Radiocarbon Dating Calculator

Results

This is an uncalibrated radiocarbon age. It is not a calendar date: atmospheric ¹⁴C has varied, so a calibration curve (IntCal20 for the northern hemisphere) and a program such as OxCal or CALIB are needed to turn it into calendar years.

How to Use the Radiocarbon Dating Calculator

1. 1. Choose what you are starting from. Percent modern carbon (pMC) and fraction modern (F¹⁴C) are the two forms a laboratory reports. A ¹⁴C/¹²C ratio needs the modern reference ratio too. The last option goes the other way: from a conventional age to the pMC it implies.
2. 2. Enter the value and, if you have it, the ±1σ uncertainty in the same unit. The age uncertainty is worked out from it.
3. 3. Add δ¹³C only if the value is raw. Labs normally report results already corrected to δ¹³C = −25 ‰. If yours is not, enter the sample's δ¹³C and the tool applies the standard correction.
4. 4. Read two ages. The headline is the conventional age on Libby's 5,568-year half-life, which is the number to quote and to calibrate. The second is the same measurement on the Cambridge 5,730-year half-life. Neither is a calendar date.

How the Age Is Calculated

Carbon-14 forms in the upper atmosphere when cosmic-ray neutrons strike nitrogen-14, and living organisms take it in with the rest of their carbon. When an organism dies the intake stops and its carbon-14 decays by β⁻ emission back to nitrogen-14. The fraction of the original carbon-14 still present therefore measures the time since death.

F¹⁴C = A_SN / A_ON  (pMC = 100 × F¹⁴C)

t = −8033 × ln(F¹⁴C)  years BP

8033 = 5568 / ln 2

A_SN = A_S × [1 − 2(25 + δ¹³C) / 1000]

σₜ = 8033 × σ(F¹⁴C) / F¹⁴C

A_SN is the sample's ¹⁴C activity, corrected for isotopic fractionation to δ¹³C = −25 ‰, and A_ON is the modern reference: 0.95 times the 1950 activity of the NBS oxalic acid I standard, which approximates the activity of pre-industrial wood. These are the conventions of Stuiver and Polach (Radiocarbon, 1977), and the F¹⁴C notation follows Reimer, Brown and Reimer (2004).

Libby 5,568 Years or Cambridge 5,730 Years?

Willard Libby's first measurements gave a half-life of 5,568 ± 30 years. Better measurements soon pushed the accepted value up, and in 1962 a conference in Cambridge adopted 5,730 ± 40 years. Rather than make every published date wrong overnight, the radiocarbon community agreed to keep using Libby's value for conventional ages, and it still does. Calibration curves are built on that convention, so a conventional age must use 5,568 to be calibrated correctly.

That is why the tool puts the Libby age first and shows the Cambridge age beside it. The two differ by a constant factor of 5,730 ÷ 5,568 ≈ 1.029, so a 6,000-year Libby age is about 6,175 years on the Cambridge half-life. Use the Cambridge half-life when you want the physical decay time and Libby's when you want the number a radiocarbon laboratory would print. The related Half-Life Calculator handles general decay problems.

Worked Example

A laboratory reports a charcoal sample at 30.00 ± 0.30 pMC, already normalised to δ¹³C = −25 ‰. Then F¹⁴C = 0.3000 and the working is:

• Libby: t = −8033 × ln(0.3000) = 9,672 years BP, with σₜ = 8033 × 0.003 ÷ 0.300 = ±80 years.
• Cambridge: t = −(5730 ÷ ln 2) × ln(0.3000) = 9,953 ± 83 years.
• Normalisation: if the same 30.00 pMC were a raw measurement on bone collagen with δ¹³C = −20 ‰, the correction factor would be 1 − 2(25 − 20) ÷ 1000 = 0.99, F¹⁴C = 0.2970, and the age would be 9,752 years — about 80 years older.

BP means "before present", with the present fixed at AD 1950 so that ages do not drift as the years pass. A date of 9,672 ¹⁴C yr BP does not mean 7722 BC: that subtraction treats radiocarbon years as calendar years, which they are not.

What Calibration Does — and What This Tool Does Not Do

The age equation assumes that atmospheric carbon-14 has always had the modern level. It has not. The level has varied with the Earth's magnetic field, solar activity and ocean circulation, so a radiocarbon year is not a calendar year. Calibration compares the measured ¹⁴C age with tree rings, corals, cave deposits and varved sediments of known calendar age. The current northern-hemisphere curve, IntCal20 (Reimer et al., Radiocarbon 62(4), 2020), reaches back to 55,000 calendar years BP.

• The answer is a range, not a number. Calibration turns one age and its uncertainty into a probability distribution over calendar years, sometimes with several separate peaks where the curve wiggles or has a plateau.
• Older dates move more. Beyond the last few thousand years calibrated dates are generally older than the ¹⁴C age, and for Ice Age material the gap is thousands of years.
• The right curve depends on the sample. IntCal20 is for northern-hemisphere atmospheric carbon, SHCal20 for the southern hemisphere and Marine20 for the ocean. Marine and freshwater samples also carry a reservoir offset that must be corrected first.
• This tool stops before calibration. It does not read a curve, so it gives no calendar date, and you should not read one into a ¹⁴C age. Calibrate with a program such as OxCal or CALIB, using the curve that fits your sample.

Frequently Asked Questions

How do you calculate a radiocarbon age?

Divide the sample's ¹⁴C activity by the modern standard to get the fraction modern, F¹⁴C, then apply t = −8033 × ln(F¹⁴C). The 8033 is the mean life from Libby's half-life, 5,568 ÷ ln 2. A sample with 12.5% of the modern activity comes out at 16,704 years BP.

Why do laboratories use 5,568 years when the half-life is 5,730?

It is a convention kept for continuity. After the 1962 Cambridge conference adopted 5,730 ± 40 years as the better physical value, the community still reported ages with Libby's 5,568 so that published dates stayed comparable. Calibration curves are defined on the Libby basis, so a conventional age should use it.

What does BP mean in radiocarbon dating?

BP is "before present", and present is defined as AD 1950, the year the standard was fixed and before atmospheric nuclear testing changed the carbon-14 level. So 3,000 BP means 3,000 years before 1950. Calibrated ages are written cal BP, on the same 1950 baseline.

How far back can radiocarbon dating go?

Around 50,000 years in the best cases, where only about 0.2% of the original carbon-14 remains. Past that, a trace of modern contamination or the instrument's background can outweigh the real signal, so an apparent age near the limit is best read as a minimum.

What are pMC and F¹⁴C?

Both express the sample's carbon-14 content against the modern standard. F¹⁴C is the fraction, so 0.25 means a quarter of the modern level; pMC is the same number times 100, so 25 pMC. Values above 1 (100 pMC) come from carbon taken up after the 1950s bomb tests and have no conventional age.

What is the difference between radiocarbon age and calendar age?

The radiocarbon age assumes atmospheric carbon-14 was constant. Because it was not, the radiocarbon age is only a measurement. Calibration against records of known age, such as tree rings, converts it to a calendar-year range, usually older for samples beyond a few thousand years.

Does this calculator calibrate radiocarbon dates?

No. It computes conventional ages from your measurement and reports them uncalibrated, which is the form laboratories quote. For calendar dates, calibrate with IntCal20 (or SHCal20 or Marine20) in a program such as OxCal or CALIB.