Radiocarbon (Carbon-14) Dating Calculator

Carbon-14 is produced continuously in the upper atmosphere when cosmic-ray neutrons strike nitrogen-14, and it oxidises to carbon dioxide that mixes through the atmosphere, ocean, and biosphere. A living plant or animal exchanges carbon with that reservoir fast enough to hold a roughly constant ratio of about one C-14 atom per 10 to the 12th atoms of C-12, corresponding to a specific activity near 13.56 disintegrations per minute per gram of carbon. Exchange stops at death, and the trapped C-14 decays by beta emission with a half-life of 5,730 years, so the age follows from the exponential law as t = -ln(A/A0) divided by lambda, with lambda equal to ln(2)/5730 or 1.2097 times 10 to the minus 4 per year. Roughly 8 to 10 half-lives can be resolved before the residual activity sinks into background, giving a working ceiling near 50,000 years with conventional counting and about 55,000 to 60,000 years with accelerator mass spectrometry, which counts atoms directly and needs only a few milligrams of carbon rather than several grams. The raw exponential age is a starting point, not a calendar date. Atmospheric C-14 has never been truly constant: solar modulation and changes in the geomagnetic field alter production, and the century-scale wiggles are known as de Vries effects. Fossil fuel combustion diluted atmospheric C-14 through the industrial era, the Suess effect, while atmospheric weapons testing nearly doubled it by 1963, which is why the convention fixes Present at 1950 CE and quotes uncalibrated results as years BP. Converting to calendar years requires a calibration curve built from tree rings, corals, and speleothems, currently IntCal20 for the Northern Hemisphere with SHCal20 and Marine20 counterparts, and flat sections of that curve can turn a precise measurement into a broad date range. Other systematic offsets include the marine reservoir effect, which makes marine organisms appear several hundred years too old, the hard-water effect on freshwater samples, isotopic fractionation corrected by normalising to a delta C-13 of minus 25 per mil, and contamination by younger rootlets or older carbonate.

The method was created by Willard Frank Libby at the University of Chicago in the late 1940s. Serge Korff had reported in 1939 that cosmic rays generate neutrons in the upper atmosphere, and Libby reasoned that those neutrons would make carbon-14 from nitrogen at a steady rate, leaving all living things faintly radioactive. Working with James Arnold and Ernest Anderson, he detected natural C-14 in biological material in 1947, then in 1949 published the first archaeological dates in Science, testing the technique against samples of known age including wood from Egyptian dynastic tombs. Libby received the 1960 Nobel Prize in Chemistry for the work, and the term radiocarbon revolution came to describe how the method freed prehistoric chronology from relative dating and regional cross-references. Libby originally adopted a half-life of 5,568 years. More precise measurements in the early 1960s established 5,730 years, but because thousands of published dates used the earlier figure, the community agreed to keep reporting conventional ages on the Libby half-life and to handle the correction during calibration, a convention formalised in guidance by Minze Stuiver and Henry Polach in 1977 along with the year 1950 as the BP datum. Hans Suess and others showed through the 1960s that tree-ring dated wood did not match radiocarbon years, and bristlecone pine chronologies built by Wesley Ferguson allowed the first calibration curves. Accelerator mass spectrometry arrived in 1977 through groups at Rochester, McMaster, and Oxford, cutting sample sizes by orders of magnitude and enabling direct dating of small artefacts such as textile threads from the Shroud of Turin in 1988. Successive international IntCal curves have refined calibration since 1986.