Radiocarbon dating is the most widely used dating technique in the world. Recent advances in Accelerator Mass Spectrometry (AMS) and sample preparation techniques have reduced the sample-size requirements by a factor of 1000 and decreased the measurement time from weeks to minutes. Today, it is estimated that more than 90 percent of all measurements made on accelerator mass spectrometers are for radiocarbon age dates. The production of ¹⁴C in the atmosphere varies through time due to changes in the Earth's geomagnetic field intensity and in its concentration, which is regulated by the carbon cycle. As a result of these two variables, a radiocarbon age is not equivalent to a calendar age. Four decades of joint research by the dendrochronology and radiocarbon communities have produced a radiocarbon calibration data set of remarkable precision and accuracy extending from the present to approximately 12,000 calendar years before present. This paper presents high precision paired ²³⁰Th/²³⁴U/²³⁸U and ¹⁴C age determinations on pristine coral samples that enable us to extend the radiocarbon calibration curve from 12,000 to 50,000 years before present. We developed a statistical model to properly estimate sample age conversion from radiocarbon years to calendar years, taking full account of combined errors in input ages and calibration uncertainties. Our radiocarbon calibration program is publicly accessible at: http://www.radiocarbon.LDEO.columbia.edu/ along with full documentation of the samples, data, and our statistical calibration model.