Reading a bone's age off its atoms.
Every radioactive isotope decays at a fixed, measurable rate. Carbon dating just runs that clock backward: measure how much carbon-14 is left in a bone, and the ratio tells you how long it's been decaying.
Elapsed t
in half-lives
0n = t / T½10 half-lives
Try
Radioactive decay follows N = N₀e−λt, where the half-life T½ sets the decay constant λ = ln2 / T½. Because λt = (ln2)·(t/T½), the same fraction remaining can be written N/N₀ = 2−ⁿ where n is just the elapsed time measured in half-lives — the two forms always agree, and 2−ⁿ is what this page computes to avoid rounding λ unnecessarily. The atom grid is a static illustration, not a simulation: real decay is a random process per atom, only statistically predictable in large numbers, and it doesn't halve the sample in one clean step the way this drawing implies. Carbon dating itself is only reliable out to about 8–9 C-14 half-lives (roughly 50,000 years) — beyond that, so little carbon-14 remains that measurement error swamps the signal, and other methods (like uranium–lead dating, used above for the geological preset) take over.