Graph of radiocarbon dating accuracy
Radiocarbon years ago may be abbreviated " The Northern hemisphere curve from INTCAL13.As of 2017 this is the most recent version of the standard calibration curve.In the example CALIB output shown at left, the input data is 1270 BP, with a standard deviation of 10 radiocarbon years.The curve selected is the northern hemisphere INTCAL13 curve, part of which is shown in the output; the vertical width of the curve corresponds to the width of the standard error in the calibration curve at that point.A normal distribution is shown at left; this is the input data, in radiocarbon years.The central darker part of the normal curve is the range within one standard deviation of the mean; the lighter grey area shows the range within two standard deviations of the mean.The curve showed two types of variation from the straight line: a long term fluctuation with a period of about 9,000 years, and a shorter term variation, often referred to as "wiggles", with a period of decades.
This has to be done by numerical methods rather than by a formula because the calibration curve is not describable as a formula.
Programs to perform these calculations include Ox Cal and CALIB.
These can be accessed online; they allow the user to enter a date range at one standard deviation confidence for the radiocarbon ages, select a calibration curve, and produce probabilistic output both as tabular data and in graphical form.
The graph to the right shows the part of the INTCAL13 calibration curve from 1000 BP to 1400 BP, a range in which there are significant departures from a linear relationship between radiocarbon age and calendar age.
In places where the calibration curve is steep, and does not change direction, as in example t in blue on the graph to the right, the resulting calendar year range is quite narrow.