Radioactive Decay Calculator
Enter a starting amount, the elapsed years, and the half-life to see how much of a radioactive substance is still left — and watch the quantity halve with every half-life.
How much is still there
Enter the initial amount, the elapsed years, and the half-life and the calculator returns the remaining amount using N = N₀ × (1/2)^(elapsed / half-life).
Match the units
Enter the elapsed span and the half-life in the same unit (years here) so their ratio is unitless and the exponent is correct.
What is radioactive decay?
Why the amount left keeps halving
This radioactive decay calculator shows how much of an unstable isotope remains after a given span. Radioactive decay is the process by which an unstable nucleus loses energy and transforms, so the amount of the original substance steadily shrinks. The pace is set by the half-life: the span over which exactly half of whatever is present decays away. From a starting amount N₀, the remaining amount after one half-life is half, after two half-lives a quarter, after three an eighth — the same fraction lost in each step, never reaching zero. It is the number behind carbon-14 dating, medical isotope dosing, and nuclear-waste planning.
Enter a starting amount, the elapsed years, and the half-life to get the remaining amount instantly.
The remaining amount is the starting amount multiplied by one-half raised to the number of half-lives that have elapsed — the elapsed span divided by the half-life.
N = N₀ × (1/2)^(elapsed / half-life)The exponent is the number of half-lives, so it need not be a whole number: a fractional exponent gives the partial decay between half-lives. Because the base is one-half, every whole step multiplies the remaining amount by 0.5. Keep the elapsed span and the half-life in the same unit so the ratio is a pure count of half-lives.
Suppose you start with 100 g of carbon-14, whose half-life is 5730 years, and 11,460 years pass.
Count the half-lives
11,460 ÷ 5730 = 2 — exactly two half-lives have elapsed.
Halve once per half-life
(1/2)^2 = 0.25 — a quarter of the original is left.
Multiply by the starting amount
100 × 0.25 = 25 g — the remaining amount of carbon-14.
The remaining amount answers one question: how much of the original substance has not yet decayed. The key insight is that each half-life halves what is present, so the fraction left runs 100% → 50% → 25% → 12.5% and so on. The drop is steepest at first and then slows, which is why decay curves flatten into a long tail rather than hitting zero. Two half-lives leave a quarter, not nothing — a common point of confusion, since "two halves" sounds like all of it should be gone. For carbon-14 dating this is exactly the logic in reverse: measure the fraction of carbon-14 left in a sample and you can read off how many half-lives, and therefore how many years, have elapsed. A heavier starting amount scales the result in direct proportion, but the half-life is the lever that sets the shape of the curve.
The formula is exact, but a couple of practical points are worth keeping in mind.
Exponential decay and consistent units
This calculator models smooth exponential decay of a single isotope, the correct description for a large number of atoms. It does not track decay chains, where the product is itself radioactive, nor the random behaviour of a handful of individual atoms. Keep the elapsed span and the half-life in the same unit — both in years here — or the exponent, and therefore the remaining amount, will be wrong.