Carbon dating range
In Accelerator Mass Spectrometry (AMS), for example, the number of radiocarbon atoms in a stream of atoms coming from the sample is counted.Thus there are statistical counting uncertainties proportional to the square root of the number of atoms counted.For example, if a sample is tested and given a radiocarbon date of 1000 BC.with a standard deviation of plus or minus 120 years, the chances are two in three that that sample dates from between 1120 and 880 BC.This, in fact, is the most significant factor contributing to loss of precision in radiocarbon dates today.
Archeologists use several methods to establish absolute chronology including radiocarbon dating, obsidian hydration, thermoluminescence, dendrochronology, historical records, mean ceramic dating, and pipe stem dating.
Modern accelerator mass spectrometry (used for radiocarbon dating purposes to separate radiocarbon atoms from stable carbon atoms and count them) is quite precise.
The technology involved is fascinating and impressive.
Measurements can be made with a high degree of precision. Aardsma submitted a sample from a reed mat known to be over 5,000 years old.
The measurement, before calibration, came back with an error bar of /- about 60 radiocarbon years. It should be noted that these measurement uncertainties do not increase linearly as one goes back in time.