N = N₀ · (½)t / T½
Radiometric dating calculator
How old is a sample if a quarter of its carbon-14 is left? Two half-lives: 11,136 years as a conventional radiocarbon age. Pick an isotope, enter the percentage of the parent left or the daughter-to-parent ratio, and get the age; or enter an age and see how much would be left.
Result
Age11,136 years BP
- C-14 left
- 25 %
- Half-lives gone
- 2
t = 5,568 years × log₂(100 ÷ 25) = 11,136 years- A conventional radiocarbon age, counted back from AD 1950 (BP) with the Libby half-life, as Stuiver & Polach (1977) define it.
- Uncalibrated. Real radiocarbon dates must be calibrated against a curve such as IntCal20 to turn them into calendar years.
How radiometric dating works
A radioactive parent isotope decays at a fixed rate: after one half-life half is left, after two a quarter, and so on, so N = N₀ · (½)t / T½ and the age is t = T½ × log₂(N₀ ÷ N). If the daughter isotope it decays into is trapped in the rock, the ratio of daughter to parent gives the same clock: t = (T½ ÷ ln 2) × ln(1 + D ÷ P). Potassium-40 is a special case, because only 10.72 percent of its decays make argon-40.
- Radiocarbon only works back about 50,000 years (USGS), because carbon-14's half-life is short. Results here are uncalibrated: real radiocarbon dates must be calibrated against a curve such as IntCal20 (Reimer et al. 2020), which runs to 55,000 years.
- Dinosaur bones are not dated directly. Most fossils lie in sedimentary rocks, which are dated by radiometric dating of volcanic layers, such as ash beds, above and below them (USGS).
- The range shown comes only from the half-life's own uncertainty; real measurements add their own errors.
Half-lives used
| Isotope | Decays to | Half-life | Source |
|---|---|---|---|
| Carbon-14 (Libby) | Nitrogen-14 | 5,568 years, by convention | Stuiver & Polach 1977 |
| Carbon-14 (Cambridge) | Nitrogen-14 | 5,730 ± 40 years | Godwin 1962 |
| Carbon-14 (evaluated) | Nitrogen-14 | 5,700 ± 30 years | IAEA LiveChart |
| Potassium-40 | Argon-40 (10.72 %), calcium-40 (89.28 %) | 1.248 ± 0.003 billion years | IAEA LiveChart |
| Rubidium-87 | Strontium-87 | 49.7 ± 0.3 billion years | IAEA LiveChart |
| Uranium-235 | Lead-207 (through a decay chain) | 704 ± 1 million years | IAEA LiveChart |
| Uranium-238 | Lead-206 (through a decay chain) | 4.468 ± 0.006 billion years | IAEA LiveChart |
Sources
- IAEA Nuclear Data Section, LiveChart of Nuclides, ground-state half-lives and decay branches (fetched 2 November 2026): www-nds.iaea.org/livechart.
- Stuiver M, Polach HA. 1977. Discussion: reporting of 14C data. Radiocarbon 19(3):355–363. doi:10.1017/S0033822200003672.
- Godwin H. 1962. Half-life of radiocarbon. Nature 195:984. doi:10.1038/195984a0.
- Reimer PJ et al. 2020. The IntCal20 Northern Hemisphere radiocarbon age calibration curve (0–55 cal kBP). Radiocarbon 62(4):725–757. doi:10.1017/RDC.2020.41.
- USGS. Geologic Time: Radiometric Time Scale. pubs.usgs.gov/gip/geotime/radiometric.html.
Questions
Can carbon dating date dinosaurs?
No. Radiocarbon only reaches back about 50,000 years, and the last non-bird dinosaurs died 66 million years ago. Their ages come from dating volcanic layers above and below the fossils.
Why are there three carbon-14 half-lives?
Conventional radiocarbon ages use the original Libby value of 5,568 years by agreement, so results stay comparable. The Cambridge value of 5,730 ± 40 years and the evaluated 5,700 ± 30 years are later measurements of the actual half-life.
What does BP mean?
Before Present, where the present is fixed at AD 1950, as Stuiver and Polach (1977) define it for conventional radiocarbon ages.