Isotope Half-Life Decay Simulator
Pick a radioactive isotope and simulate exponential decay over time with an interactive SVG chart.
Decay Curve
What is half-life?
Half-life is the time required for half of a radioactive substance (or any quantity undergoing exponential decay) to disintegrate. After one half-life, 50% remains. After two half-lives, 25%. After three, 12.5%, and so on. The concept applies to radioactive decay, drug metabolism in the body, chemical reaction rates, and even the decay of internet content popularity.
The decay follows an exponential curve: N(t) = N0 * (1/2)^(t/t_half), where N0 is the initial quantity, t is the elapsed time, and t_half is the half-life. Each substance has a characteristic half-life that is constant regardless of temperature, pressure, or the amount present.
How half-life calculations work
Given any two of the three variables (initial amount, final amount, and time elapsed), plus the half-life, you can calculate the missing value. Common calculations include: how much remains after a given time, how long until only a specific amount remains, and what the half-life is given measured amounts at two different times.
How to use this tool
Enter the half-life, the initial quantity, and either the elapsed time (to find the remaining amount) or the desired remaining amount (to find the required time). The tool also generates a decay curve showing how the quantity decreases over multiple half-lives.
Half-life examples
- Carbon-14: 5,730 years. Used for archaeological dating of organic materials up to about 50,000 years old.
- Iodine-131: 8.02 days. Used in thyroid cancer treatment and medical imaging.
- Uranium-238: 4.47 billion years. Used for geological dating of rocks and the Earth itself.
- Caffeine in the body: 3-5 hours. Half the caffeine from your morning coffee is gone by lunch.
Frequently asked questions
Does a substance ever fully decay to zero?
Mathematically, exponential decay never reaches exactly zero โ it asymptotically approaches it. In practice, after about 10 half-lives (when less than 0.1% remains), the substance is considered effectively gone. For radioactive materials, individual atoms decay randomly, so at very small quantities, the last few atoms will eventually all decay.
Can half-life be changed or controlled?
For radioactive decay, the half-life is a fixed property of each isotope and cannot be changed by temperature, pressure, chemical reactions, or any ordinary physical process. This constancy is what makes radioactive dating methods reliable. Drug half-lives in the body can vary with liver function, age, and other medications.