Hong Life CalculatorsUnderstanding the carbon-14 dating calculator — concept and principle
Radiocarbon dating estimates how long ago a once-living organism died by measuring how much of its carbon-14 is left. This calculator converts the remaining C-14, as a percentage of the modern level, into an age using two half-lives: the accurate 5730-year value and the Libby half-life of 5568 years that laboratories use for the conventional radiocarbon age.
How it is calculated
- Age with t½ = 5730: t = −(5730 / ln 2) × ln(N/N₀) ≈ −8267 × ln(N/N₀)
- Conventional radiocarbon age: t = −8033 × ln(N/N₀)
N/N₀ is the measured C-14 level divided by the modern reference level (the input % ÷ 100). 8033 years is the mean life that corresponds to the Libby half-life (5568 ÷ ln 2). The age is in years before the time of measurement; conventional ages are formally quoted as years BP, "before present", where present means AD 1950.
The principle
Cosmic rays create C-14 in the upper atmosphere. It becomes CO₂, enters plants by photosynthesis and animals by eating, so a living organism keeps roughly the atmospheric ratio of C-14 to C-12. After death no new carbon comes in and C-14 decays with a half-life of about 5730 years. Solving N = N₀e^(−λt) for t gives the formulas above. Labs keep using the older Libby value so that results published since the 1950s remain comparable; the difference is then handled by calibration.
Worked example
- Input: 25% of modern C-14, so N/N₀ = 0.25.
- ln 0.25 = −1.386294.
- With t½ = 5730: 5730 ÷ 0.693147 = 8266.64; 8266.64 × 1.386294 = 11,460 years. Exactly two half-lives, as expected for 25%.
- Conventional age: 8033 × 1.386294 = 11,136.1 years BP.
| C-14 remaining (% of modern) | Age (years, t½ = 5730) |
|---|---|
| 6.25 | 22,920 |
| 12.5 | 17,190 |
| 18.8 | 13,838.16487 |
| 25 | 11,460 |
| 31.2 | 9,615.352016 |
| 37.5 | 8,108.164871 |
| 50 | 5,730 |
How to read the result
A conventional radiocarbon age is not a calendar date. Atmospheric C-14 has varied over time, so labs convert it to calendar years with a calibration curve such as IntCal20, giving a probable date range. The method is practical up to about 50,000 years; beyond that too little C-14 remains to measure reliably.
Common mistakes
- Treating the conventional age as a calendar age without calibration.
- Using the method for rocks or for objects that never exchanged carbon with the atmosphere.
- Ignoring contamination by modern carbon, which makes old samples look much younger.
- Forgetting reservoir effects: marine and freshwater organisms can appear hundreds of years older.
Frequently asked questions
Why do labs still use 5568 years?
It is the convention set for reporting, so all conventional ages share one standard and are then calibrated.
Did nuclear tests affect radiocarbon?
Yes. Atmospheric testing in the 1950s and 1960s nearly doubled atmospheric C-14 in the Northern Hemisphere, which is used to date recent samples.
Can I date a 1-million-year-old fossil this way?
No. Other methods such as potassium–argon are used for that age range.
Sources: M. Stuiver and H. A. Polach, Discussion: Reporting of 14C data, Radiocarbon 19, 355 (1977) · P. J. Reimer et al., The IntCal20 Northern Hemisphere radiocarbon age calibration curve, Radiocarbon 62 (2020) · W. F. Libby, Radiocarbon Dating, University of Chicago Press (1952)