The Half-Life Calculator works out the remaining quantity, initial quantity, elapsed time or half-life of something that decays exponentially, and converts between half-life, mean lifetime and decay constant.
Half-life (t½) = 15.0515
| Half-life (t½) | 15.0515 |
| Mean lifetime τ | 21.714724 |
| Decay constant λ | 0.046052 |
Enter one value to find the other two.
| Half-life t½ | 15 |
| Mean lifetime τ | 21.640426 |
| Decay constant λ | 0.04621 |
Half-life is the time it takes for half of a quantity to decay. It is most often used for radioactive isotopes, but it also describes how drugs leave the body, how some chemical reactions proceed and how sound or light fades.
N(t) = N₀ × (1/2)^(t / t½) = N₀ × e^(−t/τ) = N₀ × e^(−λt). The half-life, mean lifetime and decay constant are linked by t½ = τ ln 2 = ln 2 ÷ λ.
Worked example (defaults): 100 units decaying to 10 in 50 time units. t½ = 50 × ln 0.5 ÷ ln 0.1 = 15.05 time units.
Carbon-14: about 5,730 years (used in radiocarbon dating). Iodine-131: about 8 days (used in medicine). Uranium-238: about 4.5 billion years. Caffeine in the body: about 5 hours.
After one half-life 50% remains, after two 25%, after three 12.5%, after ten less than 0.1%. Decay is random for each atom, but very predictable for large numbers.
Does a substance ever fully decay? Mathematically never, but in practice it becomes undetectable.
Can units be anything? Yes, as long as time and half-life use the same unit.
What is the decay constant? The probability per unit time that a single nucleus decays.