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Enter an initial quantity, the half-life, and the elapsed time (same time unit for both).
A half-life is the time it takes for half of a quantity to disappear through a process that runs at a steady proportional rate. After one half-life, 50% remains. After two, 25%. After three, 12.5%, and so on. The amount never quite reaches zero, but it gets very small quickly. After ten half-lives, less than 0.1% is left.
The same maths describes radioactive decay, how long a drug or caffeine stays in your body, and some chemical reactions. Anything that loses a fixed fraction per unit of time, rather than a fixed amount, follows it.
N = N₀ × (½)t ÷ t½
Here N₀ is the starting amount, t is the time elapsed and t½ is the half-life. Time and half-life must use the same unit (both days, both years and so on). To solve for time instead, rearrange: t = t½ × log₂(N₀ ÷ N).
Carbon-14 has a half-life of about 5,730 years. Starting with 100 g, after 11,460 years (two half-lives) you'd have 100 × ¼ = 25 g. Radiocarbon dating runs this calculation in reverse.
Caffeine has an average half-life in healthy adults of around 5 hours, though it varies widely from person to person. A 200 mg coffee at 2 pm leaves roughly 100 mg at 7 pm and 50 mg at midnight.
Mathematically, no. It halves forever. In practice, after about 7–10 half-lives the amount left is usually too small to matter or measure.
Yes, as long as half-life and elapsed time use the same unit. Seconds, hours, days and years all work. Mixing units, such as half-life in years and time in days, gives a wrong answer.
They describe the same process two ways. The decay constant λ is the fractional loss rate, and the two are linked by t½ = ln(2) ÷ λ ≈ 0.693 ÷ λ.
No. Published drug and caffeine half-lives are averages. Age, liver function, pregnancy, other medications and genetics can change them a lot, so treat the results as an estimate rather than medical guidance.