There are eight AMS laboratories currently operating in the Unites States.In Arizona, virtually all dating is performed by the Arizona Accelerator Mass Spectrometry (AMS) Laboratory at the University of Arizona in Tucson.This dramatically improves accuracy, and reduces the amount of carbon required from about 10 grams to only a few milligrams.In recent years, dating methods based on cosmogenic isotopes other than carbon (such as beryllium-10 and chlorine-36) have been developed, which allow for the dating of a wider variety of objects over much longer time scales.
Archaeologists are acutely aware of these and other potential difficulties, and take extreme care in the selection and handling of objects to be dated. In the 1970s a new technique was developed called Accelerator-based Mass Spectrometry (AMS), which counts the number of carbon-14 atoms directly.
In this way, calibration tables have been developed that eliminate the discrepancy.
Despite its usefulness, radiocarbon dating has a number of limitations.
So, if we find the remains of a dead creature whose C-12 to C-14 ratio is half of what it's supposed to be (that is, one C-14 atom for every two trillion C-12 atoms instead of one in every trillion) we can assume the creature has been dead for about 5,730 years (since half of the radiocarbon is missing, it takes about 5,730 years for half of it to decay back into nitrogen).
If the ratio is a quarter of what it should be (one in every four trillion) we can assume the creature has been dead for 11,460 year (two half-lives).
This turns out not to be exactly true, and so there is an inherent error between a raw "radiocarbon date" and the true calendar date.