Can you refinish a bathtub?
Yes, a porcelain bathtub can be refinished, but should be done by a professional during the warmer weather. The chemicals used to refinish the tub are extremely dangerous on the respiratory system. The bathroom has to be well ventilated.
We had a porcelain tub refinished in our second 3-bedroom home.
Check out the Habitat for Humanity ReStore; used building materials for at least half price (usually more). I've found brand new items that builders have brought in after working on a project (it's cheaper for them to claim the charitable contribution on taxes than to try to reclaim money by selling it themselves).
We've had our reglazed, but by a professional. It's not a DIY project, as there are lots of chemicals involved. It's only about $350, though, so compared to buying a new one and having it installed, it's a breeze.
I hate people who post references to product without giving the make and model of the product is simply useless. Saying I bought it at Home Depot/Lowes doesn't help.
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One can buy a product from Homax that is a tub refinishing kit. I am told it works very well but you have to have good ventilation. You prep it, paint it, and let it dry.
There are fiberglass repair kits available at a home improvement or a boating store. This is a page about refurbishing a fiberglass tub.
This is a page about restoring a claw foot tub. A restored claw foot tub can be a beautiful focal point in your bathroom. Depending on its age it may need a lot of work to bring it back to its original beauty.