Half-life calculator for radioactive decay
Work out how much of a radioactive sample is left after a given time, how long it takes to decay to a given amount, or what its half-life is.
N = N₀ × (½)^(t ÷ t½)
N₀ is the starting amount and N the amount left after time t; t½ is the half-life. Use any unit for the amounts (g, %, atoms) and the same time unit for t and t½.
How to use the calculator
Pick what you want under Solve for and fill in the other three. The amounts can be in grams, milligrams, percent or number of atoms, as long as both use the same unit. Likewise, the time and the half-life just need the same unit, such as years or days.
Worked example: carbon-14
Carbon-14 has a half-life of about 5,730 years. After 11,460 years, two half-lives, a 100 g sample has 100 × ½ × ½ = 25 g left. To find the age of a sample with 25% of its carbon-14 left, solve for t: 5,730 × log₂(100 ÷ 25) = 11,460 years.
What half-life means
The half-life is the time it takes for half of the radioactive nuclei in a sample to decay. It does not depend on how much you start with: after one half-life ½ is left, after two ¼, after three ⅛.
Each nucleus decays at random, so half-life describes large numbers of atoms, not when any single atom will decay.
FAQ
How do you calculate the amount left after several half-lives?
Multiply the starting amount by ½ once for each half-life: N = N₀ × (½)ⁿ, where n = t ÷ t½. After 3 half-lives, 80 g becomes 80 × ⅛ = 10 g.
Does half-life change with temperature or pressure?
No. Radioactive decay happens inside the nucleus, so ordinary heat, pressure or chemical reactions do not change the half-life.