Carbon-14 Dating Calculator

Carbon dating (or radiocarbon dating) is a method used to estimate the age of organic materials by measuring the amount of carbon-14 (¹⁴C) they contain. Living organisms continuously exchange carbon with the atmosphere, but once they die, the C-14 in their tissues begins to decay at a known rate. By comparing how much C-14 remains versus how much was originally present, scientists can calculate how long ago the organism died.

Carbon-14 is a radioactive isotope produced naturally in the upper atmosphere. It decays exponentially with a half-life of about 5730 years. When an organism dies, it stops absorbing new C-14, so the ratio of C-14 to stable C-12 decreases over time. Scientists measure the remaining C-14 and use the formula t = −ln(F) / λ (where F is the fraction remaining and λ = ln(2) / t½) to estimate the sample's age.

Carbon dating is generally accurate to within a few decades to a few centuries, depending on the age and quality of the sample. It is most reliable for samples between a few hundred and about 50,000 years old. Beyond 50,000 years, there is so little C-14 remaining that measurements become unreliable. Calibration against known records (such as tree rings) further improves accuracy.

Radiocarbon dating is practical for samples up to about 50,000–60,000 years old. Beyond this limit, the amount of C-14 remaining is too small to measure accurately with standard methods. For older materials, scientists use other radiometric dating methods such as potassium-argon or uranium-lead dating.

The 5568-year half-life (known as the Libby half-life) was the original value determined by Willard Libby, the inventor of radiocarbon dating. Later, more precise measurements established the Cambridge half-life of 5730 years as the accepted standard. Most modern radiocarbon dates are reported using 5730 years, but some older literature uses the Libby value. Our calculator lets you choose either.

'BP' stands for 'Before Present,' where 'Present' is defined as the year 1950 CE — the approximate time when radiocarbon dating became widespread. So an age of 3,000 BP corresponds to roughly 1050 BCE (1950 − 3000 = −1050, i.e., 1050 BCE). Our calculator automatically converts the BP age to an approximate calendar year.

The fraction remaining (F) is the ratio of C-14 atoms currently in a sample (N) to the original amount of C-14 (N₀), expressed as F = N / N₀. A value of F = 1.0 means 100% of the original C-14 is present (the organism just died), while F = 0.5 means one half-life has elapsed (approximately 5730 years). You can also express this as % modern carbon (pMC = F × 100).

Carbon-14 has 8 neutrons. All carbon atoms have 6 protons, but C-14 has 2 more neutrons than the stable isotope C-12 (which has 6 neutrons). This extra mass makes C-14 unstable and radioactive, causing it to decay over time by emitting a beta particle and transforming into nitrogen-14.