An Egyptian king died in about 2625 BC. A bone from a pit, a charred seed from a hearth, a scrap of wood from a coffin: each of them can tell you its own age, with no label, no inscription and no help from a historian. The clock is inside the sample, and it started when the living thing stopped living.
High in the atmosphere, cosmic rays knock neutrons loose from air molecules. Some of those neutrons hit a nitrogen-14 atom and turn it into carbon-14, which is a carbon atom with two extra neutrons. That makes it unstable. It combines with oxygen to form carbon dioxide, drifts down, and is taken up by plants through photosynthesis. Animals eat the plants. So every living thing carries a tiny, steady share of carbon-14: about one carbon atom in a trillion.
While you are alive you keep topping that share up with every meal and every breath. When you die, the topping-up stops. The carbon-14 already inside you keeps decaying, one atom at a time, and nothing replaces it. The share falls, and how far it has fallen is the time since death.
Each carbon-14 atom has a fixed chance of decaying in any given year, and no heat, pressure or chemistry changes that chance. The result is a half-life of about 5,730 years: after that long, half the atoms are gone. After another 5,730, half of the rest go, leaving a quarter. After three half-lives, one eighth.
The decay of any single atom is pure chance, though. You cannot say when a given atom will go. Below is a sample of 800 carbon-14 atoms. Each one has its own random moment of decay, fixed in advance, so you can drag time forward and back and the same atoms always go at the same moments. Try it.
Drag past 40,000 years and watch the count: only a handful of atoms are left, and the estimate starts to jump around.
Push the slider to the far end. After roughly nine half-lives, only about 0.2% of the carbon-14 is left, so little that it is hard to tell from contamination and background noise. In the grid you can see the same thing in a simpler way: with 800 atoms, the last one or two flicker out at random times, so the count says almost nothing precise. Beyond about 50,000 years, radiocarbon dating stops being useful, and other methods take over.
The chemist Willard Libby worked this out in the 1940s. His first big test, published with James Arnold in December 1949, used wood from the tombs of the Egyptian kings Zoser and Sneferu. Historians had dated those tombs to about 2625 BC, give or take 75 years. Libby's radiocarbon average came out at 2800 BC, give or take 250. It was close, and he had no history book to peek at. He won the Nobel Prize in Chemistry in 1960.
The method assumes the carbon-14 share in the air was always the same. It was not: it has drifted with changes in cosmic rays and in the oceans. The fix came from trees. Each ring records the air's carbon-14 level for the year it grew, and rings can be counted back year by year for about 14,000 years. Matching a sample's raw radiocarbon age to the tree-ring record converts it into a calendar date. The current standard curve is called IntCal20.
There are other corrections too. Seashells and fish carry carbon from the ocean, where deep water is old and poor in carbon-14, so marine samples look about 400 years older than they are and need their own curve.
Radiocarbon dating does not read a date off a bone. It counts how many carbon-14 atoms are left, turns the share into a number of half-lives, and then corrects it against rings of trees. Use the mystery sample above to try the middle step yourself: measure the share, find the age that predicts it, and see how close you get.