At the Arizona Accelerator Mass Spectrometry facility, the radiocarbon age are determined by mearsuring the ratio (¹⁴C/¹³C) in a sample and comparing that ratio with a similar one measured for known standards (Linick et al 1986). The measured ratios of standards and samples are corrected to values corresponding to δ¹³C = -25‰ using (¹³C/¹²C) ratios measured in a stable isotope mass spectrometer and the "fraction of modern," F, of the sample, S, is deduced from the equation

    In this equation, the δ¹³C to which the ratio has been normalized is given by the number in square brakets, and 1950 stands for the standards retrieved in 1950.

    Since the fraction modern carbon is proportional to the decay time

F = e ^{-Age / τ},

The radiocarbon age of the sample, S, is calculated from the equation

Radiocarbon Age = -τ ln F,

where τ is the Libby mean life (8033 years).