Half-life and radioactive decay calculator
Enter the starting amount and any two of the remaining amount, the elapsed time and the half-life. Leave one of those three empty and it is calculated. It works for any exponential decay: radioactive isotopes, drug concentration, or a signal that halves at a steady rate.
Remaining after each half-life
How the numbers are worked out
Exponential decay follows N = N₀ × (1/2)^(t / T½). Solving for each unknown gives N = N₀ × 2^(−t/T½), t = T½ × log₂(N₀ / N), and T½ = t / log₂(N₀ / N). The decay constant is λ = ln 2 / T½ and the mean lifetime is 1 / λ = T½ / ln 2, about 1.4427 half-lives. Time units are converted through seconds, with a year taken as 365.25 days. The model assumes a constant decay rate and a single decay path; real samples with decay chains or biological clearance in several phases need more than one half-life. Results are only as accurate as the half-life you enter, which this tool does not look up.