Carbon Dating Calculator
Turn the carbon-14 left in bone, wood or charcoal into an age, or see how much would remain after any span of time.
By Manzoor Ahmad, pharmacist turned web designer· Updated How do you calculate age with carbon-14?
Age = (5,730 ÷ ln 2) × ln(N₀ ÷ N) ≈ −8,267 × ln(fraction remaining). A sample with 25% of its original carbon-14 is two half-lives old: 11,460 years. With 10% left it is about 19,035 years old. Labs report “conventional” ages with the Libby half-life (5,568 years) and then calibrate them to calendar years.
Carbon-14 remaining over time
| Half-lives | Age (years) | C-14 remaining | Activity (dpm/g C) |
|---|
Radiocarbon age vs calendar age
- Conventional radiocarbon age (BP): calculated with the Libby half-life of 5,568 years, counted back from AD 1950.
- Calibrated age (cal BP or cal BC/AD): the conventional age corrected for past changes in atmospheric carbon-14 using a calibration curve such as IntCal20. Calibration can shift results by hundreds to thousands of years.
- This calculator gives the physics-based age; for archaeological reporting, run the conventional age through a calibration program.
The same exponential-decay math applies to any isotope or medicine; try the half-life calculator.
Carbon dating FAQs
Living things take in carbon-14 from the atmosphere and keep it at a roughly constant level. After death, intake stops and carbon-14 decays to nitrogen-14 with a half-life of about 5,730 years, so measuring how much is left reveals how long ago the organism died.
t = (t½ ÷ ln 2) × ln(N₀ ÷ N), where N/N₀ is the fraction of carbon-14 remaining and t½ = 5,730 years. Equivalently, t = −8,267 × ln(N/N₀).
Two half-lives: 2 × 5,730 = 11,460 years. With 10% left it is about 19,035 years old.
5,730 ± 40 years (the 'Cambridge' value). Radiocarbon labs still report conventional ages with the original Libby half-life of 5,568 years for consistency, then calibrate them.
An age calculated with the Libby half-life (5,568 years), measured from AD 1950 and written as years BP ('before present'). It is about 3% younger than the Cambridge-half-life age and must be calibrated to give calendar years.
Atmospheric carbon-14 has varied over time because of changes in cosmic rays, Earth's magnetic field and the carbon cycle. Labs convert radiocarbon years to calendar years with curves such as IntCal20, built from tree rings, corals and cave deposits.
About 50,000 years. After roughly 9 half-lives less than 0.2% of the original carbon-14 remains, which is too little to measure reliably.
Anything that was once alive and contains carbon: wood, charcoal, bone collagen, shells, seeds, textiles, leather and peat. Rocks and metals cannot be carbon dated.
Modern (AD 1950 standard) carbon has a carbon-14 activity of about 13.56 disintegrations per minute per gram of carbon (dpm/g). Some textbooks use 15.3 dpm/g; enter whichever reference your course uses.
Atmospheric bomb tests in the 1950s and 1960s nearly doubled atmospheric carbon-14. This 'bomb pulse' lets scientists date recent samples very precisely but means post-1950 material has more than 100% modern carbon.
Modern accelerator mass spectrometry measures carbon-14 to a precision of a few decades for samples a few thousand years old. Contamination, the reservoir effect in marine samples and calibration uncertainty add error.
Carbon-14 is used as a tracer in drug development (microdosing and ADME studies) and in the carbon-14 urea breath test for Helicobacter pylori, applications that rely on its radioactivity rather than age.
Sources
- Godwin (1962), Half-life of Radiocarbon, Nature
- Stuiver & Polach (1977), Discussion: Reporting of 14C Data, Radiocarbon
- Reimer et al. (2020), The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve, Radiocarbon
- OpenStax Chemistry 2e, Section 21.3: Radioactive Decay
- American Chemical Society: Discovery of Radiocarbon Dating (National Historic Chemical Landmark)
Ages are uncalibrated estimates assuming a closed system and a constant initial carbon-14 level. Real radiocarbon dates require calibration and laboratory error analysis.