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If you have either, a fine piece of steel wool or a copper pad work well for removing rust. However, you can also get good results from non-metal abrasive products (e.g. Brillo, SOS, etc.). If the rust is stubborn, add a little water and some mild dish-washing soap as you scrub. Normally, it's a bad idea to try to clean a cast iron pan the same way you'd clean other metal cookware, since this can remove the protective layer of seasoning. However, if your pan has rust, this has already occurred, so it's best to clean the rust from the pan and re-season later. If the rust appears to be thin and light, you can often get away with using mild abrasives you probably already have in your kitchen. For example, to use baking soda as an abrasive, sprinkle a small amount onto the surface of the pan along with some water. Stir the baking soda with the water to make a rough paste, then use a rag to scrub the paste into the rusty spots of the pan. Once you've scrubbed the rusty areas, let the paste sit for a few minutes, then rinse it off with tap water. If any rust remains, repeat as needed or switch to a different abrasive. Another easy DIY abrasive uses salt and water. This method works almost exactly like the baking soda one above: make a rough paste of salt and water in the pan, then scrub it into the rusty spots with a rag. Because the salt crystals are a little larger and rougher than particles of baking soda, the paste will be slightly more abrasive. However, salt is still considered fairly gentle. In some cases, simple abrasives won't remove rust on their own. In these cases, harsher chemical cleaners can help. For example, lower-priced toilet bowl cleaners containing roughly 20% hydrochloric acid (HCl) tend to well. HCl completely dissolves rust into a wet powder. In this state, it can easily be removed — consult the product's packaging for disposal instructions.  HCl is a strong acid, so working with it requires great care to prevent chemical burns. Protect your skin, hands, and eyes — wear gloves, a long-sleeved shirt, and safety goggles or other eye protection (which can usually be purchased for fairly cheap at universities with chemistry departments). Always use good ventilation and avoid breathing the product's fumes. Strong acids can irritate the throat and lungs, especially in people with asthmatic or lung conditions. Beware: HCl will dull coated or plated screws and polished, shiny iron or steel, and such. After cleaning, give the pan a thorough rinsing to remove any loosened rust or cleaning products. If you used HCl, consult the product's packaging for disposal instructions instead. When the pan is clean, dry with a clean rag or paper towel. Be sure to get all the water out — missing even a little can cause rust to re-form.  After drying with a towel, try heating the pan on the stove over medium heat for about five minutes. This will remove any last traces of water, leaving you with a completely dry pan. Use care when handling the hot pan. After removing rust, it is highly recommended that you season your pan. This is an easy process that essentially gives the cast iron a protective layer of fat which prevents future rusting and also keeps food from sticking as it cooks. See the section below for information on seasoning your pan.

Summary:
Scrub the rust with an abrasive pad. For mild rust, try scrubbing with baking soda. Make a salt scrub. For bad rust, use a heavy-duty cleaner. Rinse the pan and dry thoroughly. For pans with severe rust, use professional-quality abrasion.