The 1988 radiocarbon date: AD 1260-1390
Skeptics argue: three independent labs dated the linen to AD 1260-1390 with at least 95% confidence. That range fits the first secure record of the cloth at Lirey in the 1350s.
The details
On 21 April 1988 a single strip was cut from one corner of the cloth, next to the spot sampled in 1973, away from patches and burn marks. Arizona, Oxford and Zurich each got a piece of about 50 mg, plus three control cloths of known age. The lab means were 646 ± 31 BP (Arizona), 750 ± 30 BP (Oxford) and 676 ± 24 BP (Zurich), giving an unweighted mean of 691 ± 31 BP. Calibrated, that is AD 1273-1288 at 68% and AD 1262-1312 or 1353-1384 at 95%, which Nature rounded to AD 1260-1390. All three controls came out close to their known ages. The paper, published in Nature in February 1989, called the result conclusive evidence that the linen is medieval.
The full argument
This is the strongest single piece of evidence in the whole debate. AMS radiocarbon dating is a mature, well-tested method, three labs agreed within about a century, and the controls worked. The date matches the first written record, the d'Arcis memo, and Oresme's remark on a fake shroud in Champagne. Every attempt to explain the date away (fire, bacteria, carbon monoxide, neutrons, invisible repair) has either been tested and failed or has no direct evidence.
How defenders answer
The best reply is not that the method is wrong but that the sample may not represent the whole cloth. Only one strip from one corner was sampled, and later statistical work found the 12 results are not homogeneous and show a trend along the strip. Even the authors of those reanalyses say this does not prove an ancient date; it only weakens the 'conclusive' label and calls for a new, well-designed test.
Damon et al. 1989, Nature 337:611 · Damon et al. 1989, full text mirror · Wikipedia: Radiocarbon dating of the Shroud of Turin · Karapanagiotis 2025, Textiles 5(1):8 (review)