Radiocarbon Dating Calculator

Background.

Every living thing takes in carbon while it lives, and a tiny, steady share of that carbon is radioactive carbon-14, made in the upper atmosphere by cosmic rays. When the organism dies the intake stops, and the carbon-14 it holds decays at a fixed rate, halving roughly every five and a half thousand years. Measure how much is left and you can count back to when it stopped.

Laboratories report that measurement as fraction modern carbon, F: the sample's carbon-14 content, already corrected for isotopic fractionation, as a share of a standard representing the atmosphere of 1950. Turning F into an age takes one line of arithmetic, and that line is what runs here. A sample at F = 0.5 has been through one half-life; at 0.25, two.

The half-life field defaults to 5,568 years, which is not the best modern value. It is the Libby half-life, the figure Willard Libby worked with when he developed the method, and the Stuiver and Polach reporting convention of 1977 keeps it deliberately so that every conventional radiocarbon age ever published sits on one consistent scale. The better-measured 5,730 years would make each age about 3% older, but that is not how the discrepancy is dealt with in practice.

Calibration deals with it. The atmosphere's carbon-14 level has drifted over the millennia, so radiocarbon years are not calendar years, and a conventional age has to pass through a calibration curve such as IntCal20 before it can be quoted as a date. The age given here, in years BP or 'before present', with present fixed at AD 1950, is the input to that step and not a substitute for it. Background subtraction, reservoir offsets for marine or freshwater samples, and error bars stay with the laboratory report.

What is radiocarbon dating calculator?

A conventional radiocarbon age is the age implied by a sample's remaining carbon-14, calculated with the Libby half-life of 5,568 years and counted in years before AD 1950 (BP). It assumes the sample began with the carbon-14 level of the 1950 reference standard and that decay alone has lowered it since. It sits on the radiocarbon timescale, which differs from calendar years, so it is the starting point for calibration rather than a calendar date.

How to use this calculator.

1. 01Copy the fraction modern value, often labelled F14C or Fm, from the laboratory report. If the lab gives percent modern carbon (pMC), divide by 100, so 25 pMC becomes 0.25.
2. 02Leave the half-life at 5,568 years to get a conventional age that can be compared with published dates and fed into a calibration program. Change it only to explore what another half-life would imply.
3. 03Expect values of F above 1 to be refused. Material from the second half of the twentieth century onward can carry more carbon-14 than the 1950 standard because of atmospheric nuclear testing, and it needs separate treatment.
4. 04Read the age in radiocarbon years BP, then calibrate it against IntCal20, or the Southern Hemisphere or marine curve if those fit the sample, to get a calendar range.

The formula.

age = −t½ × ln(F) ÷ ln 2. Radioactive decay is exponential: after a time t the fraction remaining is F = (½)^(t ÷ t½). Taking natural logarithms and solving for t gives the formula used here. With t½ = 5,568 years the constant t½ ÷ ln 2 comes to 8,033 years, the Libby mean-life, which is why the convention is often written as age = −8033 × ln(F). Because the age depends on the logarithm of F, equal ratios give equal steps: every halving adds 5,568 years, whether F falls from 1 to 0.5 or from 0.02 to 0.01. The same logarithm makes very old samples fragile. Near F = 0.002, about 50,000 years, contamination equal to just 0.1% of the sample's carbon in modern form would make it read roughly 3,250 years younger.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Stuiver M, Polach HA. Discussion: Reporting of 14C Data. Radiocarbon. 1977.
2. [2]Reimer PJ et al. The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve. Radiocarbon. 2020.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.