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Radiocarbon dating measures how long carbon-bearing material has been isolated from a carbon reservoir. Atmospheric cosmic rays produce secondary neutrons, which create carbon-14 chiefly throughThe carbon-14 enters atmospheric carbon dioxide and then living organisms through carbon exchange, including photosynthesis and food consumption. While exchange continues, the organism's ${}^{14}\mathrm{C}/{}^{12}\mathrm{C}$ ratio tracks the relevant environmental ratio approximately.

After exchange ceases, the remaining carbon-14 undergoes beta-minus decay,while stable carbon-12 remains. With half-life $T_{1/2}\simeq 5730\mathrm{yr}$, the radioactive decay law givesThus measuring the isotope ratio $R$, or the radioactive activity per fixed amount of carbon, givesHere $a=\lambda N_{14}$ is compared at equal carbon content; $R_0,a_0$ describe the appropriate initial reservoir. Accelerator mass spectrometry counts the rare carbon-14 relative to stable carbon directly; a decay-counting method instead measures its radioactive activity.

The initial ratio is not perfectly constant. Atmospheric production changes and reservoir differences therefore require radiocarbon calibration, often using independently dated tree rings. Contamination and subsequent carbon exchange must also be controlled. The date measures closure of the carbon system, not automatically the date of every later event involving the object. The physical half-life is about $5730$ years; conventional radiocarbon ages historically use $5568$ years and must be calibrated before interpretation as calendar dates.^[ref]

Radiocarbon calibration converts conventional radiocarbon ages into calendar-age information using independently dated material and models of changes in reservoir isotope ratios. Conventional ages use the historical $5568$-year half-life, whereas the physical carbon-14 half-life is about $5730$ years.^[ref]