On the Relationship Between Radiocarbon Dates and True Sample Ages

The result of a radiocarbon determination is commonly expressed as an age given in radiocarbon years. An error is usually assigned to each value as a measure of the statistical uncertainty of the measurement. Date lists published in this journal use a standard form of reporting dates and their errors (see Editorial Statements in Radiocarbon, v. 3 and v. 4). The conversion of a radiocarbon age, given in radiocarbon years B.P. (i.e., radiocarbon years elapsed since the origin of the sample) to a true calendar year makes necessary certain assumptions with respect to: (1) the half-life of C 14 , (2) the production rate of C 14 by cosmic rays, (3) the size of reservoirs into which C 14 is distributed and the exchange rate of this distribution. Libby (1955, p. 10) has shown that as an approximation one may assume that reservoir size and production and distribution rates, and therefore the C 14 activity in atmospheric CO 2 have been constant. However, the more accurate measurements of recent years have shown that at least one of these quantities must have varied with time. This means that a more complicated relationship exists between radiocarbon age and exact calendar age of a sample than had been assumed by Libby. This relationship cannot be determined theoretically, but can be derived empirically by determination of the radiocarbon contents of samples of known age. The following summarizes our present knowledge regarding differences between radiocarbon ages and true ages and the present status of the empirical calibration of the radiocarbon time scale.