Carbon dating calculator
Enter how much carbon-14 is left, get the age.
How does carbon dating work?
Living things keep a steady level of carbon-14; after death it decays with a half-life of 5,730 years. The age is t = −(5,730 ÷ ln 2) × ln(fraction remaining) (OpenStax Chemistry 2e).
Example: the Dead Sea Scrolls
OpenStax: a sample decays at 10.8 disintegrations per minute per gram against 13.6 for living material — 79% remaining — so it is about 1,900 years old.
What is a conventional radiocarbon age?
By an international convention (Stuiver and Polach, 1977), laboratories report ages using the older Libby half-life of 5,568 years, counted in years before 1950 (“BP”). The calculator shows both.
Is the result a calendar date?
Not exactly. The amount of carbon-14 in the air has varied over time, so radiocarbon ages must be converted with a calibration curve such as IntCal20 to get calendar years.
How old can carbon dating go?
After about 10 half-lives — roughly 57,000 years — only 0.10% of the carbon-14 is left, which is very hard to measure. OpenStax Chemistry 2e (section 21.3) gives about 30,000 years as the range for accurate dates and about 50,000 years as the practical limit for reasonably accurate ones; the fractions remaining are 2.7% and 0.24%.
Can I date anything with carbon-14?
Only material that was once part of a living organism and took up carbon from the atmosphere, such as wood, seeds, paper, bone or textile. Inorganic rock does not qualify, and the age you get is the time since the organism died or the plant was cut, not necessarily when an object was made from it.
The method and what it assumes
Carbon-14 forms in the upper atmosphere when cosmic-ray neutrons strike nitrogen-14. Living organisms keep the same carbon-14 to carbon-12 ratio as the air. After death the carbon-14 decays with a half-life of 5,730 years, so the remaining fraction tells you how many half-lives have passed (OpenStax Chemistry 2e, section 21.3). The calculator takes that fraction as a percent or as two decay rates per gram of carbon (sample and living reference) and returns t = −(5,730 ÷ ln 2) × ln(fraction). The method assumes the atmospheric ratio has been roughly constant; the textbook notes it has varied, and that fossil-fuel carbon is changing it, so ages are corrected with calibration data such as tree rings.
Worked example
OpenStax’s practice problem after Example 21.6 uses seed and plant material from Tutankhamun’s tomb, which decays at 9.07 disintegrations per minute per gram of carbon against 13.6 for living material. The fraction left is 9.07 ÷ 13.6 = 66.7%, and the age is −(5,730 ÷ 0.6931) × ln(0.667) = about 3,350 years. A sample with exactly half the living ratio is one half-life old, 5,730 years. For the Dead Sea Scrolls sample in the second answer, the age is 1,906 years with the 5,730-year half-life (the book, rounding the decay constant, gets 1,910) and 1,852 years BP on the conventional Libby scale, about 3% younger.
Common mistakes
The easiest slip is entering a fraction in the percent box: 0.79 instead of 79 gives about 40,000 years rather than 1,906. Second, comparing activities that are not per gram of carbon, or a sample count against a reference measured differently, which changes the ratio. Third, reading the result as a calendar date; a radiocarbon age needs calibration, and the Libby and 5,730-year ages are two conventions that differ by about 3%. Fourth, trusting an age beyond the practical limit of about 50,000 years, where only a fraction of a percent of the carbon-14 is left. Finally, carbon dating applies only to material that once lived.
Sources: OpenStax Chemistry 2e, section 21.3 “Radioactive Decay” (first-order decay, half-life of carbon-14, radiocarbon dating assumptions and range, Example 21.6 and its practice problem); Stuiver and Polach (1977) for the conventional Libby-age convention. Related: half-life calculator, integrated rate law calculator, activation energy calculator and scientific notation calculator.