Half-Life Calculator
Pick what you want to find, enter the other three quantities and get the answer. Use the same time unit for the elapsed time and the half-life.
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Formula
N = N0 × (1/2)^(t / T)
N0is the initial amount,Nthe amount remaining,tthe elapsed time andTthe half-life.- Elapsed time:
t = T × log2(N0 / N) - Half-life:
T = t × ln 2 / ln(N0 / N) - Initial amount:
N0 = N / (1/2)^(t / T)
Worked example
Start with 100 g of a substance with a half-life of 5 years and wait 10 years. That is 10 ÷ 5 = 2 half-lives, so the amount is multiplied by (1/2)² = 1/4: 100 × 0.25 = 25 g remain, which is 25 % of the original.
Frequently asked questions
What is the half-life formula?
N = N0 × (1/2)^(t / T), where N0 is the starting amount, N what is left after time t, and T the half-life. With N0 = 100, t = 10 and T = 5 there are two half-lives, so N = 100 × 1/4 = 25.
How do I find the half-life from measurements?
Use T = t × ln 2 / ln(N0 / N). If 100 g falls to 12.5 g in 9 days, the ratio is 8, ln 8 = 2.0794, so T = 9 × 0.6931 / 2.0794 = 3 days.
How long until only a given amount is left?
Use t = T × log2(N0 / N). To go from 200 to 50 with T = 5730 years, log2(4) = 2, so t = 11,460 years.
Does this only work for radioactive decay?
No. Any process that loses a fixed fraction per unit time follows the same curve, including first-order chemical reactions and some drug elimination. Keep the elapsed time and half-life in the same unit.