Radioactive Decay Calculator
Determine how much of a radioactive substance remains after a given time. Use this when studying nuclear physics, carbon dating, or tracking isotope decay in medical and environmental contexts.
About this calculator
Radioactive decay follows first-order kinetics, meaning a fixed fraction of atoms disintegrates per unit time. The governing formula is N(t) = N₀ × (0.5)^(t / t½), where N₀ is the initial amount, t is the elapsed time, and t½ is the half-life of the isotope. Each half-life period cuts the remaining quantity exactly in half. This exponential relationship means decay slows progressively — the substance never fully disappears mathematically. The formula applies equally to mass, activity, or number of atoms. Common applications include carbon-14 dating (t½ ≈ 5,730 years), iodine-131 in medicine (t½ ≈ 8 days), and uranium-238 in geology (t½ ≈ 4.47 billion years).
How to use
Suppose you start with 200 g of iodine-131, which has a half-life of 8 years (using years for consistency), and 24 years pass. Plug into N(t) = 200 × (0.5)^(24 / 8) = 200 × (0.5)^3 = 200 × 0.125 = 25 g remaining. Enter 200 in Initial Amount, 8 in Half Life, and 24 in Time Elapsed. The calculator returns 25 g, confirming three full half-lives have elapsed and seven-eighths of the material has decayed.
Frequently asked questions
What is the half-life formula used in radioactive decay calculations?
The half-life formula is N(t) = N₀ × (0.5)^(t / t½). N₀ is the starting quantity, t is the time elapsed, and t½ is the half-life in consistent time units. Every time t equals one half-life, the remaining amount is halved. This formula is derived from the general exponential decay law N(t) = N₀ × e^(−λt), where the decay constant λ = ln(2) / t½.
How does radioactive decay differ from chemical decomposition?
Radioactive decay is a nuclear process driven by instability in an atom's nucleus, completely independent of temperature, pressure, or chemical state. Chemical decomposition, by contrast, involves rearrangement of electron bonds and is heavily influenced by environmental conditions. The rate of radioactive decay is fixed by the half-life and cannot be altered by any chemical or physical means. This makes radioactive isotopes reliable clocks for dating ancient materials.
When should I use a radioactive decay calculator in real life?
You would use this calculator when estimating how long a radioactive medical tracer remains active in a patient, determining safe storage timelines for nuclear waste, or performing radiometric dating of archaeological samples. Environmental scientists use it to track radioactive contamination levels over time. It is also useful in nuclear engineering for managing isotope inventories in reactor fuel cycles.