopes are the classic example, but the same exponential decay describes drug clearance from the body, capacitor discharge and many other processes.
Will the substance ever fully disappear?
Mathematically it approaches zero but never quite reaches it, halving again with each half-life. In practice the remaining amount soon becomes negligible.
Related calculators
Educational estimate. Check the formula and units for your exact case.