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Carbon-14 Dating Calculator

Enter the percentage of carbon-14 remaining to estimate the age.

How it is calculated

The age comes from the exponential decay law solved for time: age = −8267 × ln(P ÷ 100). Here P is the percentage of the original carbon-14 still left in the sample, and 8267 is the half-life of 5,730 years divided by ln 2, rounded to a whole number. The age is in years and is shown rounded to the nearest year. P must be above 0 and no more than 100; 100% gives an age of 0 and other values return no result. Every halving adds 5,730 years, so 50% is 5,730 years and 25% is 11,460. This is a raw radiocarbon age: it does not apply calibration for changes in atmospheric carbon-14 over time, which real labs add to the result.

Worked example

A charcoal sample keeps 30% of its original carbon-14. Fraction left: 30 ÷ 100 = 0.30. Natural log: ln 0.30 = −1.2040. Age: −8267 × (−1.2040) = 9,953 yr. That is between one and two half-lives, as expected, since 50% would be 5,730 years and 25% would be 11,460.

Try this example →

Common mistakes

  • Entering the percentage that has decayed instead of what remains. A sample that has lost 70% of its carbon-14 still has 30% remaining, so enter 30.
  • Typing a fraction like 0.3 instead of a percentage. The field is percent, and 0.3 is read as 0.3%, giving an age near 48,000 years.
  • Treating the result as a calendar date. It is a number of years before now, and real labs also calibrate it against tree-ring and other records.
  • Using it on samples that are not organic or are much older than about 50,000 years. Very small remaining percentages are too faint to measure, so the output has little meaning there.
  • Dating a sample whose carbon-14 content was measured with contamination. Small amounts of modern carbon make an old sample look much younger.

Sources

About this calculator

Carbon-14 dating estimates the age of once-living material by measuring how much of its original ¹⁴C has decayed back into nitrogen-14. Living organisms maintain a constant ¹⁴C ratio while exchanging carbon with the atmosphere, but that exchange stops at death, after which ¹⁴C decays with a half-life of 5,730 years: age = −(half-life / ln 2) × ln(fraction remaining), or equivalently, the fraction remaining after time t is (1/2)^(t/5730).

Archaeologists and geologists use this method to date organic remains — wood, bone, charcoal, shells, textiles — reliably up to roughly 50,000 years old, beyond which the remaining ¹⁴C becomes too faint to measure accurately, which is why it's the go-to technique for dating everything from ancient campfires to the Dead Sea Scrolls.

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Comments (1)

  • Editorial team

    The lower the percentage, the less you should trust the age. One percent remaining gives 38,071 years here, and near the 50,000-year edge a sample holds only about 0.2 percent of its carbon-14, where a trace of modern carbon picked up from soil or handling can make it look thousands of years too young. Treat very small percentages as a rough ceiling, not a date. What kind of sample are you working with, and what percentage did the lab report?

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