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.
After another 5,730 years only one-quarter of the original carbon-14 will remain.
Once the radiocarbon concentration in a sample has been measured, the sample's age in "radiocarbon years" is determined mathematically.
The radiocarbon age must then be calibrated to determine the sample's age in calendar years.
For example, modern biblical chronology dates Noah's Flood to 3520 /- 21 B.
Absolute dating is the process of determining an age on a specified chronology in archaeology and geology.
In archaeology, absolute dating is usually based on the physical, chemical, and life properties of the materials of artifacts, buildings, or other items that have been modified by humans and by historical associations with materials with known dates (coins and written history).
Techniques include tree rings in timbers, radiocarbon dating of wood or bones, and trapped-charge dating methods such as thermoluminescence dating of glazed ceramics.
This, in fact, is the most significant factor contributing to loss of precision in radiocarbon dates today.
However, this contribution is usually only a few decades.
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.
Thus radiocarbon serves biblical chronology mainly by helping to eliminate large-scale biblical chronology errors arising out of misinterpretation of the biblical text or textual corruption.