Carbon-14 dating calculator
Enter the percentage of carbon-14 a sample still has compared with living material, and the calculator gives its age from the exponential decay law. Or enter an age to see how much carbon-14 is left. Choose the measured half-life of 5730 years or the conventional Libby half-life of 5568 years used for radiocarbon ages.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the age, or the share of carbon-14 left.
- Enter the percentage of carbon-14 compared with a living sample (100 % = modern), or the age in years.
- Pick the half-life: 5730 years (measured) or 5568 years (Libby, for conventional radiocarbon ages).
- Age: t = T½ × log₂(100 ÷ p), where p is the percentage left.
- Share left: p = 100 × 2^(−t ÷ T½).
- Decay constant: λ = ln 2 ÷ T½; mean life: τ = T½ ÷ ln 2.
Worked example
A bone keeps 10 % of the carbon-14 of living tissue: t = 5730 × log₂ 10 = 5730 × 3.321928 = 19,035 years, or 3.3219 half-lives.
A 1000-year-old wooden beam still has 100 × 2^(−1000 ÷ 5730) = 88.6062 % of its carbon-14.
Limits
- This is a raw age. Atmospheric carbon-14 has varied over time, so labs convert radiocarbon ages to calendar dates with calibration curves.
- Contamination matters. A little modern carbon makes an old sample look much younger.
- Only once-living material such as wood, bone, charcoal or shell can be carbon-dated.
Frequently asked questions
How does carbon dating work?
Living things take in carbon, including a small, steady share of radioactive carbon-14. After death no new carbon-14 comes in, and what is there decays with a half-life of about 5730 years. Measuring how much is left gives the time since death.
What is the formula for carbon dating?
t = T½ × log₂(N₀ ÷ N) = T½ × ln(N₀ ÷ N) ÷ ln 2, where N ÷ N₀ is the fraction of carbon-14 left. With 25 % left, t = 5730 × log₂ 4 = 11,460 years.
Why are there two half-lives, 5730 and 5568 years?
Willard Libby's early value was 5568 years. Later measurements gave 5730 ± 40 years, but radiocarbon labs still report conventional ages with 5568 years so that results stay comparable, and then calibrate them to calendar years.
How old can carbon dating go?
After about ten half-lives, some 50,000 years, less than 0.1 % of the carbon-14 is left and it becomes too hard to measure. Older material is dated with other isotopes.