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Is there a free ChatGPT detector?

Yes. Quetext's AI detector scans texts for ChatGPT-generated content and is free of charge.
There are other free detectors as well. However, free versions usually limit the number of words per scan and the number of scans in a day, while paid versions allow more words and include bulk uploads. Here are a couple things to consider before relying on a free tool. The precise accuracy varies greatly; some free detectors do not offer the most up-to-date technology, thus having a very high error rate when analyzing the works by those whose English is not a native language.
As for the privacy policy for these detectors, one must check if there are any terms that state that the content sent for checking will be kept and used for training purposes. A free version is more than enough for checking a single text, however, for a consistent work on a whole class or a content creating team paid versions are necessary.