Estimate the age of once-living material from how much carbon-14 is left. Enter the percent remaining, the activity ratio or a measured activity, or go the other way and see how much C-14 remains after a given number of years.
Last updated:
I know
%
Percent of the original (living) carbon-14 level
Also called fraction modern (F¹⁴C); 1 = living material
Living carbon ≈ 13.56 dpm/g C (0.226 Bq/g C)
years
Same units as the value you entered; gives an age range
Enter your values to see the result.
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How to use the Carbon Dating Calculator
Choose what you know: percent remaining, activity ratio, measured activity, or the age.
Enter the value; for activity also enter the modern reference (13.56 dpm/g by default).
Pick the half-life: 5,730 years for textbook problems, 5,568 for conventional lab ages.
Add an uncertainty if you have one to get an age range.
Read the age and check the decay curve and table.
How carbon dating works
Cosmic rays constantly make carbon-14 in the upper atmosphere. Plants absorb it as carbon dioxide and animals eat the plants, so every living thing carries roughly the same small proportion of C-14. When an organism dies it stops taking in carbon, and its C-14 decays back to nitrogen-14 with a half-life of about 5,730 years. Measuring how much is left tells you how long ago it died.
Age from fraction remaining: t = −(t½ / ln 2) × ln(N / N₀) = t½ × log₂(N₀ / N)
Fraction remaining from age: N / N₀ = (½)t / t½
Conventional radiocarbon age: t = −8,033 × ln(F¹⁴C), using Libby's 5,568-year half-life
Activity of living carbon: about 13.56 decays per minute per gram of carbon (0.226 Bq/g)
Example: charcoal from an old hearth gives 6.68 dpm per gram of carbon against a modern 13.56 dpm/g. The ratio is 0.4926, so t = −8,267 × ln(0.4926) ≈ 5,853 years, a little more than one half-life.
Carbon-14 remaining over time
Age (years)
C-14 remaining (t½ = 5,730)
1,000
88.6%
2,000
78.5%
5,730
50%
10,000
29.8%
20,000
8.9%
30,000
2.7%
50,000
0.24%
Limits and good practice
Contamination with modern carbon makes old samples look much younger: 1% modern carbon in a 40,000-year-old sample shifts its apparent age by several thousand years.
Marine and freshwater samples can carry "old" carbon (reservoir effects) and need special corrections.
Material from after about 1950 contains extra C-14 from atmospheric nuclear tests and reads above 100% modern.
This calculator gives uncalibrated physics ages; published dates use calibration software and curves such as IntCal20.
Frequently asked questions
What is the carbon dating formula?
t = −(t½ / ln 2) × ln(N / N₀), where N / N₀ is the fraction of carbon-14 remaining. With t½ = 5,730 years this is t ≈ −8,267 × ln(N / N₀).
How old is a sample with 25% carbon-14 left?
25% is one quarter, which is exactly two half-lives: 2 × 5,730 = 11,460 years using the 5,730-year half-life.
Why are there different half-lives for carbon-14?
Willard Libby's original value was 5,568 years; later measurements gave 5,730 ± 40 years and the current best estimate is about 5,700 ± 30 years. Labs still report conventional ages with 5,568 years by convention, then calibrate them.
What does BP mean in radiocarbon dates?
BP means 'before present', where present is fixed at 1950 CE. A radiocarbon age of 3,000 BP corresponds roughly to 1050 BCE before calibration.
How far back can carbon dating go?
About 50,000 years. After roughly nine half-lives less than 0.2% of the original carbon-14 remains, which is hard to distinguish from background contamination.
What can be carbon dated?
Anything that once took in carbon from the atmosphere: wood, charcoal, seeds, bone collagen, shell, cloth, paper and leather. Rocks and most minerals cannot be dated this way; they use other isotopes such as potassium-argon or uranium-lead.
Why do labs calibrate radiocarbon ages?
Atmospheric C-14 has varied over time, so a raw radiocarbon age is not exactly calendar years. Calibration curves built from tree rings, corals and cave deposits convert it to a calendar date range.
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