Half Life Calculator
Work out how much of a decaying quantity is left, how long it took, the starting amount or the half-life itself.
A half-life is the time it takes for half of a decaying quantity to be gone. The amount left is the start times one half raised to the time over the half-life. Starting from 100 with a half-life of 5,730 years, the amount after 10,000 years is 29.83, which is 1.745 half-lives.
This calculator is for general education. It uses the standard first-order decay formula, so it fits processes that lose a constant fraction per unit of time. It is not a dosing tool, a radiation safety tool or a substitute for a laboratory method, and real samples can be affected by measurement error and by processes this model leaves out.
Amount left
29.83
- Half-lives passed
- 1.745
- Fraction left
- 29.83%
- Decay constant (per time unit)
- 0.000121
Shown to four significant figures. Uses N = N0 x (1/2)^(t / half-life).
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About the Half Life Calculator
Anything that decays at a steady proportional rate, such as a radioactive isotope, loses the same fraction in every equal span of time. The half-life is the span in which half is lost. After one half-life, 1/2 is left; after two, 1/4; after three, 1/8. So 80 units with a half-life of 8 days fall to 10 after 24 days, which is three half-lives. The general formula is N = N0 x (1/2)^(t / T), where N0 is the starting amount, N the amount left, t the time and T the half-life, with t and T in the same unit. The calculator rearranges it to solve for whichever value you leave out. Going the other way, 100 falling to 25 is two halvings, so at a half-life of 5,730 years it takes 11,460 years. The page also shows the decay constant, ln 2 divided by the half-life, which is 0.000121 per year in the first example; the textbook credited below writes ln 2 as 0.693. Amounts can be in any unit, from grams to atoms to percent, as long as the starting amount and the amount left use the same one.
Frequently asked questions
How do I calculate the amount left after a half-life?+
Divide the time by the half-life to get the number of half-lives, then multiply the starting amount by one half raised to that number. For 100 units, 10,000 years and a half-life of 5,730 years, that is 1.745 half-lives and 29.83 units left.
How do I find the half-life from a starting amount, an amount left and a time?+
Take the starting amount over the amount left, find how many times you would have to halve to get there, which is its base-2 logarithm, and divide the time by that number. Choose Half-life in the calculator and enter the other three values.
What is the decay constant?+
It is the rate constant k in the equivalent form N = N0 e^(-kt). It equals ln 2 divided by the half-life and gives the proportional rate of loss at any moment. A half-life of 5,730 years gives about 0.000121 per year.
Does a substance ever reach zero?+
In this model the amount keeps halving and never reaches exactly zero, though it soon becomes too small to measure. For a real sample of atoms, the count is a whole number, and the formula describes the average behaviour of a large number of them.
Model: based on OpenStax, Chemistry 2e (2019), section 21.3, Radioactive Decay, which gives N = N0 e^(-lambda t) with lambda = ln 2 / half-life; the calculator uses the equivalent form N = N0 x (1/2)^(t / half-life).
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