Radioactive Half-Life Calculator
Radioactive isotopes decay at a steady rate set by their half-life: the time for half the nuclei to decay. This calculator takes an initial amount, the half-life, and the elapsed time, and returns the amount remaining, the fraction left, the number of half-lives elapsed, and the decay constant. Keep the elapsed time and half-life in the same unit. It works for any quantity that decays exponentially, from sample mass to activity.
Half-life decay formula
N = N0 * (1/2) ^ (t / t_half)
Fraction remaining = (1/2) ^ (t / t_half)
Half-lives elapsed = t / t_half
Decay constant lambda = ln(2) / t_half
Each half-life halves the remaining amount. The decay constant lambda relates the half-life to the continuous exponential form N = N0 times e to the power minus lambda t.
Worked example
Carbon-14 has a half-life of 5,730 years. Starting from 100 units after 11,460 years (two half-lives): N = 100 * (1/2)^(11,460 / 5,730) = 100 * (1/2)^2 = 25.00 units. Fraction remaining = 0.25. Half-lives = 2.00. Lambda = 0.693 / 5,730 = 1.21e-4 per year.
Radioactive half-life: frequently asked questions
How do you calculate remaining amount after radioactive decay?
The amount left is the initial amount times one half raised to the power of elapsed time divided by the half-life: N = N0 * (1/2)^(t / t_half). After one half-life, half remains; after two, a quarter; and so on.
What is the decay constant?
The decay constant lambda is the natural log of 2 divided by the half-life: lambda = 0.693 / t_half. It is the probability per unit time that a given nucleus decays, and it links the half-life to the exponential decay law N = N0 times e to the power minus lambda t.
Do the time and half-life units need to match?
Yes. The exponent is a ratio of elapsed time to half-life, so both must be in the same unit, whether seconds, years, or any other. The calculator uses whatever consistent unit you enter for both fields.
Sources
- NIST: Radiation Physics Division.
- The decay law N = N0 (1/2)^(t/t_half) and lambda = ln(2)/t_half are standard results in nuclear physics.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.