Radiocarbon Dating Calculator

The technique depends on the radioactive decay of carbon-14, a rare but naturally occurring isotope of carbon. While alive, organisms continuously exchange carbon with the atmosphere through respiration and photosynthesis, maintaining a roughly constant ratio of ¹⁴C to stable ¹²C. The moment an organism dies, this exchange stops, and the ¹⁴C already present begins to decay at a known, constant rate. By measuring how much ¹⁴C remains relative to ¹²C in a sample, scientists can calculate how long ago the organism died.

Carbon-14 has a half-life of 5,730 years—meaning that after every 5,730 years, half of the remaining ¹⁴C has decayed. After ten half-lives (about 57,300 years), so little ¹⁴C remains that measurements become unreliable. This defines the practical upper limit of the technique. For very old samples—millions of years old—other radiometric methods using longer-lived isotopes such as uranium-lead or potassium-argon are used instead.

Modern radiocarbon dating uses accelerator mass spectrometry (AMS), which can detect ¹⁴C concentrations as low as one part per trillion and requires only milligram-sized samples. This has transformed the technique, allowing dating of precious artifacts, individual seeds, tiny bone fragments, and ancient DNA.

Calibration is an important refinement. The atmospheric ¹⁴C/¹²C ratio has not been perfectly constant over time due to fluctuations in cosmic ray flux, solar activity, and ocean circulation. Calibration curves—most notably IntCal, produced by an international collaboration—map radiocarbon years to calendar years, allowing raw ¹⁴C measurements to be converted to accurate calendar dates. The result is typically expressed as a calendar date with a confidence range, such as 3200 ± 80 cal BP (calibrated years Before Present, where Present = 1950).

This calculator uses the exponential decay formula to estimate the age of a sample given the fraction of ¹⁴C remaining. It is ideal for educational purposes, laboratory exercises, and quick estimates before applying full calibration curves.

The development of accelerator mass spectrometry (AMS) in the 1970s and 1980s represented a paradigm shift in radiocarbon dating capability. While conventional beta-counting methods required gram-sized samples and counting periods of many hours, AMS can measure ¹⁴C abundance in milligram samples within minutes. This technical advance opened the field to previously impossible applications: dating individual seeds from archaeological sites, testing the authenticity of historical documents and artworks, and even dating the paper and ink of disputed manuscripts.

Bomb radiocarbon dating is a specialized application that exploits the doubled atmospheric ¹⁴C concentration produced by above-ground nuclear weapons testing between 1955 and 1963. Materials formed during or after this period—including human tissues, wildlife specimens, and fraudulent "antique" items—can be dated with great precision by comparing their ¹⁴C concentration to the known bomb curve. This technique has been used in forensic investigations to determine the year of birth of unidentified individuals and to detect wine fraud (post-bomb wine sold as pre-1950 vintage).

Marine radiocarbon dating presents a specific complication: the ocean exchanges carbon with the atmosphere more slowly than the atmosphere exchanges with terrestrial systems, so marine organisms appear artificially older than their actual death date by the "marine reservoir effect"—typically 400–500 years in open ocean settings, but highly variable near upwelling zones. The Marine20 calibration curve corrects for the global average marine reservoir effect; regional corrections (ΔR values) are applied for specific locations.