Radiocarbon dating

Radiocarbon dating works out how long ago something living died, by measuring how much carbon-14 is left in it. It reaches back about 50 000 years and it is the reason we can put dates on the human past at all.

Willard Libby's team developed it in the years after the Second World War, and he won the 1960 Nobel Prize in Chemistry, in the committee's words,

for his method to use carbon-14 for age determination in archaeology, geology, geophysics, and other branches of science

The trick

Carbon-14 is made in the upper atmosphere. cosmic rays smash air molecules, the debris includes free Neutrons, and a neutron hitting ordinary nitrogen swaps a proton out:

¹⁴N + n → ¹⁴C + p

The ¹⁴C oxidises to CO₂ and mixes through the whole atmosphere. Plants breathe it in. Animals eat plants. Every living thing therefore runs at roughly the same ¹⁴C-to-¹²C ratio as the air — about one ¹⁴C atom in a trillion carbon atoms.

Death closes the account. No new carbon comes in, and the ¹⁴C that is there starts running down its half-life. Measure what fraction is left, and you have the time since death.

The nuclide

property	value
half-life	5700 ± 30 years
mean life	8223 years
decay mode	β⁻, 100% of the time
decay energy (Q)	156.4765 ± 0.0037 keV
daughter	¹⁴N (stable)
natural abundance in living carbon	≈ 1 part in 10¹²

Two things about that table shape the whole method.

The half-life sets the range. After ten half-lives — 57 000 years — a thousandth of the original ¹⁴C remains, and that is below what anyone can separate from contamination. In practice laboratories quote a limit near 50 000 years, about 8.8 half-lives.

The decay energy sets the method. At 156 keV the beta particles are feeble, and the decays are rare: a gram of modern carbon puts out only about twelve betas a minute. Libby had to count them one by one. Modern labs skip the waiting and use accelerator mass spectrometry, which weighs the ¹⁴C atoms directly instead of waiting for them to decay. That cut sample sizes from grams to milligrams and made it possible to date a single seed or a thread of a tapestry.

Two half-lives, one on purpose

This is the part that trips people up. Libby measured the half-life as 5568 ± 30 years. Later work put it at 5700 ± 30 years — about 2.4% higher.

The field never switched. A "conventional radiocarbon age" is still calculated with Libby's 5568-year value, on purpose, so that every measurement ever published stays comparable. The correction is folded into calibration instead. The other fixed conventions:

• BP means "before present", and "present" is AD 1950 — the year radiocarbon dating arrived, and the last year before atmospheric bomb testing wrecked the baseline.
• Ages are normalised to a δ¹³C of −25‰ to remove the different appetites plants have for the heavier carbon isotope.
• Results carry a ± because counting decays is a statistical business, not because the lab is being cautious.

So a radiocarbon age is not a date. It is a raw measurement in a defined unit that then has to be converted.

Calibration: the assumption that isn't true

The method assumes atmospheric ¹⁴C has always been at today's level. It has not. Cosmic-ray intensity varies with the Sun's activity and the Earth's magnetic field, and ocean circulation moves old carbon around. So a radiocarbon year is not a calendar year.

The fix is a calibration curve, built by measuring ¹⁴C in material whose true age is known independently — tree rings counted one at a time by dendrochronology, plus corals and cave deposits dated by uranium series. The current standard is IntCal20, covering 0 to 55 000 calendar years BP.

The size of the correction is not small:

calendar age (cal BP)	measured ¹⁴C age	offset
0	199 ± 11	+199
500	429 ± 10	−71
1 000	1 126 ± 13	+126
2 000	2 070 ± 14	+70
5 000	4 439 ± 15	−561
10 000	8 872 ± 21	−1 128
20 000	16 566 ± 45	−3 434
30 000	25 664 ± 92	−4 336
40 000	34 918 ± 125	−5 082
50 000	47 531 ± 354	−2 469

At the far end of the Ice Age, an uncalibrated result is wrong by more than three thousand years. Anyone quoting a raw radiocarbon age as a historical date is quoting the wrong number.

Plateaus: where the method goes blind

The curve is not just offset, it is bumpy — and where it flattens, dating stops working. The Hallstatt plateau is the notorious one:

calendar age (cal BP)	¹⁴C age
2 450	2 428
2 500	2 482
2 600	2 462
2 700	2 496

Two and a half centuries of real time compress into about 70 radiocarbon years — less than the measurement error. A sample from anywhere in the European Iron Age calibrates to a wide, flat range and no amount of laboratory precision fixes it. Archaeologists work around it with tree-ring sequences and stratigraphy instead.

Where it breaks

• Marine and freshwater samples. Ocean water carries dissolved carbon that has been out of contact with the atmosphere for centuries, so shellfish and fish-eaters date old. A separate Marine20 curve exists for this.
• Volcanic settings. Vents leak ¹⁴C-free carbon dioxide, and plants growing nearby take it up.
• Anything not once alive. Stone, metal, and pottery clay contain no biological carbon. What gets dated is charcoal in the temper, or soot on the surface, not the object.
• Contamination. A tiny amount of modern carbon on a 40 000-year-old sample shifts it enormously, because at that age there is almost no original ¹⁴C left to be swamped.
• Fossil-fuel and bomb carbon. Burning coal and oil released carbon so old it has no ¹⁴C left, diluting the atmosphere; atmospheric nuclear testing then roughly doubled it in the early 1960s. Both effects make post-1950 material a special case with its own curves — which is also why "present" was frozen at 1950.

See also: half-life, radioactive decay, beta decay, Isotope, Nuclear binding energy, chemical element.