About the Carbon Dating Calculator
Living plants and animals constantly take in carbon, including a tiny, steady fraction of radioactive carbon-14. When they die the intake stops and the carbon-14 decays away with a half-life of about 5,730 years. Measuring how much is left compared with a living sample tells you how long ago the organism died. This carbon dating calculator does that arithmetic: enter the percentage of carbon-14 remaining, or the sample's measured activity against a modern reference, and it returns the age.
You can also run it in reverse to see how much carbon-14 should remain after a given number of years, which is useful for homework problems and for understanding why radiocarbon dating stops working beyond about 50,000 years (less than 0.3% remains). Choose the modern 5,730-year half-life, the newer 5,700-year evaluation, or the 5,568-year Libby half-life that laboratories still use by convention when reporting "conventional radiocarbon ages" (years BP).
The result is a radiocarbon age, which assumes the atmosphere always held the same proportion of carbon-14. In reality it has varied, so laboratories convert radiocarbon ages to calendar dates with a calibration curve such as IntCal20; the two can differ by several centuries. Treat this tool as an educational model, not a substitute for a calibrated laboratory date.
How to use the carbon dating calculator
- 1Choose whether you know the percent remaining, the sample activity or the age.
- 2Enter the percent of carbon-14 left, or the sample and modern activities.
- 3Pick the half-life: 5,730 years for most textbook problems, 5,568 for conventional radiocarbon ages.
- 4Read the age, the number of half-lives and the decay curve.
Formula and method
Radioactive decay is exponential: after each half-life T½ half the remaining carbon-14 atoms have decayed. The fraction left after time t is (½)^(t/T½) = e^(−λt), where λ = ln 2 / T½ is the decay constant. Taking the natural log of both sides and rearranging gives the age from the measured fraction.
Activity (decays per minute per gram of carbon) is proportional to the number of carbon-14 atoms, so the ratio of a sample's activity to that of living material gives the same fraction. The calculation assumes the starting carbon-14 level matched today's modern reference and that the sample has not been contaminated with younger or older carbon.
- t
- Radiocarbon age (years)
- T½
- Half-life of carbon-14 (years)
- N / N₀
- Fraction of carbon-14 remaining
- A, A₀
- Sample activity and modern activity (dpm per g of carbon)
- λ
- Decay constant = ln 2 / T½
Worked examples
A quarter of the carbon-14 is left
25% is half of a half, so exactly two half-lives have passed: 2 × 5,730 = 11,460 years.
Charcoal with an activity of 9.2 dpm/g
The ratio 9.2 ÷ 15.3 = 0.6013, so about 60% of the carbon-14 remains. t = (5,730 ÷ 0.6931) × ln(1 ÷ 0.6013) ≈ 4,205 years.
Conventional radiocarbon age with the Libby half-life
Laboratories report conventional ages using Libby's 5,568-year half-life, so the same 25% gives 2 × 5,568 = 11,136 radiocarbon years BP. Calibration then converts this to calendar years.
How much C-14 is left after 10,000 years?
10,000 ÷ 5,730 = 1.745 half-lives, and 0.5^1.745 = 0.298, so about 29.8% remains. A modern activity of 15.3 dpm/g would have fallen to about 4.56 dpm/g.
Frequently asked questions
What is the half-life of carbon-14?+
About 5,730 years, the value most textbooks use. The latest evaluation by the Laboratoire National Henri Becquerel gives 5,700 ± 30 years, while radiocarbon labs still report ages using the original Libby value of 5,568 years by convention.
How far back can carbon dating go?+
Up to roughly 50,000 years. After about nine half-lives less than 0.3% of the original carbon-14 remains, which is too little to measure reliably above background. Older samples need other methods such as potassium–argon or uranium-series dating.
What is the difference between radiocarbon years and calendar years?+
A radiocarbon age assumes the atmosphere always had today's carbon-14 level. It has actually varied, so labs calibrate radiocarbon ages against tree rings, corals and other records (the IntCal20 curve) to get calendar dates, which can differ by hundreds of years.
What does BP mean in carbon dating?+
BP means "before present", where the present is fixed as the year 1950 by convention. A date of 3,000 BP means about 3,000 radiocarbon years before 1950, not before today.
Can you carbon date rocks or dinosaur bones?+
No. Carbon dating only works on material that was once alive and exchanged carbon with the atmosphere, and only back about 50,000 years. Dinosaur fossils are tens of millions of years old and are dated from surrounding volcanic rock using other isotopes.