How to calculate age using carbon dating
Half of the carbon-14 degrades every 5,730 years as indicated by its half-life.By measuring the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of the artifact.Obviously there will usually be a loss of stable carbon too but the proportion of radiocarbon to stable carbon will reduce according to the exponential decay law: R = A exp(-T/8033) where R is C ratio of the living organism and T is the amount of time that has passed since the death of the organism.
Both Carbon-12 and Carbon-13 are stable, but Carbon-14 decays by very weak beta decay to nitrogen-14 with a half-life of approximately 5,730 years.
Since Nitrogen gas makes up about 78 percent of the Earth's air, by volume, a considerable amount of Carbon-14 is produced.
The carbon-14 atoms combine with oxygen to form carbon dioxide, which plants absorb naturally and incorporate into plant fibers by photosynthesis.
As explained below, the radiocarbon date tells us when the organism was alive (not when the material was used).
This fact should always be remembered when using radiocarbon dates.