Items Made By "Upcycling"
You absolutely can make clothing from previous clothes (or curtains, or sheets) even if you don't know the fiber content.
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You are allowed to label "Secondhand materials — fiber content unknown" if you truly don't know the fiber content. Use this as sparingly as possible!
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Sometimes, you can take a good guess at it and if you can, you need to do the best you can at labeling it. The Federal Trade Commission allows a 3% error in either direction for most fiber content labeling (wool fiber content must be exact). So if you know that the material is polyester/spandex, you would be pretty safe labeling 95% Polyester, 5% Spandex even if it is 97%/3% or 92%/8%.
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(See more information about unknown fiber content labeling here: https://www.ftc.gov/tips-advice/business-center/guidance/threading-your-way-through-labeling-requirements-under-textile#unknown)
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If you need to know present fibers for determining if you need testing under U.S. Consumer Product Safety Commission regulations, you can do a 'burn test' (Google provides many articles on this - please be safe!).
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Can you make children's items?
Yes, but. If you use an adult's size tshirt that has a graphic on it, you probably shouldn't use it for a children's item because you will need lead testing reports for that graphic because it likely lays on top of the fibers (you know the fun tees with Disney® and Marvel® etc. characters or funny sayings on them). It would be best to use it for another adult (13 years old and up) item. (This doesn't get into the issues with copyrights & trademarks.)