Radioactive Decay Calculator
Find how much of a sample remains after a time.
Any time unit
Same unit as half-life
Results update as you type.
How it works
Radioactive decay describes how an unstable isotope loses atoms over time, and this calculator tells you how much of a sample is left after a given period. You enter the initial amount, the isotope's half-life, and the elapsed time in the same unit, and it returns the remaining amount, the percentage still present, and the decay constant. Decay is exponential rather than linear: each half-life reduces the quantity by half, so after one half-life fifty percent remains, after two half-lives twenty-five percent, and after ten half-lives less than a tenth of one percent. This behaviour is the basis of radiometric dating, where the known half-lives of isotopes such as carbon-14 or uranium-238 let scientists estimate the age of fossils, rocks, and archaeological finds. It also governs how long nuclear waste stays hazardous, how medical radioisotopes clear from the body, and how long a radioactive tracer remains useful. The decay constant is a convenient alternative to the half-life for calculations, representing the probability per unit time that any given atom decays. Because the formula depends only on the ratio of elapsed time to half-life, you can use any consistent time unit. Enter the three values to see the result.
N = N₀·(½)^(t / t½); λ = ln2 / t½
Radioactive decay is exponential, so the amount remaining equals the initial amount multiplied by one half raised to the number of half-lives that have elapsed, which is the time divided by the half-life. After one half-life, half remains; after two, a quarter; after three, an eighth. The decay constant, the natural log of two divided by the half-life, gives the fraction of atoms that decay per unit time.
Source:Nuclear physics (exponential decay law)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter initial amount (n₀), half-life and elapsed time.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Amount remaining updates instantly as you type — no button to press.
Frequently asked questions
What is radioactive decay?
Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, transforming into a different, more stable nucleus over time. Because it is random at the level of individual atoms but predictable in bulk, a large sample decays exponentially, losing a fixed fraction of its remaining atoms in each equal period. This predictability makes decay useful for dating and dosing.
What is a half-life?
A half-life is the time it takes for half of the atoms in a radioactive sample to decay. It is a constant for each isotope, ranging from fractions of a second to billions of years. After one half-life, half the original material remains; after two, a quarter; after three, an eighth. This calculator uses the half-life to project how much of the sample is left after any elapsed time.
How is radioactive decay used for dating?
Radiometric dating measures how much of a radioactive isotope remains in a sample and compares it to the amount originally present, then uses the known half-life to calculate elapsed time. Carbon-14 dates organic remains up to about fifty thousand years old, while uranium and potassium isotopes with far longer half-lives date rocks billions of years old. The same decay formula underlies all these methods.
What is the decay constant?
The decay constant, written as lambda, is the probability that any single atom decays in a unit of time. It equals the natural logarithm of two divided by the half-life, so a shorter half-life gives a larger decay constant and faster decay. It appears in the exponential decay equation and links neatly to the half-life, offering an alternative way to express how quickly an isotope disappears.
Does the sample ever fully disappear?
Mathematically, exponential decay never reaches exactly zero, because each half-life removes only half of what remains rather than a fixed amount. In practice, after around ten half-lives less than a tenth of one percent is left, which is usually negligible. For real samples made of a finite number of atoms, the last atoms do eventually decay, but the smooth formula treats the amount as approaching zero gradually.