Radioactive Decay Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/6/2026
Radioactive decay is calculated with N(t) = N₀ × (1/2)^(t ÷ T), where T is the half-life. After 2 full half-lives, exactly 25% of a radioactive element's initial quantity remains, regardless of its exact half-life.
Explanation
Radioactive decay follows a characteristic exponential law: at every time interval equal to the element's half-life, exactly half of the remaining quantity decays, independent of the starting amount. This behavior is mathematically identical to that of our drug half-life calculator in pharmacology: both phenomena follow exponential decay where a constant fraction disappears at regular intervals, the only difference being the field of application (nuclear decay here, elimination of a substance by the body in the other case); the reverse phenomenon, growth that doubles at regular intervals rather than decay that halves, is covered by our doubling time calculator. A radioactive element's half-life varies enormously from one isotope to another: a few seconds for some highly unstable isotopes, several billion years for uranium-238, with about 5,730 years for carbon-14, the isotope used in radiocarbon dating to estimate the age of ancient organic materials. This fundamental physical property makes radioactive decay predictable with great statistical precision over a large number of nuclei, even though the exact moment of decay of an individual nucleus remains, itself, fundamentally random and unpredictable.
Example: 100 units, half-life of 10, after 20
Inputs
Initial quantity: 100. Half-life: 10. Time elapsed: 20 (i.e. 2 half-lives).
Calculation
N(20) = 100 × (1/2)^(20÷10) = 100 × (1/2)² = 100 × 0.25 = 25.
Result
After 2 full half-lives, 25 units remain, i.e. 25% of the initial quantity.
Frequently asked questions
Why does exactly 25% remain after 2 half-lives, not 0%?
Because each half-life halves the quantity REMAINING at that point, not the initial quantity. After a first half-life, 50% remains (half of 100%); after a second half-life, half of that 50% remains, i.e. 25%. This repeated halving never quite reaches exactly zero, no matter how far into the future you go — mathematically, the quantity approaches zero without ever reaching it.
Can you predict when a specific radioactive atom will decay?
No, the decay of an individual atomic nucleus is a fundamentally random phenomenon in quantum mechanics: it's impossible to predict the exact instant a given atom will decay. Half-life only describes predictable behavior at the statistical scale, over a very large number of atoms (typically billions of billions in a macroscopic sample), where individual probabilities add up into a perfectly regular overall law.
How does radiocarbon dating use this formula?
A living organism continuously renews its carbon-14 through exchanges with the atmosphere, maintaining a stable proportion of this radioactive isotope. At death, this renewal stops, and the carbon-14 already present starts decaying according to its half-life of about 5,730 years. Measuring the remaining proportion of carbon-14 in an ancient organic remain therefore allows, using this formula in reverse, an estimate of how long ago the organism died.