I’m asked this question regularly and I often overhear worried students discussing it on the bus. The simple answer is no set number exists. If only life were that simple!
Turnitin is a system that looks for matching text in an assignment from its massive database of academic publications, websites and other submitted papers. Any matches are highlighted in the Originality Report along with the scary similarity percentage that students stress over. However, we should focus on the Originality Report to make a judgement about plagiarism rather than just that number.
Obviously academic writing is likely to include several references to other work and Turnitin will find matching text. It will depend on the actual assignment set as to how much and in what way. The only way to really tell if plagiarism has occurred is to look at the Originality Report and use your own academic judgement.
There are no simple answers here to the complex issue of plagiarism, but used in the correct way Turnititn can be a useful learning tool.
Read more here about interpreting originality reports and percentages.