Half-Life Calculator
Solve radioactive or exponential decay — find the remaining amount, initial amount, elapsed time, or half-life, plus the decay constant and mean lifetime. Calculates in your browser.
Show the math
A quantity halves once per half-life, so after t the remaining amount is:
N = N₀ × (½)^(t / T½) · λ = ln(2) ÷ T½ · τ = 1 ÷ λ
Keep elapsed time and half-life in the same unit. All math runs in your browser.
What this does
A half-life calculator models exponential decay, where a quantity halves every fixed period. Give any three of initial amount, remaining amount, elapsed time, and half-life, and it solves for the fourth, plus the decay constant and mean lifetime.
How to use it
- Enter any three of the four values.
- Leave the value you want to find blank.
- Read the solved value with the decay constant and mean lifetime.
- Keep time and half-life in the same unit.
How it works
After each half-life the amount halves, so the remaining fraction is one-half raised to the number of half-lives elapsed. The decay constant is λ = ln(2) ÷ T½, and the mean lifetime is 1 ÷ λ.
N = N₀ × (½)^(t / T½)
Understanding your result
After one half-life 50% remains, after two 25%, after three 12.5%, and so on — the decay never quite reaches zero. The decay constant gives the instantaneous fractional decay rate, useful for activity and dating calculations.
Example
Starting with 100 units and a 10-year half-life, 25 units remain after 20 years (two half-lives).
Sources & methodology
Last updated .
Frequently asked questions
What is the decay constant?
The decay constant λ is the fraction of atoms that decay per unit time, equal to ln(2) divided by the half-life. A shorter half-life means a larger decay constant.
Do the time and half-life need the same units?
Yes. As long as elapsed time and half-life use the same unit — seconds, years, whatever — the result is correct; the calculator does not convert between units.
Is my data stored?
No. Everything is calculated locally in your browser.
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