A half-life is the time it takes for a quantity decaying exponentially to fall to half its starting value. The Toolenza calculator solves N(t) = N₀ × (1/2)^(t/T½) for remaining amount, elapsed time, or half-life given the others.

Where this comes up

• Radioactive decay — the classic case. Carbon-14 has a 5,730-year half-life (radiocarbon dating). Iodine-131 (medical thyroid treatment): 8 days. Uranium-238: 4.5 billion years.
• Drug pharmacokinetics — most drugs clear with first-order kinetics. Caffeine half-life is 4–6 hours in adults. Ibuprofen: 2 hours. Warfarin: 36–48 hours, which is why it's dosed once daily.
• Concentration of solutes — first-order chemical reactions follow the same math. "How long until 90% of the reactant is gone?" is a half-life problem.
• Software metrics — knowledge half-life, technical-debt half-life, and similar metaphorical uses (where the math is the same but the underlying process isn't strictly exponential).

The "five half-lives" rule

After 5 half-lives, only 3.1% of the original remains — close enough to "none" for most purposes. After 10 half-lives, 0.1% remains. This is why drug "washout periods" are typically 5× the half-life of the drug being cleared.

Pitfall

First-order (exponential) decay assumes the decay rate is proportional to what's left. Zero-order processes (constant decay regardless of how much is left) follow a different formula and have no constant half-life. Alcohol metabolism in humans, for example, is roughly zero-order at high concentrations — the liver can only clear ethanol so fast.