Nuclear Decay Calculator
Find out how much of a radioactive sample remains after a given time. Enter a starting quantity, half-life, and elapsed time to see the full exponential decay breakdown.
Calculate Radioactive Decay
Enter your starting quantity, the isotope’s half-life, and the time elapsed. The calculator will show the remaining amount, the decay constant, and how many half-lives have passed.
Decay Solver
Project remaining quantity using the half-life decay formula
Decay Quick Facts
Essential concepts behind radioactive decay
Understanding Radioactive Decay
Radioactive decay follows a simple, predictable pattern at the level of a large sample, even though it’s random for any single atom. Here’s the logic behind the calculation.
Start With the Half-Life
Every radioactive isotope has a fixed half-life, the time it takes for half of any sample of it to decay. This value is unique to each isotope.
Convert to a Decay Constant
The decay constant λ = ln(2) / half-life gives the fraction of atoms decaying per unit time, which is what actually drives the exponential formula.
Apply the Exponential Formula
The remaining quantity is N = N₀ × (1/2)^(t / half-life). Each time t reaches another full half-life, the quantity halves again.
Read Off the Result
The output tells you how much of the original material is left, how much has decayed, and how many half-lives have elapsed in total.
Common Isotope Half-Lives
Approximate half-lives for some widely referenced isotopes, useful as starting points for the calculator above.
| Isotope | Approximate Half-Life | Common Use / Context |
|---|---|---|
| Carbon-14 | ≈ 5,730 years | Radiocarbon dating of organic material |
| Iodine-131 | ≈ 8.02 days | Medical imaging and thyroid treatment |
| Cobalt-60 | ≈ 5.27 years | Industrial radiography, radiotherapy |
| Radon-222 | ≈ 3.82 days | Naturally occurring indoor air contaminant |
| Caesium-137 | ≈ 30.17 years | Environmental contamination studies |
| Uranium-235 | ≈ 703.8 million years | Nuclear fuel and geological dating |
| Uranium-238 | ≈ 4.47 billion years | Geological dating of rock formations |
| Potassium-40 | ≈ 1.25 billion years | Potassium-argon geological dating |
| Plutonium-239 | ≈ 24,100 years | Nuclear fuel and weapons material tracking |
Nuclear Decay FAQ
Answers to the most frequently asked questions about radioactive decay and half-life calculations.
Half-life is the time it takes for half of the radioactive atoms in a sample to decay into a different, more stable form. It’s a fixed, characteristic property of each isotope, so a sample of a given isotope always takes the same amount of time to fall to half its original quantity, regardless of how much you start with.
The remaining quantity after time t is N = N0 × (1/2)^(t / half-life), where N0 is the starting quantity. This can also be written using the decay constant as N = N0 × e^(−λt), where the decay constant λ equals ln(2) divided by the half-life.
No. Radioactive decay is a random process at the level of an individual atom, so there is no way to predict exactly when any one atom will decay. Half-life only describes the statistical average behaviour of a very large number of atoms, which is why decay calculations work reliably for real samples containing trillions of atoms.
For almost all practical purposes, no. Radioactive decay rates come from the nucleus of the atom, which is essentially unaffected by the surrounding chemical or physical environment, including temperature, pressure, and the chemical compound the atom is part of. This is different from ordinary chemical reactions, which do speed up or slow down with these conditions.