Half-Life Calculator
Calculate remaining quantity after a number of half-lives, or solve for any one variable. Works for radioactive decay, drug elimination, or any exponential decay.
Inputs
Remaining amount
โ
Amount decayed
โ
Fraction remaining
โ
Decay constant (ฮป = ln2/T)
โ
Mean lifetime (1/ฮป)
โ
About Half-Life Calculator
Half-life formula
N(t) = Nโ ร (1/2)^(t/T) where T is the half-life. Equivalently, N(t) = Nโ ร e^(-ฮปt) where ฮป = ln(2)/T. Use whichever form is convenient.
Real-world examples
Caffeine half-life โ 5 hours. Iodine-131: 8 days. Carbon-14: 5,730 years (used in dating organic remains). Uranium-238: 4.5 billion years (โ age of Earth).
When does it run out?
Mathematically never โ only the model breaks down. In practice, after ~10 half-lives less than 0.1% remains, considered effectively zero.