Model exponential decay. This free half-life calculator solves for the amount remaining, elapsed time, or the half-life itself, and shows the fraction left, decay constant and mean lifetime.
Solve for
units
units
Use any consistent time unit (seconds, years…) — keep time and half-life in the same unit. Amount can be mass, atoms, activity or a percentage; only the ratio matters.
Result
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Enter the values
Fraction remaining
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Half-lives elapsed
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Decay constant λ
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Mean lifetime τ
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Decay follows N = N₀ × (½)^(t / T½). The decay constant is λ = ln2 / T½, and the mean lifetime is τ = 1 / λ = T½ / ln2. After each half-life, half of what remains decays.
Use this free half-life decay calculator to find how much of a substance remains, how long decay takes, or the half-life itself. It also gives the decay constant and mean lifetime.
What this half-life calculator does
A half-life calculator models exponential decay. Choose what to solve for — the amount remaining, the elapsed time, or the half-life — and enter the known values.
Starting from 100 with a half-life of 1, after 3 half-lives only 12.5 remains. Going from 100 to 25 takes exactly 2 half-lives.
How much remains after each half-life
Half-lives
Fraction left
Percent
1
1/2
50%
2
1/4
25%
3
1/8
12.5%
4
1/16
6.25%
10
1/1024
~0.1%
Half-life, decay constant and mean life
The half-life is the time for half the substance to decay. The decay constant (λ) is the fraction decaying per unit time, and the mean lifetime (τ) is the average time an individual atom survives — always a bit longer than the half-life.
How to use the half-life calculator
Pick what to solve for — amount, time, or half-life.
Enter the known values (use one consistent time unit).
Read the result, plus fraction left and decay constant.
Half-Life FAQ
How do I calculate half-life decay?
Use N = N₀ × (½)^(t / T½). For example, starting at 100 with a half-life of 1, after 3 half-lives 12.5 remains.
How do I find how long decay takes?
Switch to time mode and enter the initial amount, remaining amount and half-life. Going from 100 to 25 with a half-life of 2 takes 4 units of time.
How do I find the half-life from measurements?
Use half-life mode with the initial amount, remaining amount and elapsed time. From 100 to 25 over 4 units gives a half-life of 2.
What is the decay constant?
The decay constant λ is ln2 ÷ half-life — the fraction that decays per unit time. The mean lifetime τ is 1 ÷ λ.
What units should I use?
Any consistent time unit, as long as time and half-life match. Amount can be mass, atoms, activity or a percentage, since only the ratio matters.
Is the half-life calculator free?
Yes, this half-life calculator is completely free, needs no sign-up, and gives instant results in your browser.
