What half-life means
The half-life is the time it takes for half of something to decay or be removed. After one half-life 50% is left, after two 25%, after three 12.5%, and so on. It applies to radioactive isotopes and to any first-order process, such as a medicine being cleared from the body.
The formula
Amount left = starting amount × (1/2)time ÷ half-life
Carbon-14 has a half-life of about 5,730 years. From 100 g, after 11,460 years (two half-lives): 100 × (1/2)2 = 25 g. The time need not be a whole number of half-lives: after 8,000 years, 100 × 0.58,000 ÷ 5,730 = about 38 g.
Solving for the time
Time = half-life × log2(starting amount ÷ amount left). If a sample has 10 mg left of an original 80 mg and the half-life is 8 days, then 80 ÷ 10 = 8, log2(8) = 3, so 24 days have passed.
Solving for the half-life
Half-life = time ÷ log2(starting amount ÷ amount left). If 1,000 counts fall to 250 in 6 hours, two half-lives have passed, so the half-life is 3 hours.
The Half-Life Calculator solves for whichever of the four values you leave out.